THE UNIVERSITY OF MICHIGAN INDUSTRY PROGRAM OF THE COLLEGE OF ENGINEERING AN EXPERIMENTAL INVESTIGATION OF THE COMBINED EFFECTS OF PRESSURE, TEMPERATURE, AND SHEAR STRESS UPON VISCOSITY John Do Novak A dissertation submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy in The University of Michigan April, 1968 IP-820

ACKNOWLEDGMENTS The author is most grateful to his thesis committee for their continuous interest, counsel, and cooperation throughout the period of this research. The understanding and assistance of the author's chairman, Professor Ward O. Winer, is particularly appreciated. The many discussions with Mr. W. A. Wright were very interesting and educational. The author is also indebted to him for his help in obtaining several of the experimental fluids. The research reported herein was supported in part by the National Science Foundation (GP-2737) and by the donors of the Petroleum Research Fund, which is administered by the American Chemical Society (PRF #2468). Grant-in-aid assistance was also received from the Sun Oil Company, Dow Corning Corporation, Dow Chemical Company and the American Oil CompanyO These companies and the Rohm and Haas Company also donated the experimental fluids and the corresponding descriptive data. Fellowship support from the Chrysler Corporation (1967-1968), an NDEA Title IV grant (1966-1967), and a Ford Fellowship in Mechanical Engineering (1966-1967) are greatly appreciated. The author also wishes to thank Miss Ruth Howard for her assistance in typing this manuscript and especially Mr. Hossein Ehya for his able assistance in a wide variety of tasks. Finally, this work would have been much more difficult had it not been for my understanding wife Juley who assisted me where ever possible. ii

TABLE OF CONTENTS Page ACKNOWLEDGMENTS................................................. ii LIST OF TABLES............................................... v LIST OF FIGURES................................................. vi CHAPTER I INTRODUCTION...................................... 1 Ao Need for this Research.......................... 1 B. Previous Research............................... 4 1. Fluid Properties.............................. 4 2. Experimental Equipment.............. 4 C. Equipment Selection.......................... 6 II EXPERIMENTAL METHOD.................................... 8 A. Basic Concepts................................... 8 B. Data Reduction Techniques..........................16 III EXPERIMENTAL EQUIPMENT.................................19 A. Description......................... 19 Bo Experimental Limits..............................30 Co Calibration..................................... 37 Do Verification............................... 41 E. Error Analysis..................................... 45 IV FLUID BEHAVIOR......................................... 52 A. Experimental Fluids............................52 B. Experimental Results............................ 53 1o General Trends................................. 54 2e Specific Fluids........................ 57 a. Diester.............................57 b. Paraffinic Based Fluids.................... 57 co Naphthenic Based Fluids................... 63 do Polybutene................................. 65 e. Siloxane Fluids..........6.....6.......o. 66 iii

TABLE OF CONTENTS (Continued) Page C. Correlation.......................... 66 1o Techniques........................... 66 2, Results.......................................109 D. Tabulated Data.........i..... o ll V CONCLUSIONS AND RECOMMENDATIONS.......................136 Ao Experimental Equipment......................... 136 B. Fluid Behavior.....................1...............40 VI APPENDICES................................ 146 A. Fluid Descriptions.........................146 B. Experimental Equipment............................ 152 1o Operating Procedure.......................152 2. Instrumentation......................... 155 a. Measurement Errors.....................155 bo Transducer Details and Calibration Data.....................................161 i o Pressure Transducers............... 161 iio Displacement Transducers............ 166 co Electronic Circuits......................171 do Visicorder Oscillograph.................. 185 C. Data Reduction Computer Program...............187 1o Program Objectives o....................... 187 2. Program Description and Equations............ 187 3. MAD Symbol Definitions....................... 191 4. Program Listing............................. 194 5. Typical Input-Output....................... 197 VII BIBLIOGRAPHY....................................... 199 iv

LIST OF TABLES Table Page I Displacement Transducer Signal Summary................ 28 II Differential Pressure Transducer Signal Summary....... 29 III Pressure Level Transducer Signal Summary.............. 30 IV Capillary Geometry....................................37 V Summary of Reported and Measured Data for Fluid A...... 43 VI Experimental Fluids............................. o 52 VII Data Summary o.....................................56 VIII Elastic Energy Calculation Summary..................... 59 B1 Pressure Transducer Calibration Data.............. 159 B2 Differential Pressure Transducer Calibration Summary.........................................166 B3 Pressure Level Transducer Calibration Summary..........167 B4 Galvanometer Data......................................186

LIST OF FIGURES Figure Page 1 Elastic Energy Correction............................. 12 2 Schematic Drawing of Viscometer....................... 20 3 Exploded View of High Pressure Moveable Seal........ 22 4 General View of Experimental Apparatus......... o 23 5 Capillary Test Section................................ 24 6 Typical Transducer Output............................. 26 7 Approximate Experimental Limits...................... 31 8 Schematic Drawing of Atmospheric Pressure Capillary Viscometer.................................. 39 9 Typical Calibration Curve for Differential Pressure Transducers.................................. 42 10 Comparison of Reported and Measured for Fluid A (Diester).......... o............................ 44 11 Flow Curve for Fluid A (Diester).............. o.. 46 12 Possible Random Error in Viscosity Measurements....... 49 13 Flow Curves for Fluid B..... o o.......................... 67 14 Viscosity-Temperature Relation for Fluid B...... o 68 15 Viscosity-Pressure Relation for Fluid B............... 69 16 Flow Curves for Fluid C.o........................... 70 17 Viscosity-Temperature Relation for Fluid C............ 71 18 Viscosity-Pressure Relation for Fluid C.............o 72 19 Flow Curves for Fluid D o7............. 73 20 Viscosity-Temperature Relation for Fluid D.......... 74 21 Viscosity-Pressure Relation for Fluid D.oo........... o.o.... 75 22 Flow Curves for Fluid E........... o. o.... o. o o o. o. o. o o o 76 vi

LIST OF FIGURES (Continued) Figure Page 23 Viscosity-Temperature Relation for Fluid E............. 77 24 Viscosity-Pressure Relation for Fluid E................ 78 25 Flow Curves for Fluid F................................ 79 26 Viscosity-Temperature Relation for Fluid F...o......... 80 27 Viscosity-Pressure Relation for Fluid F............. 81 28 Flow Curves for Fluid G.............................. 82 29 Viscosity-Temperature Relation for Fluid F............. 83 30 Viscosity-Pressure Relation for Fluid G........... 84 31 Flow Curves for Fluid H................................o o 85 32 Viscosity-Temperature Relation for Fluid H............. 86 33 Viscosity-Pressure Relation for Fluid H............. 87 34 Flow Curves for Fluid I.............................. 88 35 Viscosity-Temperature Relation for Fluid I.. o 89 36 Flow Curves for Fluid J............................... 90 37 Viscosity-Temperature Relation for Fluid J............. 91 38 Viscosity-Pressure Relations for Fluids I and J........ 92 39 Flow Curves for Paraffinic Based Fluids at Atmospheric Pressure.............................. 93 40 Recoverable Shear Strain in Petroleum Oils.. 94 41 Flow Curves for Paraffinic Based Fluids at 20,000 psig......... e o o o..... o...........o o95 42 Viscosity-Temperature Relations for the Paraffinic Based Fluids at 10,000 psig o 96 43 Viscosity-Pressure Relations for the Paraffinic Based Fluids at 100~F o..O o.. o e o..o o e.o.......... o. o 97 44 Effect of Polymer in Paraffinic Base Oil.........o....o 98 vii

LIST OF FIGURES (Continued) Figure Page 45 Flow Curves for Naphthenic Based Fluids at Atmospheric Pressure............................... 99 46 Viscosity-Temperature Relations for Petroleum Oils. 100 47 Viscosity-Pressure Relations for Fluids A, B, C, D, E, F, G, H......................................... 101 48 Graphical Presentation of Viscosity Data for nonNewtonian Fluids....................................... 104 49 Generalized Non-Newtonian Flow Data................. 106 Al Molecular Weight Distribution for Fluid H........o.. 151 Bl Typical Pressure Transducer Calibration Curve......... 157 B2 Pressure Level Transducer Calibration Curve............ 168 B3 Pressure Level Transducer Output Signal Curve..........169 B4 Typical Displacement Transducer Calibration Curve...... 170 B5 Instrumentation Block Diagram..................... 172 B6 Instrumentation Control Box Panel......................174 B7 Transducer Cables —Schematic Diagrams..................175 B8 Deviation Amplifier Cables —Schematic Diagrams...... 176 B9 Visicorder and Battery Cables —Schematic Diagrams...... 177 B10 Control Box Schematic —Differential Pressure Transducer Circuits....................o 178 Bll Control Box Schematic —Differential Pressure Transducer Circuits (Continued)............. 179 B12 Control Box Schematic —Pressure Level and Displacement Transducer Circuits.....................o 80 B13 Equivalent Circuit for Differential Pressure Transducer.......o............o.......................182 viii

LIST OF FIGURES (Continued) Figure Page B14 Equivalent Circuit for Pressure Level Transducer........................................ 183 B15 Equivalent Circuit for Displacement Transducer......... 184 ix

CHAPTER I INTRODUCTION The viscosity of several well defined fluids was measured in a capillary-type viscometero The fluids were subjected to pressures up to 80,000 psi, temperatures of 100, 210, and 300~F and shear stresses from 300 to 1.2 x 106 dynes/cm2. The shear stress was varied via the pressure differential across the capillary which was independent of pressure levelo Four interchangeable capillaries were employed to cover the shear stress range. The viscosity range examined was from lo0 to 100,000 centipoise. The behavior of ten fluids was observed including one (bis-2ethyl hexyl sebacate) which had been previously examined and reported in (10) the 1953 ASME Pressure-Viscosity Report. Agreement within two percent was obtained between the present results and the ASME reporto Data correlation and presentation techniques were also investigated in order to facilitate comprehension of the significant trends and interrelations among the fluids examinedo Ao Need for this Research There is a need for knowledge of the rheological behavior of liquid lubricants under the combined effects of high pressure and high shearing rates (or shear stress). Such information will not only contribute to the understanding of the physics of lubrication mechanisms but also act as a guide in the formulation of future lubricants. Many mechanisms of lubrication formerly thought to be in the category of "boundary" lubrication (i.e. dependent on the chemical interaction of the -1

-2lubricant and the surface being lubricated) are, in light of recent analytical and experimental investigations, now thought to be of the (3,4,5,6) elastohydrodynamic type (i.e. dependent on the mechanical interaction of the physical properties of the lubricant and those of the solid being lubricated). Orcutt(7) in his studies in elastohydrodynamic lubrication and others (c.f, 8) recommend that the rheological models of the lubricant be modified to include effects of shear stress and time dependence. Existing work does not consider either of these effects because of the mathematical complexity involved and lack of realistic physical properties. Thus, a major problem associated with the work in the area of elastohydrodynamic lubrication is the lack of data on the behavior of the liquids when they are subjected to the combined effects of high pressure and high shear rate. This lack of realistic data arises because the viscosity-pressure relation has generally been investigated at low values of shear stress, and the viscosityshear stress relation has only been investigated at pressures up to 15,000 psigo The research described herein is an attempt to determine the combined effects of pressure, temperature and shear rate on lubricating fluids. A capillary viscometer has been employed and ten chemically well defined fluids investigated. Only time independent properties have been determined. It is recognized, however, that time dependent properties may be significant in high speed, highly loaded devices. Therefore some lubricants may behave differently in some applications than they did in this investigation.

-3This data should contribute to the understanding of the relative importance of the two modes of lubrication in highly loaded contacts such as gears, cam followers and rolling element bearings. A better understanding of the relative importance of boundary and elastohydrodynamic lubrication mechanisms is clearly of value in the formulation and use of lubricants because on the one hand the chemical properties of the lubricant are more important and therefore must be studied and enhanced, and on the other hand the physical properties are more important. A clear understanding of the two modes of lubrication is also of value in the mechanical design of lubricated mechanisms. The results of this research will also allow elastohydrodynamic lubrication theory to be advanced by extending the knowledge of the combined effects of pressure, temperature, and shear stress upon rheological properties. These effects can be considered in future rheological models. The existing models may also be improved by using more realistic data. Previous investigators have examined the rheological properties of lubricants over wide temperature and pressure ranges at low shear rates. There is a need to include viscosity data over a wide shear stress range in order to obtain a better understanding of the lubricant behavioro The knowledge gained from data obtained over a wide range of these three variables could then be used to improve the behavior of lubricants by the addition of viscosity-index improvers to hydrocarbon lubricants or by changing the chemical composition of synthetic lubricants, i.e., silicone fluids could be altered by varying molecular structure.

-4B. Previous Research 1. Fluid Properties The effect of pressure upon the viscosity of liquids has received much attention. The earliest investigation reported was dated in 1892.(9) The most extensive single investigation was that reported by the ASME in 1953. This ASME viscosity-pressure report presents viscosity and density data for forty lubricating fluids of known composition at pressures to 150,000 psi and temperatures to 425~F. Hersey(11) summarized the work reported in the literature prior (12) to 1952 and more recently' has summarized the work conducted between 1952 and 1965. The maximum pressure in past investigations has ranged from as low as 2000 psi to as high as 425,000 psi by Bridgmen. With few exceptions the research into the effect of high pressure on viscosity has been conducted with a falling-body type viscometer. The disadvantage of this type of instrument is that the fluid is subjected to very low shear stresses (approximately 250 dynes/cm in 10) and therefore gives no indication of the effect of shear stress upon viscosity. 2. Experimental Equipment One exception to the trend of low shear stresses has been the (14) work of Philippoff in which he employed a vibrating crystal viscometer in a pressure cell. This technique made possible the measurement of viscosity at discrete shear rates which are a function of the crystal geometry used. By employing a reduced variable approach the data could then be made applicable to a wide range of shear rates. Philippoff's maximum pressure was 15,000 psi which was limited in part by the fact

-5current instrumentation for vibrating crystal viscometers is limited to the measurement of viscosities below about 5 to 10 poise. The National Aeronautics and Space Administration has published a bibliography on "Lubrication, Corrosion, and Wear, 5 which contains abstracts of reports and journal articles published during the period January, 1962 —March, 1965. This bibliography indicates that very few researchers have investigated effects of elevated pressure upon viscosity during that time. The only paper directly concerned with high pressure rheology of fluids is that by Bell (16) in which he reported an attempt to determine rheological behavior of a lubricant in the contact zone of rolling contact bodieso This was accomplished by rolling two contacting disks together with a small amount of sliding superimposed on a relatively high rolling velocity. This equipment does not readily produce viscosity data because the specimen is not uniformly stressed in the contact region (extreme pressure variation, for example). Therefore interpretation of the experimental results is necessary and it remains to be seen how well the results can be used to infer purely rheological properties of a fluido Two additional previous investigations deserve special mention because of their relation to this work. These are the works of Hersey and Snyder in 1932 and that of Norton et.al., in 1941o Both of these investigations also employed a capillary viscometer to determine the pressure-viscosity variationso Hersey and Snyder studied the flow of liquids in capillaries which exited to the atmosphere with inlet pressures up to 40,000 psio This pressure was high enough to cause an appreciable change in the

-6viscosity of the test fluid. Thus, the viscosity could not be treated as uniform throughout the capillary. The results were put in the form of Poiseuille's law with a correction factor obtained by integration of the empirical viscosity-pressure relation for each fluid. If the form of the viscosity-pressure function was unknown, it was determined by differentiation of the flow rate versus inlet pressure curve. This method was less sensitive and less accurate but much more rapid than the rolling ball and falling weight methods previously used. Norton was the first to eliminate the problem of viscosity variation along the capillary at elevated pressures. His equipment had a maximum pressure level of 50,000 psi and eliminated the viscosity variation by using two capillaries in series. The first was a short test capillary with a Bourdon pressure gage at each end. The second capillary was a long flow resistance tube with atmospheric pressure at the exit. This technique enabled him to subject the test fluid to a high pressure level and still maintain a small pressure drop across the capillary. The results were presented as preliminary and the problems associated with the technique were not solved before his untimely death. The lack of repeatable accuracy of the Bourdon gages was the major problem in accurately measuring the pressure drop across the capillary. C. Equipment Selection The viscometers most frequently used to detect non-Newtonian behavior are the rotational and capillary types. Since many varieties of these are commercially available, a survey was made to determine if any available viscometers could be modified to obtain data over the desired ranges of temperature, pressure, and shear stress.

-7Two commercially available high pressure viscometers are (19) described by Van Wazer. The first has a maximum operating pressure of 2,000 psi, the second 30,000 psi. Since this research is concerned with much higher pressures, neither of these was acceptableo Van Wazer also describes several other types of viscometers. Some of them utilize a rolling ball, a rising bubble, or a vibrating reed to determine the viscosity. All of the commercially available viscometers have the same major limitation. That is, they do not operate at the desired high pressure levelso Since an existing viscometer could not be modified to obtain the desired range of variables, a viscometer was designed specifically for this research. As previously mentioned, the viscometers most frequently used to detect non-Newtonian behavior are the rotational and capillary types. Therefore, the feasibility of using both types was investigated. The two most common rotational viscometers are the concentric cylinder, and the cone and plate types. One of the advantages of these viscometers is that it is not necessary to account for the elastic energy stored in the fluid (if any exists), while this energy can be very significant in capillary viscometers. The major disadvantage of rotational viscometers for this research is the difficulty of accurately measuring torque through a high pressure seal. Another disadvantage is that temperature control of the test fluid is very difficult. For these reasons a capillary viscometer was designed. The details of this viscometer are presented in Chapter III. * The elastic energy correction is discussed in Chapter II.

CHAPTER II EXPERIMENTAL METHOD The basic concepts of capillary viscometry are discussed in the first section of this chapter. The second section contains a discussion of the data reduction techniques used in this research. A. Basic Concepts The data necessary to determine the viscosity of a fluid in a capillary viscometer are the volumetric flow rate, pressure difference across the capillary, and the capillary geometry. Since viscosity is greatly affected by temperature and pressure, both of these must also be measured. The pressure difference and capillary geometry are used to determine the fluid shear stress at the capillary wall. The volumetric flow rate and capillary diameter are used to calculate the shear rate (i.e. velocity gradient), also at the capillary wallo The viscosity of the fluid at any set of conditions is the ratio of shear-stress to shear-rate. For a detailed justification of the standard techniques employed in capillary viscometry the reader is referred to Philippoff2 and other standard references (cf. 19). An analysis of the forces acting on the fluid shows that the shearing stress at the capillary wall is determined by the expression (cf. 21): AP 4(/D) (1) where APt is the total, or measured pressure differential across the capillary, L and D are the capillary length and diameter, respectively. -8

-9This shear stress is a mathematical reference quantity and is only correct for the special case of an infinite capillary where all of the mechanical energy supplied to the fluid, APtQ, is dissipated in shearing the fluid "layers". In the general case for capillary viscometry, however, Philippoff(20) states that the energy balance for the capillary can be written as: APtQ = APcQ + KE + EE (2) or Pt = AP + KE/Q + EE/Q (3) where zPc is the pressure differential held in equilibrium inside the capillary, KE is the kinetic energy of the fluid leaving the capillary and EE is the elastic energy stored in the fluid. This last term, EE, also accounts for any geometrical end correction. A fluid which discharges from a capillary may have an appreciable amount of kinetic energy. Thus, an error in the viscosity calculation will result unless this energy is reversibly recovered in a pressure rise or considered separately. For a parabolic velocity distribution (i.e. Newtonian fluid) the kinetic energy correction per unit volume, KEC, is expressed by: KEC = KE/Q = pv/g (4) * where p is the fluid density and V is the average velocity. If a fluid acquires an elastic energy in steady flow, this energy is imparted to the liquid at the capillary entrance, carried For a uniform velocity profile, the kinetic energy is expressed by KEC = (1/2) pV2/g

-10through the capillary, and finally dissipated outside the capillary. (20) In Philippoff's discussion of the elastic energy he states that a measure of this energy per unit volume is the "normal stress", constant for each shear rate, which acts as a tension in the flow direction. He has shown (cf. 22) that the normal stress, Pn' is a product of the true shearing stress, Tcr, and the recoverable shear, Sr o EE/Q = Pn = Tor Sr (5) Thus Equation (3) can be rearranged to give APt = APc + KEC + Pn (6) Since any real capillary has a finite length, the entrance region in which the fluid velocity profile is developed must be considered. This region increases the active capillary length by 6L = nR, where n is proportional to the Reynolds number and is called the "Couette Correction".* The true shearing stress at the capillary wall is then AP AP,, (7) cr 4(L+6L)/D 4(L+nR)/D Substituting Equations (5) and (7) into Equation (6) results in APt KEC = Tcr ( + S r) (8) Thus the true shear stress at the capillary wall is APcorr cr 4(L/D)+EEC where The entrance region is discussed further in the next section of this chapter.

-11AP = APt - KEC, (10) corr t EEC = (2n + Sr). (11) APcorr is the corrected pressure differential across the capillary and EEC is the elastic energy correction. The elastic energy stored in the fluid must be evaluated experimentally by obtaining constant shear rate data from capillaries with different length-to-diameter ratios. Philippoff(20) presents two techniques for evaluating EEC which are based on the fact the APcorr is a linear function of the capillary length-to-diameter ratio for constant shear rate. Equation (9) can be rearranged to give Pcorr = tcr [4(L/D) + EEC]. (12) By letting APcorr approach zero, one obtains EEC = - 4(L/D) (13) This technique is presented in Figure l(a) which shows that when the corrected pressure drop across the capillary is plotted against four times the length-to-diameter ratio, the intercept of the resulting straight line with the abscissa is equal to the negative of the elastic energy correction. An equivalent method for evaluating the magnitude of the elastic energy correction utilizes the calculated shear stresses (including the kinetic energy correction) and the capillary diameter-tolength ratios (Figure l(b)). The corrected shear stress, T, is corr

-12\'4, o~~ D-~~o X\) 6.) 33y Ads 88037 ma~~~~~~~~~~~~~~~~Q ^ ^~~~~

-13defined as: T corr Corr 4 4(L/D) / Substituting Equation (12) into Equation (14) and simplifying, gives corr = cr ( 4+DiL). (1 Equation (13) is again obtained by letting T corr approach zero. In this method, however, the intercept of the resulting straight line with the abscissa is equal to the negative of the reciprocal of the elastic energy correction (i.e. - 1/EEC). Thus a horizontal line is obtained when the fluid has negligible elastic energy whereas the previous method resulted in a line passing through the origin when the elastic energy is negligible. This latter technique leads to an easy method of determining whether or not an elastic energy correction is negligible. It is negligible if, at a constant shear rate, the corrected shear stress is the same for all capillaries. In other words, the elastic energy is negligible if the uncorrected data are consistent between capillaries of different length-to-diameter ratios. The flow curves of each fluid readily indicate whether or not an elastic energy correction must be made. If data from different capillaries coincide, or "over-lapt, the correction is unnecessary, i.e. elastic energy is negligible. The above discussion is valid for all fluids because it is only based on force and energy balances and is independent of the fluid properties and fluid behavior. The technique used to evaluate the fluid shear rate (i.e. velocity gradient), however, is dependent upon the fluid

-14behavioro The technique assumes the fluid has a Newtonian behavior and then applies the Rabinwitsch(23) analysis to determine the correct shear rate at the wall where this method indicates that the fluid has a non-Newtonian behavior. Steady laminar flow of a Newtonian fluid through a circular tube produces a parabolic velocity profile (cf. 21). This is expressed by 4 _ (R) where AP = pressure difference across tube (psi) R = radius (inches) L = length (inches) [i = absolute viscosity (poise). The velocity gradient at the wall is dv _ AP R N = dr R= 2~'7) R Integration of Equation (16) shows that the volumetric flow rate through the capillary is 8P (in3/sec). (18) Thus from Equations (17) and (18), the shear rate at the capillary wall for Newtonian fluids is expressed by the relation 32Q 8v 1 N D3 D (s ) c-(19) where V is the average fluid velocity. This technique is often referred to by other names such as MooneyMetzner or Weissenberg.

-15The shear stress and shear rate data obtained by using the above techniques, (Equations (9) and (19)), can then be used to determine whether or not the assumption of a Newtonian fluid in the shear rate calculation is valid. For Newtonian fluids, these data produce straight * lines with a unit slope when plotted on log-log paper. Similar curves for non-Newtonian fluids may be straight lines with a slope greater or less than one, (i.e. Power Law Fluids), or curved lines, (i.e. Psuedoplastic Fluids). The Rabinowitsch analysis is valid only for purely viscous (19) fluids with time independent properties. Van Wazer presents a complete discussion of this analysis and lists the following basic assumptions: 1. steady, laminar flow, 2. no radial or tangential velocity components, 3. no slippage at the wall, 4. negligible end effects, 5. incompressible fluid, 6. no external forces, 7. isothermal conditions prevail throughout, 8. viscosity does not change appreciably with the change in pressure down the tube, and 9. the shear rate is an arbitrary function of the shear stress. This analysis shows that the true shear rate at the capillary wall is~ (= ( ) N- (20) or = (3) 23 (21) where S is the slope of the YN versus shear-stress curve For a Newtonian fluid T = p.N log T = log p + log 7N

-16plotted on log-log paper. As mentioned previously, this slope is unity for Newtonian fluids and thus the additional factor reduces to unity. Of the assumptions listed by Van Wazer, only the following four need to be checked in this work: (a) time steady flow, (b) negligible entrance length, (c) negligible viscous heating, and (d) the absence of thixotropic or rheopectic fluid behavior. B. Data Reduction Techniques The raw data as described in Chapter III were transcribed into digital form and analyzed by a computer program which determined the pressures, kinetic energy, shear stress, shear rate, viscosity and additional quantities such as the Reynolds number and entrance length. The details of these calculations are presented in Appendix C as well as an explanation of the computer program. This computer program only evaluates one of the four assumptions listed by Van Wazer which needed to be checked, namely the magnitude of the entrance length. The validity of the other three assumptions was checked by other means. The entrance length is that distance from the capillary entrance in which the fluid velocity profile is developed to some percentage (i.e. 95%) of the profile which would exist in an infinitely long capillary. This distance is expressed by the relation (cf. 20) Le = 0.029 Re D (22) where Re is the fluid Reynolds number and D is the capillary diameter (approximately 0.01 inch). In general the Reynolds number was not greater than 20 and always less than 750. Therefore, the entrance length

-17was a negligible fraction of the total capillary length. Note that this also insures that only laminar flow conditions (i.e. Re < 2000) exist. The shape of the capillary ends were not well rounded, but the method of determining the capillary diameter included the appropriate end correction (cf. 20). Time steady flow could be assured by observing the recording * of the transducer signals because the fluid motion transient time was at least one order of magnitude shorter than the slowest responding element in the recording system. Hence, if the data record indicated steady behavior over a time period large enough to obtain readings, the fluid motion was steady during that time. The problem of viscous heating in capillary experiments has often lead to misleading results. Physically it cannot be avoided because the experiment is based on the visous dissipation of mechanical energy supplied to the system. The only question is whether or not the thermal energy is removed at a rate sufficient to keep the resulting (24,25,26) decrease in viscosity negligible. The work of Gerrard et al. was used to minimize heating effects. No correction was applied to the data for any possible heating effect. The absence of thixotropic or rheopectic behavior is indicated by the agreement between data on the same fluid taken in capillaries of differing length-to-diameter ratios as long as there was no gelatin in the fluid. Gelatin results from the solidification of some constituents in the fluid at certain combinations of pressure and temperature. It was readily deteteed in the instrument because it caused the differential * See Chapter III, Section B for calculations.

-18pressure signals to be delayed with respect to the displacement signal and resulted in an inability to repeat data successively under supposedly identical conditions. The temperature-pressure combinations at which gelatin was observed to begin agreed well with those at which "solidification" was reported in the ASME Viscosity-Pressure Report(10) for similar fluids. Although it may be possible, no attempt was made to systematically determine the rheological behavior of the fluids when a gel structure existed. The gelatin problem is discussed further in Chapter III. C. Summary The mathematical model used to reduce the raw experimental data was basically the Hagen-Poiseuille relation for flow in a tube. Modifications of this model were made when necessary to account for the kinetic energy, elastic energy, and/or non-Newtonian behavior of the test fluid. The viscosity was determined from the following expression: ( 2t - KEC) (23) Q 4 L/D + EEC/ where 4 = viscosity (poise) K = constant APt = measured pressure differential across the capillary (psi) KEC = kinetic energy correction (psi) Q = volumetric flow rate (in3/sec) L = capillary length (inches) D = capillary diameter (inches) EEC = elastic energy correction (in/in).

CHAPTER III EXPERIMENTAL EQUIPMENT A. Description The experimental apparatus* used to measure the steady-state rheological behavior of liquids was a two-way high pressure capillary viscometer which has an upper pressure limit of 100,000 psi. The temperature of the test sample was controlled by a constant temperature bath which has a range of approximately -30 to 450~F. A schematic drawing of the test apparatus is presented in Figure 2. The test fluid is in two reservoirs, R1 and R2, the high pressure tubing, and the capillary section. The fluid in the test section is pressurized by pumping low pressure hydraulic fluid into cavity I and venting hydraulic fluid from cavity II. The high pressure is generated by an intensifier which has a 50 to 1 area ratio between piston PI and the high pressure piston P2. After the test fluid is pressurized, the moveable ram is locked in position by sealing both cavities I and II. Flow through the capillary is caused by venting hydraulic fluid from cavity IV and pressurizing cavity III which results in the translating piston (pressure chamber) moving along the high pressure rams. The test fluid is then forced from reservoir R2 through the capillary into reservoir Rl. The motion can be reversed. The test section, the high pressure tubing, and the pressure transducers are attached to the translating piston, and, therefore, move with it. 4340 steel used for all components except as noted. -19

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-21The moveable high pressure seals at P2 and P3 were Bridgman type seals with urethane washers and metal anti-extrusion backup rings. The pressure transducers were sealed with standard "O-rings". The remaining high pressure seals, in the standard 100,000 psi tubing, were metalto-metal conical seals. Figure 3 is an exploded view of the high pressure moveable seals which shows the seal head (No. 1), the anti-extrusion rings (No.2), the polyurethane washer (No. 3), and the base of the seal (No. 4) which is actually the end of the moveable ram in reservoir Rl and the end of the fixed ram in reservoir R2 (Figure 2). Figure 4 is a general view of the experimental apparatus which shows the high pressure viscometer, low pressure hydraulic system and the instrumentation cart as well as the constant temperature bath. Control of the low pressure hydraulic system is achieved by two manual pumps and a series of valves. The pump with the lower operating pressure (800 psi maximum, 1.08 in3/stroke) is used primarily to control the translating piston motion. The major function of the other pump (3,000 psi maximum operating pressure, 0.28 in /stroke) is to pressurize the test fluid. One valve is positioned between the two pumps which allows both pumps to pressure the test fluid, move the translating piston, or to be isolated from each other. There are eight additional values in the hydraulic system, two for each cavity. Four of these are connected to the common pressurizing line, the other four are connected to the common return line. The capillary section (Figure 5) consists of a fine-bore stainless steel capillary of 0.01 inch nominal inside diameter pressed into a 3-1/2 inch long nipple of standard 100,000 psi tubing. Four capillaries * Purchased from American Instrument Company, 1/4 inch OoD., 1/16 inch I.Do, Chrome Molybdenum Alloy.

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-25were available for this research which had length-to-diameter ratios of 11.6, 50.9, 100.2 and 280.0. The method used to determine the diameter of each capillary is discussed in Section C of this chapter. In addition to the capillary diameter, the data required consisted of the fluid temperature and pressure, the volume flow rate, and the pressure drop across the capillary. The temperature of the bath, in which the capillary section and much of the high pressure tubing was immersed, was determined with the calibrated mercury-in-glass thermometer. The bath temperature was controlled by a proportional temperature controller which could maintain a temperature variation of less than 0.1~F. Three pressure transducers and a displacement transducer were used to obtain the remaining data. The signals from these four transducers were supplied to galvanometers in an ultraviolet oscillographic recorder and were recorded continuously as a function of time. A time base signal was also recorded. A typical recording trace is shown in Figure 6. The volume flow rate was determined by measuring the displacement between the fixed high pressure ram and the translating piston (see Figure 2). This measurement was made with an inductance displacement transducer. Precautions were taken to keep the fluid which was in the high pressure tubing above the constant temperature bath from flowing into the capillary section. The permissible volume displaced was calculated and this calculation was confirmed by performing an experiment ASTM 64-F, 66-F, and 67-F thermometers were used.

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-27with thermocouples mounted in the test fluid at each end of the capillaryo The maximum volume permissible was 0.037 in3 which was more than required to obtain the necessary data. *. Two displacement transducers were available which enabled a wide range of displacement magnitudes to be measured. Table I contains data which show that the available transducer signal-to-displacement ratios (amplification) range from a minimum of 4.24 to a maximum of 28700 The sensitivity switch position refers to the five position rotary switch on the instrumentation control box. The first five positions are for the model 1000 transducer and the second five positions are for the model 050 transducer. One of the important features of the instrumentation is that the fluid pressure and the differential pressure across the capillary are measured directly in the high pressure fluid and thus the influence of seal friction on these measurements is eliminated. The unique innovation of the system, however, is the differential pressure measurement. The instrumentation is capable of measuring small pressure fluctuations about the high pressure level with considerable accuracy (i.e. 1.0 psi variation about 10,000 psi is detectable). The pressures (pressure level and pressure differential) were measured with three identical commercial strain gage pressure transducers, two mounted at one end of the capillary and the third mounted at the other Model 7DCDT-050 and 7DCT-1000 manufacturered by the Sanborn Division of Hewlett-Packard Company. *Norwood model 114 manufactured by the Advanced Technology Division of American-Standard.

-28TABLE I* DISPLACEMENT TRANSDUCER SIGNAL SUMMARY Sensitivity Transducer Amplification Shear Rate Slope Switch (/d) (54/) Position (SS4) (in/in) sec-l/(in/sec). 1 119.1 1.68 x l04 2 4.24 4.72 x 105 3 6.41 3.12 x 105 4 18.55 1.08 x 105 5 74.8 2.67 x 10 6 2870. 7.2 x 102 7 26.6 7.51 x 104 8 40.9 4.89 x 104 9 113.1 1.53 x 104 10 722. 2-77 x 103 Six-volt excitation. The first five positions of the sensitivity switch, SS4, are for the model 7DCDT1000 displacement transducer. The last five positions are for model 7DCDT050. end. The pressure level of the test fluid was measured with pressure transducer G1, (see Figure 2). The pressure differential across the capillary was measured with a pair of pressure transducers, G2 and G3, which were placed at opposite ends of the capillary. At any pressure level, the electrical outputs of G2 and G3 were nulled through electrical balancing. Then, by amplifying the signals from these transducers through high gain dc amplifiers, small pressure fluctuations about the high pressure level were detected.

-29The maximum sensitivity of the differential pressure instrumentation is such that a galvanometer deflection of 0.11 inch was produced when the pressure in the dead weight gage was increased from 10,000 to 10,0001 psi. Thus the maximum sensitivity was 9.1 psi/inch. However, in order to increase the maximum measurable pressure differential the data were collected with lower amplifier gain settings (12.1-256 psi/ inch)-. The following tables summarize the galvanometer output of the three pressure transducers. These tables show the sensitivity and range of each signal assuming six volt excitation for all transducers. The sensitivity of the differential pressure transducers can be increased or decreased by changing the gain of the appropriate amplifier. The ranges of the three pressure transducer signals were calculated assuming a maximum galvanometer deflection of five inches. TABLE II DIFFERENTIAL PRESSURE TRANSDUCER SIGNAL SUMMARY.. Transducer No. 1 Transducer No. 2 Sensitivity. Switch Position Galvanometer Signal (SS1) Sensitivity Range Sensitivity Range (psi/in.) (~psi) (psi/in.) (~psi) 1 247. 1235. 256. 1280. 2 82.1 410. 84.7 423. 3 37.0 185. 38.5 192. 4 12.1 60.5 13.0 65.0

-30TABLE III PRESSURE LEVEL TRANSDUCER SIGNAL SUMMARY Galvanometer Signal Sensitivity Switch slope Range Position (SSl) (psi/in.) (psi) 1 15300 0-77400y 2 9470 0-48000 3 6070 0-29500 4 3420 0-18000 100,000 psi can be measured by recording the output signal at any arbitrary pressure, then electrically nulling the output, and finally increasing the pressure. The correct galvanometer signal, 63, is equal to the sum of the nulled signal and the recorded signal. B. Experimental Limits The two measurements which limit the range of experimental data are the shear stress and the flow rate. The minimum shear stress 2 obtainable (approximately 300 dyn/cm ) is limited by the largest capillary length-to-diameter ratio and the smallest measurable pressure differential across the capillary. The maximum shear stress obtainable (approximately 1.2 x 106 dyn/cm2) is limited by the smallest capillary lengthto-diameter ratio and the pressure difference at which the viscosity of the test fluid in the capillary cannot be considered uniform. These limits are represented by the vertical lines in Figure 7. The positions of the two constant shear rate lines in Figure 7 are determined by maximum and minimum flow rate. If the viscosity of the test fluid is greater than 200 cp, the minimum obtainable shear stress is limited by the smallest measurable flow rate (shear rate of 100 sec-1). Similarly, if the viscosity is less than 150 cp, the maximum obtainable shear stress is limited by the maximum measurable flow rate (shear rate of 106 sec1).

-31o6 I0 10 b, / 03 I ~>~ 1010 r 2 02 03 04 5 06 107 10 10 lo4 10 1im WALL SHEAR STRESS (dyn/cm2) Figure 7. Approximate Experimental Limits.

-32The shear stress range (3 x 102 to l.2 x 106 dyn/cm2) is satisfactory and there is little to be gained by any extension less than an order of magnitude. There are only two possibilities for increasing the maximum shear stress. Namely, increase the maximum pressure differential across the capillary or decrease the capillary length-to-diameter ratio. The maximum pressure difference across the capillary (1000 psi) already causes a significant viscosity variation inside the capillary. Therefore increasing this variable by an order of magnitude is not permissible. The capillary length cannot be shortened much less than the existing 0.1 inch without causing fabrication problems. The 0.01 inch capillary diameter cannot be increased significantly without increasing the flow resistance of the high pressure tubing (I.D. = 0.06 inch) to an unacceptable magnitude. The minimum obtainable shear stress approaches the magnitude obtained in falling weight viscometers and thus the lower range does not need to be extended. The minimum measurable flow rate is determined by the smallest displacement transducer signal which can be accurately measured. Thus any reduction in the flow rate measurement must be accompanied by an increase in the transducer signal. Amplification of the existing transducer signal is not practical because machinery induced vibration may result in an unacceptable noise level. Vibration isolation might solve this problem, however. A more sensitive displacement transducer may be helpful, but any such transducer should be able to measure large displacements as well as small ones. Thus a cantilevered beam. for example, would not be satisfactory even though it would have an increased sensitivity.

-33The most promising method for decreasing the measurable flow rate would be to increase the flow time. Thus satisfactory displacement signals could be obtained, even though the slopes of these signals would be decreased. This solution requires that the steady flow period be increased by increasing the duration of constant pressure in the low pressure hydraulic system. The above limits are only imposed by the differential pressure transducers, the capillary geometry, and the displacement transducer. There are other factors, however, which may further reduce the experimental rangeo These include significant viscous heating, the low pressure hydraulic system characteristics, seal friction, the transient response of the test fluid, and gelation of the test fluid. In Chapter II it was mentioned that the problem of viscous heating could not be avoided because the experiment is based on the viscous dissipation of mechanical energy to determine the viscosity of the fluid. This heating effect can be reduced, however, by employing short capillaries and low pressure drops to obtain the high shear rate data' In this investigation the pressure drop across the capillary was generally in the range of 100-200 psi and always less than 1000 psi. For a given capillary, shear rate, and shear stress, various fluids will exhibit differing viscous heating behavior depending on their thermal diffusivity, and viscosity-temperature characteristics. The thermal diffusivity does not vary greatly for the fluids examined, hence, the viscosity-temperature characteristics will have the most influence on viscous heating effects. The fluids with the greatest change of viscosity with temperature will be more likely to show the effects of viscous heating.

-34The best indication of the extent to which viscous heating was negligible is found in Figures 11, 13 and 25 where fluids which are expected to be Newtonian exhibit Newtonian behavior to shear stresses of 600,000 d/cm 2 Figure 25 shows the viscosity of the naphthenic base oil 2 beginning to decrease at a shear stress of 220,000 d/cm, (shear rate of 45,000 sec-1), or a shear-rate shear-stress product of 1010 ergs/sec cm3 (1 kw/cm3) at the wall. This fluid has the largest variation of viscosity with temperature of those examined. Thus it seems that the viscosity decrease is the result of viscous heating and not a pseudoplastic behavior of the fluid. Hence the data itself is an indication that viscous heating is negligible over the range of shear-rate shear-stress product up to 103 watts/cm3M The capillary geometry and the short time duration required to obtain data appear to be the reasons that viscous heating is not a problem below 103 watts/cm3. This high rate of viscous dissipation only occurs for a few seconds at the capillary wall. Thus the volume of fluid actually subjected to this high rate of energy input is extremely smallo T-he high thermal capacity of the capillary wall enables it to act as an effective heat sink during this short time period, thus justifying the assumption of an isothermal wall. The low pressure hydraulic system characteristics also influence the range of experimental data because a constant flow rate of the hydraulic fluid is necessary to obtain steady flow through the capillaryo This factor is only a problem when the viscosity of the test fluid is relatively low and thus only a very small hydraulic pressure is necessary to move the translating piston. Various methods such as applying weights to the pump handles and using the control valves as

-35flow restrictors were only partially successful in eliminating the relatively minor problem of unsteady flow through the capillary. The easiest solution to this problem is to use an experienced operator with a "gentle touch". Friction between the high pressure seals and the translating piston can also reduce the experimental data range because of stick-slip behavior at low shear rates and pressures above 60,000 psio This behavior increases the difficulty of obtaining steady flow through the capillaryo One additional factor which might have further restricted the range of useful data is the transient flow behavior of the test fluido (21) Bird presents the solution to the problem of transient flow in a tube for a fluid initially at rest and subjected to a step pressure gradient. The solution shows that the time, t, required for the fluid to reach more than 92 percent of its final velocity ist -- (sec) where R = tube radius, v = kinematic viscosity. For the available capillaries, R. 0005 inch. Thus, (.5)(5 x 10_3 in)2_ 807 x 10~- sec 1.55 x 10-3 (in s) v (cs) ~whe ~re~~cs where

-36Vmin % 1.0 cs, and Vmax e 105 cs, Therefore, tmax = 8.07 x 10-3 sec and tmin = 8.07 x 10-8 sec. The response time for the differential amplifiers is approximately 0.1 sec, therefore the transient behavior of the test fluid is negligible compared with either the amplifier response or the normal test runs of 0.4 second or greatero As mentioned in Chapter II, gelationof the test fluid results from the solidification of some constituents in the fluid at certain combinations of pressure and low temperatures (usually below 0~F). For this research, gelationof the paraffinic and naphthenic based fluids occurred in the high pressure sections outside the constant temperature bath. The existence of this phenomena is readily observed because the differential pressure transducer signals lag the displacement transducer signal, thus making the results meaningless. An unsuccessful attempt was made to prevent this gelation problem by heating the appropriate sections with electrical heaters. Other possible solutions were also considered but were not feasible for various reasons. Therefore it was concluded that the gelation problem could not be eliminated for certain fluids without major equipment modifications Another factor which might have further restricted the range of useful data, or required correction, was change in the capillary diameter at elevated temperature and/or pressure. This factor was

-37investigated analytically and the possible effect on the viscosity data was shown to be negligible. C. Calibration In this section the method used to determine the capillary diameter is discussed. The calibration methods for each of the four transducers are also explained. Typical calibration curves and a summary of the calibration data for each transducer are presented in Appendix B as well as a discussion of the accuracy of each transducer signal. The diameter of each capillary was determined by passing a viscosity standard fluid through the capillary and measuring the volumetric flow rate, the pressure drop, and the capillary length. These quantities were then substituted into the Hagen-Poiseuille equation to determine an "average" or "effective" diameter. This was performed separately from the high pressure system and employed relatively low pressure drops (i.eo 50 psi) across the capillary which exited to atmospheric pressure. Table IV contains the dimensions of the four capillaries availableo TABLE IV CAPILLARY GEOMETRY Capillary Length Diameter Length-to-Diameter No. (in) (in) Ratio 1 Oo109 0.00938 11.6 2 0.501 oo009834 50.9 3 1.007 00 o01o4 100o2 4 20933 0.01048 280o0 These fluids conform to the ASTM viscosity standard and were purchased from the Cannon Instrument Companyo

-38The instrument (Figure 8) used for the calibration of the capillary diameters was also used to obtain the atmospheric high shear data. It consisted of a pressure source (bottled gaseous nitrogen), a pressure regulator, a ballast tank, a pressure gage, the fluid reservoir, the capillary section, a fluid collector, and a flow meter. The capillary inlet pressure, was measured with a calibrated 500 psi Heise bourdon gage. The capillary exit was connected to one end of a glass fluid collector. The other end of this collector was connected to a calibrated bubble meter. The bubble rise time was measured with an electronic timer which was triggered by pulses from a Wheatstone bridge circuit containing two light sensitive resistors. When the bubble passed between the light source and corresponding resistor, a signal pulse was generated which started or stopped the timer. The temperature of the fluid in this system was controlled by placing the fluid reservoir, the capillary section and the fluid collector in a constant temperature batho The temperature was measured with a calibrated mercury-in-glass thermometer (ASTM 64-F). Calibration of the displacement transducers was very straight forward because the core of the displacement transducer was attached to a micrometer head mounted on the translating piston. Thus the calibration was obtained by recording micrometer displacement versus recorder galvanometer displacement. Table I (Chapter III, Section A) contains a summary of the amplification ratios availableo The calibration curves are presented in Appendix B. The manufacturer of the three strain gage pressure transducers supplied calibration data for each transducer up to 100,000 psio Because

-39IJJc/) ai ~ I~: 0 U~ 0II oC..) C/') LI, J'(~TM L. -j N. - 0 4 /b 00 ~LJJ O Sl w 1~ =t4'-'1 Cam Cl) d~~W~ 0*H U) e. DI~~~~~~~~~~~~) wo) cn* h- D

-40bf the extreme amplification of the signal from the two gages used for the differential pressure measurement further calibration was made. This consisted of a calibration on a dead weight gage to 12,000 psi and of the measurement of viscosity in the system of a well defined fluid for which viscosity-pressure data had been reported. The dead weight gage calibration is discussed in the following paragraphs and the system verification procedure which compared measured data with reported data is discussed in the next section of this chapter. The goals of the calibration procedure for the pressure transducers were (1) to check the accuracy of the manufacturer's data where possible, (2) to determine equivalent pressures for the calibration resistors, and (3) to demonstrate the feasibility of the method for determining the pressure difference across the capillary. The ideal equipment to calibrate these transducers would have been a dead weight gage capable of accurately producing small pressure variations about any pressure level between atmospheric pressure and 150,000 psi. The small pressure variations should have been between one and one hundred psi. Since there is no such dead weight gage in existence, it was necessary to use the equipment available at the University of Michigan. The dead weight gage which was available was a Ruska Model 2400. With certain corrections, this device is capable of accurately determining pressures to within ten parts per million at any pressure level below 12,140 psi. Without using any corrections, the accuracy is approximately 0.2 psi. The existing instrumentation could not detect pressure deviations of this latter magnitude and thus it was not necessary to use any corrections for the calibration data.

-41Since the available dead weight gage had an upper pressure limit of 12,140 psi, it was necessary to rely on the supplied calibration data above this limit. The Ruska equipment did allow a means of satisfying above mentioned goals for pressures below 12,140 psi. The equivalent pressures for the calibration resistors are summarized in Appendix B. The method for determining the pressure difference across the capillary is based on the assumption that the slopes (percent output versus pressure) of the calibration curves are constant between the calibration points supplied by the manufacturer. The accuracy of all experimental data therefore depends upon the accuracy of this assumption. Figure 9 shows that this assumption is verified at 10,000 and 12,000 psio Since it was not possible to obtain the desired calibration data above 12,000 psi, it was necessary to verify that the equipment worked properly for pressures greater than 12,000 psi. This was accomplished by comparing the measured low shear viscosity values of a chemically well-defined fluid with those published by the American Society of Mechanical Engineers. (10) This verification procedure is discussed in the next section. D. Verification As mentioned previously, it was necessary to verify that the accuracy of the experimental apparatus was satisfactory above 12,000 psi because calibration above this pressure level was impossible. This verification procedure consisted of comparing the measured low shear viscosity data of a chemically well-defined fluid with the data published (1by the American Society of Mechanical Engineers. 0) by the American Society of Mechanical Engineers. The fluid used for

-42150 / 00 o P 1-10,000 o Q. m 50 _ AP=P-P12,000 psi 0,_L- Li_ 0 1.0 2.0 3.0 4.0 GALVANOMETER DEFLECTION (inches) Figure 9. Typical Calibration Curve for Differential Pressure Transducers.

-43this purpose was Plexol 201, bis-2-ethyl hexyl sebacate, (ASME, A-i), donated by the Rohm and Haas Company. The properties of all other fluids examined are presented in Appendix A. Figure 10 is a curve of visccsty-versus-pressure for this fluid (Fluid A) which contains both the reported ASMES data and the mean value of the measured data. This figure shows that both sets of data agree favorably. Table V is a summary of the reported and measured data, the percent deviation between the two data sets, and the standard deviation for the measured data. TABLE V SUMMARY OF REPORTED AND MEASURED DATA FOR FLUID A BIS 2-ETHYL HEXYL SEBACATE Pressure If *- Deviation Standard S/ (psig) ASME Data Measured (Percent) Deviation (cps) (cp) for p(S) 0 11.22 10.95 -2.40 10,000 29.0 28.8 o.69 1.24.043 18,800 60.0 59.0 -1.67 2.14.0357 29,500 133. 131.6 -1.04 4.0.030 37,300 232. 235. 1.29 15..o64 47,500 455. 455. -- 30..0675 58,500 880. 870. 1.14 18.2.0210 67,500 1500. 1460. 2.66 89.8.o60 79,300 2900. 2900. -- 153..0527 Data taken from Viscosity-Pressure Curve, Figure 10.

-44E / — 105 103 o 104 102 0 Cu 0 )/ 0n3 / >-!0 3 / -10 > - _m _t ~/ TEMPERATURE= 100~ F 0a1/ o ASME DATA 102 0 10 ZT / A MEASURED DATA 1.0 lO"^ —- - I I 110.1 0 20 40 60 80 100 120 140 PRESSURE (x 1-3psi) Figure 10. Comparison of Reported and Measured for Fluid A (Diester).

-45Figure 11 is a curve of viscosity versus shear stress for the same fluid. It shows that Fluid A is Newtonian at both atmospheric pressure and 50,000 psi for the shear stress range shown. The data in Table V deviated from the reported values by less than 1.7 percent for all but one case. This is within the two percent accuracy estimated for the comparison data. As a result of this verification procedure, it can be concluded that the accuracy of the experimental apparatus is sufficient ( < ~ 5%) for the complete range pressure levels obtainable. The overall accuracy of the equipment is further discussed in the last section of this chapter. E. Error Analysis The major source of error which limits the accuracy of the data was the measurement of the galvanometer signals on the recording. The magnitudes of these signals were determined by using a scale, with 0o01 inch graduations, to measure the distance between the projected references and the galvanometer traces. Thus both the projection of the reference points and the measurement of the distance between the reference points and the galvanometer traces were possible sources of erroro The possibility of error in the reference projection was minimized by first setting all four galvanometer traces to convenient positions and then running several inches of recording paper before the signals were produced. The maximum error in the distance measurement between the reference lines and the galvanometer traces was estimated to be less than 0.02 inch. Thus the percentage of error could be reduced by obtaining large galvanometer deflections. * The linearity of any deflection is with ~+2 percent of the readingo

-46NCx (3SIOd) AlISOOSIA o o ~ or 0 0 0.o U0 0 Io I D 0 0'1 FI, An so j< XX a.1~ ~~~~~~~~ 1 00 0 x I I ( aa 0 X 3 CO ot~ u!i \x X I Q 0 l SE I H ir O" 3 (d) 1X X x IAr' 1 o 1 ll ^ ~fy1 \ i r O- o - \ Jx n 0 _, P0 0 >0 I <I 0 0 00 0~ ~(d3) A11S0SIA'~'.3 (~~~~~~~~~~~~~~~~~~

-47The possible calibration error is discussed in Appendix B, Section 2. This discussion shows that the error of the galvanometer signals for all four transducers was less than one percent of the phenomenon being measured. Therefore, the measurements of the galvanometer signals during data acquisition presented a much greater possibility of error than the possible error in either the transducers calibrations or the calibration constants. Hence, the following discussion only considers the measurement error of the data acquisition signals because this was the most important factor. From the Hagen-Poiseuille equation, the viscosity, [, of a fluid is: = D4 AP (24) 128 LQ where D is the capillary diameter in inches, L is the capillary length in inches, AP is the pressure drop across the capillary in psi, Q is the volumetric flow rate through the capillary in in3/seco The length of each capillary was measured with a micrometero The diameter to the fourth power of each capillary was determined by passing a fluid of known viscosity through the capillary and measuring the pressure drop and volumetric flow rate. The equipment used to determine the capillary diameters is described in Section C of this chaptero The test fluid temperature was controlled by a constant temperature bath and was measured by a calibrated mercury-in-glass thermometero Thus for each available capillary, the equation for viscosity was reduced to

-48= k AP (25) Q where AP = (K1 51 - K2 52) - KEC Q = k2 54/t o 81 and 62 = galvanometer displacement for the two differential pressure signals 64 = galvanometer displacement for the displacement signal t = time during which 84 occurred* KEC = kinetic energy correction The displacement signal 64, was only measured for discrete time increments, thus reducing the possible error of the time measurement to a negligible quantityo Since K1 was approximately equal to K2 and the kinetic energy correction was usually negligible, the viscosity equation reduced further to~ K(61-82) l -:. — (26) Figure 12 shows the maximum possible random error in the viscosity calculation as a function of the galvanometer signalso The smallest possible random error of ~ 1.0 percent would be reached if the three galvanometer signals each produced their maximum displacement of five inches. For the majority of the experimental data, however, the displacement transducer signal was between 005 and lo5 inches while the differential pressure signalswere between 1.0 and 3o0 incheso Thus from Figure 12 it can be seen that the random error for one data point was usually between + 200 percent and approximately ~ 6.0 percento Time signals were produced by the internal circuitry of the oscillographic recorder with an accuracy of approximately one percento

-~9" 12t~ ~....._...= _.M-,.0?O.5 8 \ 6..,_. — *.-. 0.50 _..00 u) -2"- 61-...-'^-''.0.50 ooft-8 | Ide:LECTlONS 10 GaLVANO-TER DEC.O.. g pressure signor {incheSs) Figure 12, possible RandomError

-50It must be emphasized that Figure 12 shows the maximum possible error for any one data point. The probable error for each point is less than the values shown in Figure 12 because the possible errors o:f the three signals may tend to cancel each other. The reliability will also be increased if several data points are obtained and their mean value used. This fact is exemplified by the data for fluid A recorded in Table V. The majority of this data would have a maximum possible random error of approximately four percent if Figure 12 was used. The mean value of several data points, however, deviated from the reported values by less than 1.7 percent for all but one case. Only a few data points were taken for the mean viscosity value which deviated from the reported value by 2.66 percent. The accuracy of pressure level data will also significantly affect accuracy of the measured viscosity data. The slope of the viscosity-pressure curve, S, (plotted on semilogarithmic paper) is: d (log10 ~) 1 d(log e) dP 2.3 dP 1 1 dt S = 2 d2 (27) 2.3 i dP Thus the fractional change of viscosity with pressure is e 2.3 S AP (28) where AP is the possible inaccuracy of the pressure measurement. The possible error in the pressure measurement, Ep, is Ep- p x 100 (29) P P

-51and therefore AP =EP (30) 100 Thus the possible error in the viscosity measurement, E., is E = A- 100 = 100 x 2.3 x S x AP (31) Hence, substituting Equation (30) into Equation (31) results in E = 2.3x x Ep x P (/) (32) The fractional change of viscosity with pressure (2o3 x S) for fluid A, for example, varies from about 1.07 x 10-4 psi-l at low pressure to 0.59 x 10-4 psi-l at high pressure. The maximum error in the pressure level, which is the sum of the calibration error and the galvanometer signal measurement error is approximately one percent. Therefore the resulting inaccuracy of the viscosity measurement is about 1.1 percent at 10,000 psi and 5.9 percent at 100,000 psi.

CHAPTER IV FLUID BEHAVIOR Ao Experimental Fluids The ten fluids investigated in this research are listed in Table VI and further characterization of the components of each fluid is shown in Appendix A. These fluids were chosen because they are well defined counterparts of some typical commercially available lubricants and this selection enables several trends and interrelations to be investigated, The list of fluids includes both a paraffinic and a naphthenic oil and these blended with two polymeric viscosity-index improvers. It also includes four synthetic fluids. TABLE VI EXPERIMENTAL FLUIDS Lretter Description A Diester-Plexol 201 bis-2-ethyl hexyl sebacate B Paraffinic Base Oil R-620-12 C B + 4% polyalkylmethacrylate (PAMA) D B + 8% polyalkylmethacrylate (PAMA) E B + 4% polyalkylstyrene (PAS) F Naphthenic Base Oil R-620-15 G F + 4% polyalkylmethacrylate (PAMA) tH Polybutene LF-5193 I Dimethylsiloxane J' Trifluoropropylmethylsiloxane Some of the questions to be answered by the experimental data (and the fluids chosen to do so) are presented in the following list. The answers to these questions are presented in detail in Section B of this chapter and summarized in Chapter'V. -52

-531. What is the effect of adding various amounts of a given polymer to a given base oil? (Fluids B, C, D) 2. How are the results affected when a given amount of different polymers are added to a base oil? (Fluids B, C, E) 3. How are the results for a given amount of polymer affected by the selection of the base oil? (Fluids B, C, F, G) 4. How does the behavior of some synthetic fluids differ from that of the petroleum oils? (Fluids H, I, J) B. Experimental Results The figures presented in the following discussion are visual aids which help in understanding the behavior of the experimental fluids and do not contain all of the data obtained. Section D of this chapter does contain a complete tabulation of the experimental data. All of these tabulated data do account for the kinetic energy of the fluid leaving the capillary while some data account for the elastic energy stored in the fluid and/or account for the effect of a non-parabolic velocity profile (i.e. the Rabinowitsch analysis). Since a parabolic velocity profile does exist for Newtonian fluids and the elastic energy is negligible, or nonexistent, the tabulated data for the Newtonian fluids (A, B, F, H, I, J) are in final form and therefore need no further interpretation. However, for the non-Newtonian fluids, the effect of a non-parabolic velocity profile must be investigated and also the magnitude of the elastic energy must be determined. These two effects are discussed later in this section. The density of the experimental fluids at all temperatures and pressures was determined from bulk modulus correlations.(' These density data were necessary in order to convert the experimental

-54absolute viscostiy data to kinematic viscosity necessary for the standard ASTM viscosity-temperature charts. 1. General Trends The flow curves, the viscosity-temperature relations, and the viscosity-pressure relations for all ten fluids examined are presented in Figures 10, 11, and 13 through 38. These figures indicate the following general behavior: (1) The flow curves show that the basic behavior of a fluid is not affected by temperature or pressure unless gelation occurs. Six of the fluids (A, B, F, H, I, J) exhibit a Newtonian behavior at all temperatures and pressures examined. The other four fluids (C, D, E, G) are non-Newtonian at all temperatures and pressures. (2) Straight line relations are obtained on the ASTM viscosity-temperature charts for all fluids when pressure and shear stress are constant. (3) The viscosity-pressure relations for the silicones are basically different than the viscosity-pressure relations for the other fluids examined. The viscosity-pressure curves for the silicones (Figure 38) posses inflection points while similar curves for the other fluids do not, (4) The flow curves for the four non-Newtonian fluids show that the viscosity is constant in a low shear stress range (initial Newtonian region) and then begins to decrease with increasing shear stress. The shear stress value at which this temporary viscosity loss begins seems to be only a function of the viscosity level, and independent of the temperature. This is observed by noting that for Fluid C

-55the flow curve (Figure 16) for 100~F and 20,000 psig is almost superimposed on the flow curve for 210~F and 50,000 psig. This same trend is indicated by the flow curves for Fluid G (Figure 28). As the first Newtonian viscosity increases, the maximum shear stress in the first Newtonian region increases while the corresponding shear rate decreases. Thus the temporary viscosity loss seems to begin near a line of constant energy input, i.e. a line of constant shear-stress shear-rate product. No permanent viscosity loss was observed.in these fluids. These four general trends were observed after Fluids A, B, C, F, and G had been examined and this information led to the conclusion that it was not necessary to obtain flow curves over a wide shear stress range at all temperatures and pressures in order to define the behavior of the remaining fluids. Therefore, the decision was made to eliminate any further data at 300~F. Additional flow curves were only obtained at atmospheric pressure and both 100~F and 210~F as well as at some elevated pressure and 100~F. Low shear data, however, were still obtained at several pressures and temperatures of 100~F and 2100F. This reduced quantity of data still enabled the validity of the above mentioned trends to be examined for each additional fluid. A partial summary of the experimental data is presented in Table VII which contains viscosity values as well as viscosity-temperature and viscosity-pressure coefficients at two pressures for all fluids examined.

-56o Q) 0) T OD ^ 0 ONO Cd CO LrN Lf\ Cn Q\ r-l r- LU?o 0 rt LC\ OC' C\ r-n r-l OL O ~ O- - C o n 1- *H *H 0 CH. 0 0 0 - >a 0 0 0F4 I-( rl r( (D r l 0 O(Y-)~ 0~ O 0 CH O z H I > H H a a O O O O U H Oj LC\ O Cj 0 OD CD, OD O._ N rl Lr 0 r-r-I - r-I 0 r -I'- LN >- I Ln. O" O CN, \ 0 II,r-I -I vc v v - r-l. P H ~ ~ O el LR O O O N — CO O CO O ~'~ C 0 v-/ I Lrx \) ~- Lr'X ~ —I ~' ~-t 0 - 0 COF cO " O o.i C.. Uc\ ('D (HCD 0n iD H2 cV O O O O C ~ O O O >.....0 H-' H L R C O CO CO 0N O 0 0 0 I.) en._) 0-J- 0 —.-I' G,._if 0 0 - <' - 0 0 )I 0'O 0 H oD o C 0 Lc N cO r0Q LN CO oQ O i0t'H ~'H r-l'-) H., 01 1 ~ U0 1 e L e en <0 en * <0 0 e C O C) - C CO t- en 0 1O en - O - C O O CO CO CO ON 0 CO O 0c, - 1H 04 p.DH -D O( 0r - I C - Le ee rA CT H 0 - r-l en - 0 C C \S 0 O CO E' 0 0 C3 CO (D ( C e C).-I ON ~*N U 0ON- 0H O*- r-4 CU < 49 C0 CU <0 ON C- 0 0 (D (D r-I II I- 0 I ~H rI 0 *-l C C) 0'v-I'CI- C O q J l O G O l kD H C O - 0l 0

-572. Specific Fluids a. Diester As mentioned previously, the diester (Fluid A) was investigated to verify the accuracy of the experimental equipment. Figures 10 and 11 contain the experimental results for this fluid which have been discussed in Chapter III. b. Paraffinic Based Fluids Figures 13 through 24 and 39 through 44 contain data for the paraffinic based fluids with varying amounts of two polymer additives (Fluids B through E). Gelation limited the maximum pressure to 50,000 psig for these fluids. As discussed in Chapter III, Figure 13 shows that Fluid B (Paraffinic Base Oil) is Newtonian at all temperatures and pressures examined and indicates that viscous dissipation was negligible for this fluid. The flow curves for Fluids C, D, and E (Figures 16, 19, and 22) show that these fluids are non-Newtonian at all temperatures and pressures investigated. The elastic energy stored in these fluids is negligible below a shear stress of approximately 105 dyn/cm2 as indicated by the consistency of the data obtained with different capillaries. The data at atmospheric pressure and 100~F show that a small elastic energy is present in these fluids for shear stresses greater than 105 dyn/cm2. Figure 39 contains the flow curves of the four paraffinic based fluids at atmospheric pressure and temperatures of 100~F and 210~Fo The flow curves are drawn through the data points which contain the elastic energy correction. The uncorrected data points are also included. The elastic energy stored in these fluids was evaluated from the data presented in this figure according to the method discussed in Chapter IIe

-.58Table VIII and Figure 40 summarize the elastic energy calculations for the four non-Newtonian fluids. Figure 40 shows that, at a temperature of 100~F and a given shear rate, the elastic energy in Fluid E is greater than the energy in Fluid C and less than the energy in Fluid Do It was not possible to evaluate the elastic energy in any of the non-Newtonian fluids at atmospheric pressure and 210F because the lower viscosity values made it impossible to obtain the necessary high shear data in' the available equipment. Equation 23, Chapter II, and Figure 39 show that if the elastic energy stored in the fluid is not taken into account, the viscosity data will be higher than the correct value. Figure 41 contains the flow curves for Fluids B, C, D, and E, at 20,000 psig and 1000F, and shows that the high shear viscosity of these fluids does not begin to approach the viscosity of the base oil (Fluid B). This relatively small temporary viscosity loss led to some speculation that the recoverable shear strain, Sr, might be large. Considerable effort was expended, with little success, to evaluate the magnitude of the elastic energy stored in the polymer blends at elevated pressures by obtaining data with different capillaries. With the present high pressure data on Fluid C it is not possible to evaluate the elastic energy above 105 dyn/cm because this data was obtained with a single capillary. The high pressure data for Fluid D are also insufficient to evaluate the elastic energy because the maximum shear stress (2.8 x 105 dyn/cm2) obtained with capillary Number 2 (L/D = 50.9) was smaller than the minimum shear stress (4.7 x 105 dyn/cm2) obtained with capillary Number 1 (L/D = 11.6). These data, however,

-59TABLE VIII ELASTIC ENERGY CALCULATION SUMMARY* Fluid Temperature Pressure Shear Stress Shear Rate Recoverable (~F) (psig) (dyn/cm2) (sec-1) Shear Strain (in/in) C 100. 0. 1.5 x 105 3.2 x 105 4.7 C 100. 0. 3.0 x 105 7.6 x 105 7.2 D 100. 0. 1.4 x 105 1.2 x 105 7-1 D 100. 0. 2.4 x 105 2.8 x 105 8.2 D 100. 0. 4.4 x 105 5.9 x 105 10.1 D I 100. 50,000. a 3 x 105 103 0 < SR < 13.8 E 100. 0. 2.6 x 105 4.2 x 105 6.5 G 100. 0..94 x 105 2.1 x 105 4.6 *i5 G 100. 0. 1.5 x 105 4.1 x 105 11.8 G 100. 0. 2.5 x 105 8.0 x 105 15.5 *The values in this table were calculated from data obtained from capillaries Number 1 and 2. With these capillaries, the smallest measurable recoverable shear strain is approximately four.

-6owere sufficiently close together to enable an estimate to be made of the possible bounds of the elastic energy correction. This was accomplished by placing a band of ~ 5 percent around each data point obtained with capillaries Number 1 and 2o When a smooth curve is drawn through these data, it indicates that no elastic energy is stored in the fluid at a shear stress of approximately 3.3 x 105 dyn/cm (shear rate of 103 sec, viscosity of 330 poise). When separate curves are drawn, the curve through the capillary Number 2 data is below the corresponding curve through the capillary Number 1 data, thus indicating that elastic energy is stored in the fluido When this energy is taken into account the resulting viscosity (280 poise) is 15 percent below the uncorrected value. The elastic energy in Fluid E cannot be evaluated at high pressures either because of insufficient data. Thus it was not possible to obtain the necessary high pressure data with the existing equipment. However, the high pressure data which was obtained did show, that the elastic energy effect is not large. The atmospheric pressure data confirmed that the elastic energy correction is small for the shear stress range investigated. The corrected data in Figure 39 also show that the high shear viscosity of the polymer blends does not reach a second Newtonian value close to that of the base oil, as expected. Thus it appears that the small temporary viscosity loss at high shear stresses for the fluids examined is the actual behavior of the fluids and is not caused by an elastic energy effect. However, the recoverable shear strain is known to increase with shear stress, (20) to some maximum value and hence the Chapter V contains further discussion of the elastic energy in these fluids subjected to high pressure.

-61temporary viscosity loss may increase significantly outside the experimental shear stress range obtained in this research and thus a second Newtonian region may occur in which the viscosity is significantly closer to the viscosity of the base oil than the data obtained. The technique employed to determine whether or not any permanent viscosity loss was caused by high shear stresses applied to the fluids consisted of first obtaining the low shear viscosity data and then obtaining data at ever increasing shear stresses. After the maximum shear stress is obtained, the fluid is again passed through the capillary with a low shear stress. If the two low shear stress viscosity values agree, it is assumed that a permanent viscosity loss was not caused by the high shear stresses. The fallacy in this method is that it does not assure that the permanent viscosity loss is negligible because only the fluid near the capillary wall is actually subjected to the high shear stress and therefore permanent viscosity loss only occurs in a small percentage of the fluid. When the fluid is repassed through the capillary, the probability will be very small that the "ruptured" fluid will again be near the capillary wallo Thus a permanent viscosity loss may not be detected by this technique when subsequent low shear data are obtained. The Rabinowitsch analysis for Fluids C, D, and E showed that the effect of non-parabolic velocity profiles increased the shear rate at the wall by less than five percent in all cases. Therefore, the resulting reduction in viscosity was also less than five percent. Since in many data sets it was impossible to account for the elastic energy stored in the fluid, the Rabinowitsch analysis could not be used because these data must be corrected for the elastic energy stored in the fluid

-62before the true shear stress can be evaluated, and hence the true shear rate determinedo Contant pressure data for Fluid B yield straight line relationships on an ASTM viscosity-temperature chart, Figure 14. The slopes of these lines decrease with increasing pressure. However, the percentage change in viscosity, for a given temperature increase, actually increases with increasing pressure. Constant pressure and constant shear stress data for Fluids C, D, and E also yield straight line relationships on an ASTM viscosity-temperature chart (Figures 17, 20 and 23). The slope of any viscosity-temperature line for Fluid C is less than the slope of the corresponding line for Fluid B and greater than the corresponding slope in Fluid D. This trend was expected because the viscosity of polymer blends is known to decrease less with increasing temperature than the viscosity of the base oil. This viscosity-temperature curves at 10,000 psig for the paraffinic based fluids (Figure 42) and the viscosity-pressure curves for these fluids (Figure 43) at 100~F indicate that the four percent styrene (Fluid E) has both a steeper viscosity-temperature slope and a higher viscosity-pressure coefficient than the four percent methacrylate (Fluid C). Figure 44 shows the effect of polymer in the paraffinic base oil as a function of pressure. The viscosity-pressure curves for the paraffinic based fluids partially answer the first question presented in Section A of this chapter: what is the effect of adding various amounts of a given polymer to a given base oil? Figure 43 shows that the slope of the viscositypressure curve for Fluid B decreases with increasing pressure. The same trend is true for Fluid C except that the viscosity-pressure curve tends

-63to become straight near 50,000 psi. The corresponding curve for Fluid D has a constant slope throughout the pressure range examinedo Thus while the slopes of the viscosity-pressure curves decrease with increasing polymer content at atmospheric pressure the opposite is true at 50,000 psi. This trend can readily be seen by studying the viscosity-pressure coefficients for these fluids presented in Table VII. Figure 44 also helps to explain the effect of various amounts of polyalkylmethacrylate (PAMA) in the paraffinic base oilo This figure shows that viscosity of the blend increases with increasing polymer content as expected, but it also shows that eight percent PAMA has more of an effect at 50,000 psi than it does at lower pressures. c Naphthenic Based Fluids The data for the naphthenic based fluids (Fluids F and G) indicate a behavior similar to the corresponding paraffinic based fluids (Fluids B and C), as anticipated. The flow curves for the naphthenic base oil (Figure 25) show that this fluid is also Newtonian at all temperatures and pressures examined and indicates that viscous heating appears to be negligible below a shear-rate shear-stress product 1010 2 dyn/cm seco The flow curves for Fluid G (Figure 28) indicate that this fluid is non-Newtonian at all temperatures and pressures investigatedo The elastic energy stored in Fluid G appears to be negligible below 105 dyn/cm2 at elevated pressures. Figure 45 contains the flow curves of these two fluids at atmospheric pressure and temperatures of 100~F and 2100Fo As in Figure 39, the flow curve is drawn through the data points which contain the elastic energy correction and the uncorrected data points are included for completeness. The values of the recoverable

-64shear strain obtained from these atmospheric data are presented in Table VIIIo These data indicate that, for a constant shear rate, four percent polyalkylmethacrylate has a larger elastic energy when blended with the naphthenic base oil (Fluid G) than when blended with the paraffinic base oil (Fluid C). As with the paraffinic based fluids, the high pressure data for Fluid G were not sufficient to evaluate the elastic energy. The general comments regarding the elastic energy in Fluids C, D, and E also seem to be applicable to Fluid G. These comments areo lo the high pressure data indicate that the elastic energy is not large; 2o the atmospheric pressure data confirmed that the elastic energy correction is small for the experimental shear stress range; and 3. it appears that the small temporary viscosity loss observed at high shear stresses is the actual behavior of the fluids and is not caused by an elastic energy effect. The third comment must be qualified by noting that the recoverable shear (20) strain increases with shear stress, to some maximum value, and hence the temporary viscosity loss may increase significantly outside the experimental shear stress range obtained in this research and thus a second Newtonian region may occur in which the viscosity is significantly closer to the viscosity of the base oil than the data obtained. The Rabinowitsch analysis for Fluid G showed that the effect of non-parabolic velocity profiles increased the shear rate at the wall by less than 10 percent for the high shear data at atmospheric pressure and a temperature of 100~F. For all other data sets the resulting increase in the shear rate was negligible or it was not possible to apply the Rabinowitsch analysis. As explained previously, in some data sets

-65it was impossible to account for the elastic energy stored in the fluid and thus the true shear rate could not be determined. Straight line relations are obtained on ASTM viscosity-temperature charts when constant pressure data are plotted for Fluid F and when constant pressure and constant shear stress data are plotted for Fluid G. The slope of any constant pressure line for the polymer blend (Fluid G) is less than the slope of the corresponding line for the base oil (Fluid F), as expected. Figures 46 and 47 contain data comparing the naphthenic based fluids with some of the other fluids examined. Figure 46 contains the viscosity-temperature relations at atmospheric pressure for the six petroleum oils examined and shows that at 100~F, (1) the viscosity of the naphthenic based fluids is less than that of the paraffinic based fluids and (2) the viscosity of the naphthenic based fluids decreases more with increasing temperature than the viscosity of the corresponding paraffinic based fluids. Table VII shows that the viscosity-pressure coefficients for the naphthenic based fluids are greater than those for all other fluids examined except the polybuteneo Figure 47 contains the viscosity-pressure data for five of the petroleum oils as well as the diester and the polybutene. d, Polybutene Figure 31 is the flow curve for the polybutene which shows that this fluid also has a Newtonian behavior at all temperatures and pressures investigated. The viscosity-temperature and the viscosity-pressure relations are presented in Figures 32 and 33. Table VII shows that the

-66viscosity of this fluid changes more with temperature and pressure than the viscosity of the other nine fluids investigated. Thus the viscosity of 1.2 x 105 cp. at 39300 psig and 100~F was the largest value obtained in this research (cf. Figure 47). e. Siloxane Fluids The flow curves for the siloxane fluids (Figures 34 and 36) indicate a small temporary viscosity loss (11 percent for Fluid I and -15 percent Fluid J)o As mentioned previously, the viscosity-pressure relations for these fluids are basically different than the viscositypressure relations of the other fluids examined. The viscosity-pressure curves for the silicones (Figure 38) possess inflection points while similar curves for the other fluids do not. This behavior was also observed by Bridgman on dimenthylsiloxane fluidso Figure 35 and 37 contain the viscosity-temperature data for these fluids. The dimethylsiloxane examined has the least change in viscosity with temperature of the ten fluids'examined. C. Correlation 1o Techniques The experimental data obtained covered a wide shear stress range at various pressures and temperatures. The effect of these three variables upon viscosity is very desirable, but it also presents a problem in presenting the experimental results in a convenient form, Therefore, a literature survey was made to determine whether or not any satisfactory data correlation and presentation techniques were readily availableo The.techniques surveyed included analytical and graphical

-67(3SIOd) AllSOOSIA 0^~~~~~~~ - 0 0 L 0 ii C 0 oI ~0 0\ 0\""0 - \' " I''U04i 9Q. 00>\. a- 0 - 4 0,r, I on / L -,"1 1:3 "s 8 ^', \'1 I I\ 8 I\. I Iy ^- II U*b^., I I ii ( -H'Ib 0\ 0 0 n \ 0 0" (d\ ) aI oiS e~ % a. Q- \-,T. 0 0 r"Q~ 0~ (dO) AIISOOSIA

-68c& s0. _. o 0o o o o o 0 0 o 0 /~ OO /~ ~m c0' 0 0 Q..eH CLI / / / / I - CM 0 0(S)0 0 Q 0 (SO) ALISOOSIA

-624,o2 10 10 0~~- I/02/100~ F 2" -/0~ I0 -?0 1.0,, — / - 300- F r, 1) 0.1 o.0 - l I| I- | 0.0o 0 10 20 30 40 50 PRESSURE (X 10-3 psi) Figure 15. Viscosity-Pressure Relation for Fluid B.

-70(3SIOd ) AISOOSIA 0 0 0 0\ "n, 0 - o0 0\ 61X L00 L 0 ^\ 9? o \, o- o, _ -0 _ — __7 C\L 7 \ 0 ) lS K \ ox, I.., I4 E 0 1 \U.\ U I?,'1,?\^ j o.\ o.-0.1 i l I ) 1313 i1i "' 13 ~Iti I II ~ i", 0 r() N v (dO) AJ.ISOOSIA

-71n *..CL 0 0 - o'~ ~ _ 0 C 10 0 00 0 O~0 0 / o O o 0O 00 0 Q (ISOLl 0 W 0 00 0 E S'D,'H 000 0 0 Q (SO) AI$SODSIA

-72105 103 ~~104;~.~I 100 OF 1 2 10 / 10o 3 C X o0210~F,)n I- / H / -0 o / / 0 ok~ /^ g=104 dyn/cm2.0 010 0. co 0no iO 300 OF 1.0 104, dyn/cm2 I0. I1 0 10 20 30 40 50 PRESSURE (X10-3 psi) Figure 18. Viscosity-Pressure Relation for Fluid C.

-73( 3SIOd ) A1ISOOSIA \% - ~ 0 U. \ U- 0 0 0 6, o o o \ 0x i -\,6 8o 8 o o e 00 eO, N 0 bOOo CH C\l~ I x |,x C 0 -~06 - t t, x Q i< l OOXQ3 \ I =9~ 0 0 (dO ) 0 ISOSIA (dO ) AJISO3SIA

-740 0 0 0 00 0 0W0 0 tr) CH U~in~~ ^i~~ ~ -- 0,~ o ro / 0 a.oo w 03 l0S0 0 0 0 0 (SO) AIlSOOSIA

-75510 03 0 100 OF 2 104 _ / 102 CIn / 1 Jo 0-. 0 -= 3 -/ 210 oF o> lo 10 o 0o Cn C/ 02.0' o10 0 1.0 0 10.1 0 10 20 30 40 50 PRESSURE (X10-3 psi) Figure 21. Viscosity-Pressure Relation for Fluid D.

-76(3SIOd ) AIISOOSIA 1o 0 0 0 C; ad^ o\ |\/~ / / c;I0. U.LLL. *-\\ C)\ 5, \d O \ t 0 0 0 0 0 ~ 00 0 Q N 0 \o I \A\6 \ / \CL \O ~ U 0.1 _ I P I t iE 0. 0~~~~~~~~~~~~~~~~~~~~~~ %wo..~~~ 1~~0 I~~~~~~~C 00 C/ 0F/ f \ IX? ^: ~~~~~~~~~~~~~~IQ~~~~~~~~~~~~~~~~~~~~~~~~Q c. ~ ~ ~ ~ 9 \l' N" ~ ~~1 - CM rocc \^ I~~ ~~ 0, H t~o Y x \"o O~~~~\\ r!~ i a\ o a\ O c> \r fr I 0 t~ ~~ 01 1 ho >b 13 0 iiilii <0 N. \1 0o 0o 0'o s ( d3 ) AIISOOSIA

-77U)'w QS 0. o o,- - 0 o 0 oI. - 0 0 oCH r__ 0-p r-I LL 0 w E C) 00 (3 0 S3 I0.O N 0 0 0 0 C (SO) AIISOOSIA

-7810o5 10.o3 I04 10 w a. 00 0 0 1 0 >O0 -- H5~~~~~~~ /~~~~~~~~C/) cl) 0 0 C/) 0I) 20- - 1.0 - 210 ~F'= 104 dyn/cm2 10'I —-- I I I —---- I [- 0.1 0 10 20 30 40 50 PRESSURE (XI0-3 psi) Figure 24. Viscosity-Pressure Relation for Fluid E.

-79(3SIOd) AIISOSIA o. _ — 0 0 ~ \g 00-U- 0 II oo\"oo0do E C/) r \Z 00 0 \* I w I I ** \ 0 0 Y\ \x \ ci 0 x 0 X g NI I I 0 o\ oI\ 0 I 0.. 0 N 0 " ~ ~(0 d0 0o (d3) AILISOOSIA

-80Q. 0. o o- ( 0. rA 0 O 0 _ 0 -' o. Ow. 0 ~~0 t0 Od -- 0 0 0~~a0 / i /L 00 - 0 -' /0 w ~-00 Q\0 - (LS L I ~ I, ~ ~ I,, ~tI * 0 0 0~ 0 cl (SO) AIISOOSIA

-81104 102 0 100 OF 103 10 w U) H a. > I/ 0>' 10 / A >1. I J-300 OF 0 10 1- 0.1 0 10 20 30 40 50 PRESSURE (X 10-3 psi) Figure 27. Viscosity-Pressure Relation for Fluid F.

-82(3SIOd) AIISOOSIA 0 0. LLLUo 0 0 o,o _I Ii _ \ 4 \ 1 I0 g \ I \ o SU ^ ^ - *\ 4~ /0 -0,I 7\I' \ o c II, I I ill I,,Js~Xl I % ~ V1Q 8 a, I"o "'o ~~o o_ w O _~ IO ) ^ I\ 0 0 5:w 0N 9 O - 0 I I I I I I O ) I I W

-83_. 0. 0 0 O oo-. i cu - ~ o | O4 oQ 0 0 U.. St G;2U) O / C 3 O _ _o _. -o'_o lI S" at ^ o CM tP, 00 0 (SO)C ISOOSIA mJ wm (SO) ALISOOSIA

-84104 I02 103 P 1000 F 1~ h. 0Q 0 0' 100 / I1.0 > o 0- 210~ F - o 0 C) — ) 0 / 0 - / O~ 300~ F 10( 0 0.1'= 104 dyn/cm2 1.0 l --- - ---— I —I I I I- 0.01 0 10 20 30 40 50 PRESSURE (X10-3 psi) Figure 30. Viscosity-Pressure Relation for Fluid G.

-85(3SIOd) AIIS03SIA oo 0 000 ~' [I'[... 8 0\ C om 0 NCM 0' 1 H C 4 4 a.0 ^90d a EC)~ ~~~~~~ rj0.4 00 0 Un oZ o 0o Cb rb o W [.(:'r i SCL CH x 00.I t0' x 0 9, 0'" "-, I O — 0 I JI tI N. (D, 0c 00 0 O 0 0 _0 _.o ( C\b AO (d3) AIISI)SIA

- 06em em em em U) ) ru) u) Q. Q. Q. Q. 0 0 0 0. 000 0 0 0 0 0 000 0 O O ~ O. 0O 0 r3 O O O 0 -- -p OO O O ~ (S-) AISOSIA (So) AISOO0SIA

-87105 0 —.. 103 _r~ /I ~100 F 0 104 10! lo3s - / 210~ F I 10 > 102 - 1.0 0 ~ 0 I10 I/ 1 1 1 a0.1 0 10 20 30 40 50 PRESSURE (Xo-3 psi ) Figure 33. Viscosity-Pressure Relation for Fluid H.

(3SIOd) A1ISOOSIA _0 0 _o q d% K L LL - 8 L a0. 1 o S? L ~i..- 1- La.. oo o _ ^ K \o "<. ( Ob <?\ 0 ^ ^ r. 0o O Ol 0 Cl \ *) c5 C\\0o o. \ 0\ <or o.O _H -, IX 0,, U o oo.- - -,,. 0l i I ob: U Q> 4 \ 13. I I r\ I U) 0 o 1100 LO CM O, \iii il " N 0g ~(I. ( d0 0 Lw.r 0 dO) ALI.SOOSIA

-89s0.0 0. 0. _00. 0 0 000 H 00 00 0 o I 00 -H 0 LLP 00 000 0 0 0 0- 00 (SO) ALISOOSIA

-90(3SIOd) AUJSOOSIA 0. \ 0 0\ \0 \ 0 0 LL0LL 0 0o o - 3 \u <\0g\ CL 0 1 10 N 0 <\ 0s I. - I I l C 4.0 o / N, (0.0 e\ (a0 I (/) I\ r~K PC)\ K \d\ U * I 0 ~ o O KK I0 0i ~ XI'% i0 ~ ~ ~-=0.?~.'^~0 o0 - (Dq.(O CA 1 OD 0 U) r - I x Im I I II N,' x -10 t C 0 (dO) AIISOOSIA

-910. 0. O. 0 c 0 o o o l o 0r n o Io C o ~ / 0 H 0 00 l0 w 0 00 0 0 E II I 0 oI I (SO) AJI-SOOSIA

-925 3 10 olO ~ FLUID J / /~ FLUID I 2 104 / o102,0 F LUID J 0 0 /" FLUIDJ 3./ 0 5 uo-10 /' 0- 10 a 0n 0 i0~ / 1 /. 0 o 0 - 0 /3 /V R 0/ / -/ / o/, -2100~ F 0 --- 2100 F Fi6 gue 3 i I — I r i I d 0.1 0 10 20 30 40 50 60 70 80 PRESSURE (XI(S3 psi) Figure 38. Viscosity-Pressure'Relations for Fluids I and J.

-93(3SIOd) AIISO3SIA Uo — Nr')l'Cl u. LLU. 4A0T 00 \i0 00 / in |<^tlo 0 O X 0d rr I 3\ (]I I 4i I CE I c:.), J fI. -"' I wI I \' *' I o arCH \ Ig< B i (dD) AISOSA) r I J!'. on / I'"%, (dO) A11SOOSI A ~ NoII ~'I I~4

-94(00 00 CrJ~ ~ ~ ~~~c U )a mQ ~ ow (U!/Ui) NI~~IS -l'd3HS 318~~3~033f Q 0~~~ 0~~~~~~~~~~~~~~~~~~~ )r~~~~~Q 0 O ~ ~~o __ 0U)~~ 0) <l~~~~ua\~0 - t0) 44 Cs 0 0 (U/u) I.H t36AO (u!/"() Nlt~dlS dV~3HS 3"18U3A03 3 a | Cl)~~~C 0~~~~~~~~~~~~~~0 LO~~~~~~~~( NO 0~~~~~~~~~~~~~~~~~

-95(3SIOd) AIISOS IA 0, O~~ O - 0 r *r" I I^ I I 11 i I 1 1 1 - 1 \\ o 0~sI O - 0 - m G,/-)\ 1 t \. E t X_ -- r 00 X II - 0 I I - - o >.o o oo 14 H 1 I Ic 5D~~~ Q0~~) IH I L -r' 03 I(d) A11SO*SIA

-96C O, 000 Q ) Q Qc E)O ~rO C/ a 0 LACM LLU CH O0 U~ 0 0 ~ 00 ~j 1 000 (SO) lllSODS ~Q0 -P Ow. -P FH i 00.H PA 0 0 U) // / 0 d I I/ 0 I I/1 S AD S o S 0m00 0 0 PA _t _C) (\J~* (SI) AIISOSIA^

-975 03 xFWID D FLUID E ~~104-C/ D X FLUID C -2 104 r~~=104 dyn/cm2l10 FLUID B 0 0 0 0 0 00 oo PRESSURE 10-3 psi ) Figure 43. Viscosity-Pressure Relations for the Paraffinic Based Fluids at 100~F. -=104 dyn/cm2 to I 0.1 0 10 20 30 40 50 PRESSURE (X10'3 psi) Figure 43. Viscosity-Pressure Relations for the Paraffinic Based Fluids at 100~F.

-98105 _> 31 / - 20,000 -psi-~ 104 ~10,0 l ~ 4-0 0 - 0 0 0 3 — 20,000 psi - _ -, 102 000-l ^ 0 psi -a.- 00 0 _ __ --- % STYRENE - ^^-'**"'^ ----- % METHACRYLATE TEMP. = 100~F T- 104dyn/cm2 10 LI I I....... I, 0 2 4 6 8 POLYMER CONTENT (%) Figure 44. Effect of Polymer in Parraffinic Base Oil.

-99(3SIOd ) AIISOOSIA 1 111 1 i P O ^r O- C ONO CO ) crf co' _,0,' \ LL. 0- 0~ 0 N. o'-/ ~.r-Iq0 0 0 (dO) A.LISODoS CI\ OO (d3) AIISO~SIA

-100a ULJ D (0 U. 0 O O ad j c].~4 o ooo o 0 LL(L LLL LL Lu < 01' / 0 Q: 0 0 O0O a. ~ 0 I I // 1 s 0O 0 0 0 A (O A S~So (S3) A1IS03SIA

-101105 _ 13 10 10. 10 10 20 30 5010,04Fi ur ~- - C, C.) o 29 1.0 TEMPERATURE= 1000 F F Z'=i04 dyn/cm2 100 10 I r2 0.1 0 1 0 20 30 40 50 -3 PRESSURE (X 16 psi) Figure 47. Viscosity-Pressure Relations for Fluids A,BC,E,F,G,H.

- _02methods for both Newtonian and non-Newtonian,fluids (References 29-38). Of these several techniques, only the four to be discussed were investigated because they were considered to be the most promising and useful. Graphical presentation of the data for the six Newtonian fluids was considered sufficient since these data are independent of shear stresso The most informative presentation of these data are lines of constant temperature on viscosity-pressure curves. Flow curves and lines of constant pressure on viscosity-temperature curves are also presented for completeness. The analytical method investigated for Newtonian fluids was (29) the following equation presented by Appeldoorn.( log 1/[o = a log (T/To) + bP + cP log (T/To) (33) or k/4= (T/Ta+cP 0bP (34) where i is the dynamic viscosity, T and P are the temperature and pressure, respectively, and the subscript o refers to reference values. These equations are only valid for fluids which have a constant slope on viscosity-pressure curves. Thus these equations cannot be used for the diester, the paraffinic base oil, the polybutene, or the silicones. They are valid, however, for the naphthenic based fluids as well as the paraffinic base oil blended with eight percent polyalkylmethacrylate. This technique was successful for Appeldoorn because his data were limited to pressures below 15,000 psigo Since the viscosity-pressure relations for the data obtained in this research can also be approximated by straight lines at low pressures, this technique should also be applicable

-103in this narrow pressure range. The method was not employed, however, because the majority of the data was outside the limited pressure range in which satisfactory correlations could be obtainedo Graphical techniques for the presentation of non-Newtonian data are not very useful if quantitative information is desiredo But the carpet plots presented in Figure 48 can be helpful in qualitatively understanding the fluid behavioro One advantage of the analytical techniques in general is that they readily permit viscosity values to be predicted outside the limits of experimental data thus allowing the range of variables to be expanded, A disadvantage of these techniques for non-Newtonian fluids, however, is that the fluid behavior is generalized in such a manner that physical interpretation of the data is not possible as when the flow curves, the viscosity-temperature relations, and the viscosity pressure curves are used. Another possible difficulty is that the final equation may require a large number of data sets to evaluate all necessary constants and hence the value of the correlation is limited. The two analytical techniques for non-Newtonian fluids which seemed to be the most promising were reported by Wright(30) and Philipoffol4) The first method reduces the viscosity-shear stress data (at a given temperature and pressure) to a straight line by plotting the energy dissipated by the fluid (shear-stress shear-rate product) against a flow functiono The second method is more general because it considers all three variables~ temperature, pressure, and shear rate. The technique presented by Wright() is valid for fluids whose flow curves are characterized by the existence of initial and ultimate

-1040 ud -P ) 4 -Q~C) in -~rCH 0 0- 0 rcd \ I - - u - eQ -F /I I ~~~~~~~~~~r4~~.

-105Newtonian flow regions. It is postulated that the lograithm of the viscosity has a normal distribution between the limits of the first and second Newtonian regions when referred to the logarithm of the rate of energy inputo Thus for a given temperature and pressure the flow data can be expressed as a straight line relationship (Figure 49). Even though the data for the non-Newtonian fluids examined are not complete enough to assure the existence of an ultimate Newtonian region, this method was investigated in detail because of the possibility that it could be expanded to include the effects of temperature and pressure. This technique was employed by assuming that the viscosity of the fluid in the initial Newtonian region was equal to that of the data point with the lowest shear stress (point 1 on Figure 49). Similarly, the viscosity of the fluid in the ultimate Newtonian region was assumed to be equal to that of the data point with the largest shear stress (point 2 on Figure 49). The flow function which is plotted against the rate of energy dissipation is defined as log() - log([) ( 0 = - --- 7 --- S ---- - --- 7 --- T(35) log(t1) - log(2)3 or (36) where [i is the absolute viscosity and the subscripts 1 and 2 refer to initial and ultimate Newtonian regions, respectively. A computer program was written which, at each temperature and pressure, calculated and printed the values of the slope and intercept of the line in Figure 49. The viscosity was then calculated from the measured energy input and this value was printed along with the corresponding temperature, pressure,

-1o62 w 0,o8__.....__... - 10 W3 WI 104 102.001.01.10.30.50 70.90.99.999 VISCOSITY PARAMETER (') Figure 49. Generalized Non-Newtonian Flow Data.

-107shear stress, energy, flow function, measured viscosity, and the percent deviation between the two viscosity values. The results obtained from this method and the reduced variables technique are discussed later. Ferry(31) described a reduced variables technique for correlating viscosity-temperature-shear rate data. This method resulted in a straight line relationship when the logarithm of the reduced viscosity was plotted against the logarithm of the reduced shear rate. The equations used for obtaining the reduced variables are: ired = iT,7 (k /1T,o) (37) 7red = aT Y (38) and ToPo aT = (To/) Tp (39) where Lred = reduced viscosity, IT,7 = viscosity at T and y, [IT 0= viscosity at T and 7, T,o [ = viscosity at To and low 7, 7red = reduced shear rate, 7 = measured shear rate, aT = shear rate scale factor, T = absolute temperature, p = density, and the single subscript o refers to the reference values. Philippoff(14) expanded Ferry's reduced variable technique to include the influence of pressure. One difficulty immediately encountered was that the scale factor aT requires viscosity values obtained at low

-108shear rates. Since Philippoff's equipment was not capable of producing the necessary low shear rates, he had to obtain these data by other methodso Ordinary capillary viscometers were used at atmospheric pressure and different temperatures. But he could not obtain low shear rate data at different pressures. This difficulty was circumvented by noting that for his data the relative viscosity of the polymer blend is nearly constant with pressure. That is, the polymer blend has the same viscositypressure slope as the base oil at low shear rates. Thus knowing the behavior of the base oil under pressure, the low shear viscosity of the blend at the given temperature and pressure (IT, p o) could be calculated. Hence Philippoff's equation for the shear rate scale factor, aT.P was ToPo n 1'T P0o \ aP = [ - (_) TpaTP (T T /Blend k Base Oil (p [ Base Oil 7red = aTP (41) kred =TP(P) O (t42) kt 1Base Oil The definitions of terms in the above equations are identical to those in Equations (37), (38), and (39) except for the addition of the subscript P for pressure, Since the experimental apparatus used in this research enabled the low shear viscosity to be measured, it was not necessary to use the method presented by Philippoff and the following equations were used: Relative viscosity is defined as the ratio of the viscosity of the blend to the viscosity of the base oil. Table VII shows that this relation is not true for the petroleum oils used in the research.

-109ToPo ~T, P, o aTP = (43) Tp N 7red = aT,P Y (44) Fred = TP,y TP (45) where all terms are identical to those in Equations (40), (41), and (42). A computer program was also written for this method which was very similar to the one written to apply the generalized non-Newtonian technique. At each temperature and pressure, the shear rate scale factor was calculated and printed as well as the slope and intercept of the straight line. The measured shear rate was then used to calculate a viscosity and this value was printed along with the corresponding temperature, pressure, shear stress, measured viscosity, and the percent deviation between the two viscosity values. 2. Results These two analytical techniques employed for the non-Newtonian fluids both reduced the viscosity-shear stress data to straight line relationships for a given temperature and pressure. Therefore the slopes of the resulting straight lines and their intercepts with the ordinate had to be determined for each temperature and pressure. The reduced variables technique also required that a scale factor be evaluated as a function of temperature and pressure. This latter method also required that all data be represented by a single line. Therefore, the slope and intercept had to be constant for all temperatures and pressures. The objective of the correlation for the generalized nonNewtonian technique was to obtain equations for both the slope and the

-110intercept which were explicit functions of temperature and pressure. The objectives of the reduced variables technique were (1) to determine whether or not a single curve could represent all the experimental data, and (2) to obtain an expression for the shear rate scale factor which was an explicit function of temperature and pressure. If the objectives for either correlation could be accomplished, it would then be possible to predict viscosity values under a wide range of conditions and possibly the results could be extended to include the effect of polymer content. The first step in each of these correlation methods consisted of applying the technique to the data and determining whether or not the methods were satisfactory at each temperature and pressure. If the methods did give satisfactory results, the next step could be taken to determine the necessary explicit functions, if possible. Both the generalized non-Newtonian method and the reduced variables technique produced satisfactory results at any given temperature and pressure as the error between the calculated and measured viscosity values was in general less than ten percent. The results for Fluid C, for example, showed that the slope of the straight line in the generalized non-Newtonian technique decreased with increasing temperature and pressure, while the intercept increased with pressure up to 20,000 psig. The intercept for 50,000 psig, however, was less than that for 10,000 psig. Both the intercept and the slope in the reduced variables technique behaved in a similar manner. As a result the intercept in the generalized non-Newtonian technique could not be evaluated by a linear equation. It could be described by a higher degree polynomial but this is unsatisfactory because

-111of the increased number of data sets required to evaluate the necessary constants. Since the slope and the intercept in the reduced variables technique varied with temperature and pressure, the experimental data could not be represented by a single curve. In summary, both of the analytical correlation techniques investigated for the non-Newtonian fluids produced satisfactory results at each temperature and pressure. The generalized non-Newtonian technique was developed for atmospheric pressure data and it was also shown to be applicable to high pressure viscosity data, but it could not be generalized to include the effects of temperature and pressure. Philippoff(1) has previously shown that the reduced variables technique was capable of correlating viscosity data at pressures up to 15,000 psig for certain fluids, but this method could not be successfully applied to the data obtained in this research. D. Tabulated Data As mentioned previously, all of the tabulated data account for the kinetic energy of the fluid leaving the capillary, while some data account for the elastic energy stored in the fluid and/or the effect of a non-parabolic velocity profile. The capillary number listed with each data set can be used to determine whether or not the elastic energy has been evaluated. These capillary numbers contain one, two, or three digits. The one digit numbers (one through four) refer to the stainless steel capillaries designed for this research. The three digit numbers refer to the standard glass capillaries used to obtain the low-shear, atmospheric pressure data. The data sets with the one or the three digit

-112capillary numbers do not account for the elastic energy in the fluid. Only the data sets with two digit capillary numbers account for this energy. The two digit number is formed by using the numbers of the two stainless steel capillaries employed. For example, a data set with a capillary number of 12 means that the elastic energy was evaluated by using data obtained from capillaries 1 and 2. Where necessary, some of the tabulated data sets for the non-Newtonian fluids contain two viscosity values. The first value, in parentheses, is the final value which does account for all necessary effects, including a non-parabolic velocity profile. The second value accounts for the kinetic and elastic energies where necessary but does not account for the non-parabolic velocity profile. The shear rates in these data sets correspond to the second viscosity value.

-113FLUID A TEMP. PRESS. DENSITY VISCCSITY SIEAR SHEAR CAPILLARY STRESS RATE NUMBER (DEG. F) (PSIG) (GM/CC) (POISE) {(CN/SC.CM.) (SEC-1) 100 0.903 110 0 0 100 100 0.903.106 3440 32453 3 100 0.903.110 S050 82273 2 -i-'CC -.903.-l — i8 100 164545 2 100 0.903.109 3 2CC 332110 2 100 0.903.11C 72000 654545 2 100 C0040.940.298 1C37 3480 4 100 1C040.940.280 1281 4575 4 100 1 C040.940 — 29 1 3 29 4460 4 100 10040.940.285 2055 7211 4 100 C.99.940.285 2388 8379 4 100 10040.940.302 5C20 16623 4 100 18770 964.609 1C41 1709 4 100 1 77T.964.614 2661 4334 4 100 18830.964.554 2 E5 5226 4 o00 1 830.964.593 2963 4997 4 100 18830.964.578 4C97 7088 4 100 18830.'964 *592 4638 7834 4 100 29530.989 1.26C 2678 2125 4 100 29590.989 1.320 2740 2C76 4 100 2S59C.989 1.370 3346 2442 4 100 29590.989 1.330 3610 2714 4 100 2959C.989 1.340 3865 2884 4 100 2-650.989 1 300 3'66 2974 4 100 29530.989 1.260 4597 364 4 100 2959C.989 1.33C 4599 345 4 100 29530.989 1.300 5C44 3880 4 100 2S590.989 1.350 166 3827 4 100 29590.989 1.310 S927 7578 4 100 37460 1.030 2.420 2 53 1C96 4 10C 37160 1.030 2.18C 3319 1522 4 100 37310 1.030 2.490 3795 1524 4 100 37310 1.030 2.260 4C07 1773 4 100 37610 1.030 2.290 4173 1822 4 100 3746C 1.030 2.480 4400 1774 4 100 37460 1.030 2.23C 4~33 2078 4 100 37460 1.030 2. 53C 4739 1873 4 100 37310 1.030 2.29C 4762 2C79 4 100 47360 1.200 4.33C 1233 285 4 100 47360 1.200 4.84G 1543 319 4

-1T4FLUID A TEMP. PRESS. DENSITY VISCOSITY SE.EP SHEAR CAPILLARY STRESS RATE NUMBER (DEG. F) PS'IG) (GM/CC) (POISE) (CYN/SQ.CM.) (SEC-1) 100 47510 1.200 4.630 2484 537 4 100 47510 1.200 4.74C 3028 639 4 100 47360 1.200 5.0CC 3098 620 4 100 47510 1.2'0 4*47C 46 57 1042 4 100 47510 1.200 4.2CC 5310 1264 4 100 47590 1.200 4.88C E780 1799 1 100 47590 1.200 4.30C 33260 7735 1 100 47590 1.200 4.13C 63880 15467 1 100 47590 120 4.-3-4^C 6E"5 158'64 100 47590 1.200 4.54C EC490 17729 1 100 47590 1.200 4*350 S8240 22584 1 100 4759C 1.200 4.470 119S00 26823 1 100 47590 1.200 4.43C 124600 28172 1 100 47290 120 4.36C 13T6-0 30183 I 100 47590 1.200 4.14C 141100 34082 1 100 47590 1.200 4.34C 142800 32903 1 100 4S280 1.200 5.22C 169500 32471 1 100 46430 1.200 4.730 274300 57992 1 100 58350 -1.370 8.910 7611 854 4 100 58670 1.370 8.84C 16390 1854 4 100 5E510 1.370 8.50C 16600 1953 4 100 58350 1.370 8.770 17980 2050 4 100 58510 1.370 8.450 19240 2277 4 100 67700 1* 500 14. C0C 5575 398 4 100 67540 1.500 1560C 1 3300 853 4 100 67540 1.500 13. 0C 18380 1342 4 100 67700 1.500 14.10C 23470 1665 4 100 7S780 1.650 29.400 17450 594 4 100 78670 -.650 28.SOC 19420 672 4 100 7S460 1.650 27.20C 21220 780 4 100 78980 1.650 30. EC 211C 945 4

-115FLUIC 8 TEMP. PRESS. DENSITY VISCOSITY ShEAR SHEAR CAPILLARY STRESS RATE NUMBER (DEG. F) (PSIG) (GM/CC! (POISE) (CYN/SC.CM.) (SEC-l) 100 0.849.292 0 0 2CC 210 C.809.045 0 0 100 300 0.777.C19 0 0 150 10Q0 0 9. 295 20 12 441 4 100 0.849.29C 4616 16607 4 IC 0C.849.286 SC30 31573 4 100 0.849.295 1C860 36814 2 100 3.849.286 18100 63287 2 100 0.849 2-27Z 295 108456 T 100 9945.882 1.C2C 4436 4349 4 100 9945,882 1.02C 5537 5428 4 10 9 979.882 1.100C 434 7667 4 100 S945.882 115 16680 14504 4 100 lOQ S91.882- T.T IE 1 70 1 6730 100 9911,882 1.120 24070 21491 4 iOC 10140.882 1.07C 74230 69374 1 100 10180. 82 1.04C 87450 84087 1 100 1C020.882 1.040 1C3200 99231 1 100 10060.88-2 -.C40 -44-00- 96T15 100 20070.908 3.350 2604 777 4 100 19940.908 3.290 6174 1877 4 100 20C70.908 3.28C 7202 2196 4 100 1S500.908 3.35C 18150 5418 4 100 1 440. 08 3. 360 1 50 9271 4 100 19440.908 3.410 33400 9795 4 100 19380.908 3.4CC 47640 14012 4 100 1 380.908 3.350 49600 14806 4 100 19440.908 3.440 188900 54913 1 100 19630.908 3.33C 426700 128138 1 100 49080.961 7270CC 39F30 544 4 100 46770.961 72. 00 44970 625 4 100 50530.961 76.200 3C6600 4026 4 100 4S900.961 73 500 4752CO 6465 1 100 50220.961 76. 500 52120C 6813 ~I 100 49900.961 77.20C0 25CO 6808 1 210 0.809 C44 2408 55229 4 210 0.809 046 8240 179913 4 210 0.809,C47 18100 381053 2 210 1C270.849.134 866 6463 1 210 10160.849.128 1699 13273 1

-116FLUIO B TEMP, PRESS. DENSITY VISCOSITY ShEAR SHEAR CAPILLARY STRESS RATE NUMBER (DEG. F) (PSIG) (GM/CC) (POISE) (CYN/SQ.CM.) (SEC-1) 210 10250.849.130 2194 16877 4 210 1 C 330 -. 849- -*.-135 2400- 1 777 8 4 210 1C370.849.124 6309 50879 4 210 T3OT 849 124 6-734 543-6 4 210 20260.878.325 1104 3397 4 210 20190.878.299 1650 5518 4 210 20-260.878. 29O 56 65 19 53 4 4 210 49420.935 2.40C 4499 1875 4 2T&- 49420.935 2.380 6784 285T 4 210 48940.935 2.360 7302 3094 4 210 48960.935 2.450 29450 1220C 1 210 49280 *935 2.30C 40700 17696 1 300 1180.825. C43 1191 27698 4 30o 1 C180. 825.C44 14 30 32 500 -4 300 1C220 *825.C46 1506 32739 4 300 1C180.825.C46 3316 72C87 4 300 19630.857.088 5 13 5830 4 300 19630.857 C91 1211 13308 4 300 19690.857.088 2818 32023 4 300 19750.857.086 5160 60000 4 300 20130.857.089 24380 273933 1 300 2C130.857,090 31480 350889 1

-117FLUID C TEMP. PRESS. DENSITY VISCOSITY SHEAR SHEAR CAPILLARY STRESS RATE NUMBER (DEG. F) (PSIG) (GM/CC) (POISE) (DYN/SC.CM.) (SEC-1) 100 0.849.720 0 0 200 100 0.849.414 303000 731884 12 100 0 849.688 1204 1750 4 100 0.849.651 4816 7398 4 100 0.849.633 9C30 14265 4 100 0.849.515 68000 132039 2 100 0.849.485 132000 272165 2 100 0.849.469 152000 324094 12 100 0.849.518 167500 323359 1 100 0.849.479 353000 736952 1 100 10290.882 2.200 2014 915 4 100 10610.882 1.360 557OO 409559 1 100 10210.882 2.140 5364 2507 4 100 10280.882 2.140 8963 4188 2 100 10280.882 2.120 11250 5307 2 100 9902.882 1.980 14200 7172 4 100 10280.882 2.110 15540 7365 2 100 10130.882 1.800 17940 9967 1 100 9936.882 2.000 21880 10940 4 100 10280.882 1.950 24420 12523 2 100 10130.882 1.810 29940 16541 1 100 9902.882 1.950 32460 16646 4 100 10280.882 1.820 32920 18088 2 100 9760.882 1.900 43360 22821 4 100 10280.882 1.830 44220 24164 2 100 10470.882 1.840 65C00 35326 2 100 10210.882 1.740 71200 40920 1 100 10430.882 1L780 73110 41073 2 100 10510.882 1.820 84420 46385 2 100 10510.882 1.810 S1450 50525 2 100 10510.882 1.750 113500 64857 2 100 10290.882 1.510 117900 78079 1 100 10170.882 1.400 195600 139714 1 100 10250.882 1.320 272100 206136 1 100 19950.908 6.230 15530 2493 4 100 20070.908 4.370 712700 163089 1 100 19740.908 6.400 2C420 3191 2 100 20140.9 08 5. 980 23210 3881 4 100 19800.908 5.410 50820 9394 2 100 19860.908 5.370 72360 13475 2

-118FLUID C TEMP. PRESS. DENSITY VISCOSITY SHEAR SHEAR CAPILLARY STRESS RATE NUMBER (DEG. F) (PSIG) (GM/CC) (POISE) (OYN/SC.CM.) (SEC-1) 100 19630.908 5.180 84600 16332 1 100 19760.908 4.750 116300 24484 1 100 19880.908 4.280 223300 52173 1 100 19880.908 4.180 414700 99211 1 100 49740.961 123 13400 109 4 100 47400.961 105 231300 2199 2 100 49900.961 120 26360 220 4 100 47870.961 119 55680 468 2 100 47720.961 109 61100 563 2 100 47870.961 109 S5890 884 2 100 47720.961 110 170300 1554 2 100 47560.961 109 197000 1812 2 100 47560.961 106 226000 2124 2 100 49420.961 106 328600 3109 1 100 49260.961 100 840200 8394 1 210 0.809.125 0 0 150 210 0.809.111 3440 30991 3 210 0.809.105.16200 154286 2 210 0.809 110 44600 405455 2 210.0.809.111 57600 518919 2 210 10650. 849 309 929 3006 4 210 10250.849.171 120300 703509 1 210 9945.849.296 1900 6419 4 210 10240.849.287 4345 15139 2 210 9945.849.289 4876 16872 4 210 10200.849.275 6910 25127 2 210 9877.849.249 7804 31341 4 210 10160.849.272 8C42 29566 2 210 10220.849.264 8990 34053 2 210..9945... 849.235 9329 39698 4 210 10240.849.261 10160 38927 2 210 10160.849.248 12580 50726 2 210 10330.849.251 15690 62510 1 210 10410.849.238 18780 78908 4 210 10090.849.249 22750 91365 1 210 10370..849.219 41550 189726 1 210 10290.849 181 109100 602762 1 210 22370.878.758 1255 1656 4 210 19940,878.445 21S500 493258 1 210 22370.878....,747 4037 5404 4

-119FLUID C TEMP. PRESS. DENSITY VISCOSITY SHEAR SHEAR CAPILLARY STRESS RATE NUMBER (DEG. F) (PSIG) (GM/CC) (POISE) (DYN/SC.CM.) (SEC-1) 210 19800.878.610 9468 15521 2 210 19740,878.589 12340 20951 2 210 19770.878.565 14360 25416 2 210 19740.878 *545 17150 31468 2 210 19710.878.507 24600 48521 2 210 19680.878.466 39790 85386 2 210 19750.878.463 93250 201404 1 210 19750.878.443 128800 290745 1 210 19940.878.451 167100 370510 1 210 50840.935 5.320 24260 4560 2 210 51330.935 3.70 lC39000 268475 1 210 51660.935 5.770 24480 4243 4 210 51820.935 5.45C 28060 5149 4 210 50840.935 5.140 28600 5564 2 210 50840.935 5.160 35600 6899 2 210 50840.935 5.020 42340 8434 2 210 51000.935 4.820 54570 11322 2 210 50840 *935 4.790 67160 14021 2 210 50840.935 4.720 1C7200 22712 2 210 50690.935 4.030 195100 48412 1 210 51010.935 3.960 629100 158864 1 210 50530.935 3.950 925400 234278 1 300 10970.825.145 356 2455 4 300 11610.825.100 37770 377700 4 300 11250.825.144 1103 7660 4 300 11210.825.128 3167 24742 4 300 11130.825.111 12190 109820 4 300 10690.825.106 19590 184811 4 300 11590.825.102 30000 294118 4 300 19500,857.245 1910 7796 4 300 20000.857.190 15570 81947 4 300 19750.857.188 23560 125319 4 300 19750.857.195 29380 150667 4 300 19750.857.187 34350 183690 4 300 50530.917 1.280 5889 4601 4 300 5C370.917.925 56340 60908 4 300 49100.917 1.260 6048 4800 4 100 50210.917 1.100 19700 17909 4 300 50370.917 1.100 40920 37200 4 300 50580.917 1.000 47C40 47040 4

-120FLUID C TEMPo PRESS.'DENSITY VISCOSITY SHEAR SHEAR CAPILLARY STRESS RATE NUMBER (DEG. F) (PSIG) (GM/CC) (POISE) (DYh/SQ.CM.) (SEC-1) 300 59450.949 2.200 4973 2260 4 300 59850.949 2.160 24340 11269 4 300 59930.949 1.990 9872 4961 4 300 59610.949 1.950 15650 8026 4 300 0.777.055 0 0 100

-121FLUID D TEMP. PRESS. DENSITY VISCOSITY SFEAR SHEAR CAPILLARY STRESS RATE NUMBER (DEG. F) (PSIG) (GM/CC) (PUISE) (OYN/Si CM. (SEC-1) 100 0.849 1.57C 0 0 300 100 0.849.746 438000 587131 12 100 0.849 1.540 3440 2234 3 100 0.849 1.490 9C50 6074 2 100 0.849 1.320 17200 13030 3 100 0.849 1.140 68800 60351 2 100 0.849 1.01 126C00 124752 12 100 0.849.883 240000 271801 12 100 0.849 1.180 145000 122881 1 100 0 849.985 170CO0 172589 2 100 0.849 1.040 283000 272115 1 100 0.849.909 534000 587459 1 100 10100.882 5.580 3860 692 4 100 10140 882 3*880 18570 4786 4 100 10180.882 4.920 5910 1201 4 100 10140.882 4.420 87 3 2234 4 100 10140.882 4.230 12500 2955 4 100 10140.882 4.250 13420 3158 4 100 10140.882 4.250 14110 3320 4 10 10100.882 3.920 16460 4199 4 100 19750.908 14.530 204 427 4 100 19500.908 12.290 32520 2646 4 100 19640.908 13*670 11650 852 4 100 19500.908 12.900 17850 1384 4 100 19500.908 12.600 19060 1513 4 100 51320.961 448 22700 51 4 100 51160.961 269 1C40000 3866 1 100 51010.961 414 37100 90 4 100 51010.961 414 43900 106 4 100 51000.961 424 49240 116 2 100 50850.961 401 75C85 187 2 100 51000.961 415 98870 238 2 100 51000.961 424 110400 260 2 100 50610.961 386 188400 488 2 100 50650.961 332 285600 860 2 100 51480.961 308 477S00 1553 1 100 51240.961 300 641500 2138 1 100 51480.961 275 72230 Q2627 1 100 51160.961 271 S83500 3629 1 210 0.809.296 0 0 150

-122FLUID 0 TEMP. PRESS. DENSITY VISCOSITY SHEAR SHEAR CAPILLARY STRESS RATE NUMBER (DEG. F) (PSIG) (GM/CC) (POISE) (OYh/SC.CM.) (SEC-1) 210 0.809.171 130000 760234 1 210 0.809.232 S03 3892 4 210 0.809.216 3439 15921 3 210 0.809.212 16S00 79717 2 210 0.809.208 38800 186538 1 210 0.809.182 63700 350000 2 210 0.809.179 88400 493855 1 210 0.809.172 118900 691279 2 210 10160.849.692 2106 3043 4 210 10060.849. 565 7070 12513 4 210 10180.849.646 2721 4212 4 210 10120.849.632 4100 6487 4 210 10120.849.589 6400 10866 4 210 19870.878 1.530 2777 1815 4 210 19570.878 1.120 31930 28509 4 210 19810.878 1.47C 3S86 2712 4 210 19810.878 1.440 5647 3922 4 210 19720.878 1.240 10750 8669 4 210 19660.878 1.210 14500 11983 4 210 19530.878 1.120 25600 22857 4 210 50060.935 12. 600 4790 380 4 210 50060.935 9.830 37000 3764 4 210 50060.935 11.000 10630 966 4 210 50060.935 10.900 15600 1431 4 210 50060.935 10.800 23360 2163 4 210 50060.935 10.300 27900 2709 4 300 0.777.122 0 0 150

-123FLUID E TEMP. PRESS. DENSITY VISCOSITY ShEAR SHEAR CAPILLARY STRESS RATE NUMBER (DEG. F) (PSIG) (GM/CC) (POISE) (0YN/SC.CM.) (SEC-1) 100 0.849 1.240 0 0 300 100 0 *849.616 259000 420455 12 100 0.849 1 160 3440 2966 3 100 0.849.975 17200 17641 3 100 0.849.868 68500 78917 2 100 0.849.825 73750 89394 1 100 0.849 734 135C00 183924 2 1_00 0 *.849.729 1417500 202332 1 100 0.849. 01 295000 420827 1 100 10090.882 4.570 3650 799 4 100 9911.82 3.690 35970 9748 4 100 10170.882 4.440 4213 949 4 100 10170.882 4.420 5405 1223 4 100 10130.882 4.120 6823 1656 4 100 10170.882 3.990 S781 2451 4 100 9945.882 3.830 13080 3415 4 100 9945.882 3.740 26160 6995 4 100 19880.908 17.200 5C44 293 4 100 20190.908 10.300 650000 63107 1 100 19820.908 16.600 5840 352 4 100 19820.908 16.900 6438 381 4 100 19190.908 15.000 12080 805 4 100 19770.908 14.900 15080 1012 2 100 19570.908 14.700 16550 1126 4 100 19630.908 14.500 17120 1181 4 100 19800.908 15.30C 22500 1471 2 100 19820.908 15.000 25100 1673 4 100 19880.908 14.100 32600 2312 4 100 19740.908 13.800 33880 2455 2 100 19620.908 13.300 54270 4080 2 100 19750.908 13.400 68210 5090 1 100 19650.908 12.300 83740 6 08 2 100 1 9620.908 12.200 90420 7411 2 100 19620.908 12.000 115700 9642 2 100 19630.908 11.200 187200 16714 1 100 20080.908 10.300 201800 19592 2 100 20170.908 10.300 241800 23476 2 100 19750..908 10.900 274200 25156 1 100 20000.908 10.300 547700 53175 1 100 29400.925 54.00C 29780 551 2

-124FLUID E TEMP. PRESS. DENSITY VISCOSITY SHEAR SHEAR CAPILLARY STRESS RATE NUMBER (DEG. F) (PSIG) (GM/CC) (POISE) ( YN/SQ.CM ) (SEC-1) 100 29590.925 36. 00 592000 16444 1 100 29400.925 49.C00 37210 759 2 100 29340.925 45.600 71610 1570 2 100 2S280.925 43.300 94750 2188 2 100 29280 925 40.100 103400 2579 2 100 29590.925 44.400 1C7200 2414 1 100 29660.925 40.300 123100 3055 1 100 29590.925 37. 100 168900 4553 1 100 29030.925 33.500 240200 7170 2 100 29530.925 34.400 318200 9250 1 100 29590.925 35.700 534800 14980 1 100 39240 943 174 15550 90 4 10C 39590.943 122 470400 3872 1 100 39240.943 174 23910 137 4 100 39860.943 178 57580 324 2 100 39860.943 160 75750 474 2 100 39860.943 161 87380 543 2 100 39740.943 154 8.9550 581.. 100 39710.943 156 105700 679 2 100 39740.943 153 106200 694 1 100 39860.943 143 157900 1107 2 100 39710.943 128 218800 1716 2 100 39740.943 120 255700 2136 1 100 39560.943 113 278900 2459 Z 100 39740.943 116 297200 2562 1 100 50530.961 516 105400 204 1 100 50370.961 372 617300 1659 1 100 50370.961 446 142500 320 100 49980.961 463 143400 310 2 100 49900.961 400 243800 610 2 100 50370.961 389 480000 1234 1 210 0.809.180 0 0 150 21.0 0 809.124 36200 291935 210 0.809.153 3440 22484 3 210 0.809.141 18100 128369 2 210 IC410.849.478 2309 4831 4 210 10550.849.414 7590 18333 4 210 10410.849.452 3604 7973 4 210 10410.849.448 5840 13036 4 210 20200.878 1.130 2033 1799 4

-125FLUID E TEMP. PRESS. DENSITY VISCOSITY SHEAR SHEAR CAPILLARY STRESS RATE NUMBER (DEG. F) (PSIG) (GM/CC) (POISE) (ODY/SQ.CM.) (SEC-1) 210 20390.878.850 34860 41012 4 210 1S820.878 1.110 3641 3280 4 210 20130.878. 991 7217 7283 4 210 20130.878.904 10620 11748 4 210 20130.878.868 11490 13237 4 210 20070.878,861 19920 23136 4 300 0 *777.073 0 0 150

-126F'LUD T. F TFM.'PRFS$S. DNSTTYY VISCvSITY SH FAAR SHFAR CAPILLARY STRFSS RATE NUJMBER (DEG. F) (LSIG) (G!M/CC) (POISE) (DYN/SQ.CM.) (SEC-1) 100.904.217. 200. 2'1"..8'...'2.'. o -100.00 _ o.8J35.014 0 0 150 C, 4. 91?4 5258 4 1 0.C 0,Ore4 4.2 29 9428 36803 4 109 04.238 181nO 76050?.....n -a r.i-." -:Q36' 0 119? 2 4 4 ]n.. n 10440.9'3 1.100 4289 33899 4 100 10 7.9. 36 1. 06 9570 37330 4 100r 1 073.936 1.045 r940 49981 4 100 1 O'1. r240.9 6 1.040 51970. 49971 1..100l' 10,0'320:.. o....9. 1 1210 1 132 1 10 I 400,.936.940 18820 2,0021 1!1"~ 10.r5. 2~.o 336.92'2190 21.253 1 100. 2140.96. 4.640 10300 2220 4 1.: 2 01 j,0.96L 4.60 2.q40 6397 4...0.'.9n.'- 4..490 35301 7862 4'iO0 2n140.o6 4.10 42749 9916 1 100 1q..'6, 28. 5691 0 132967 1 1...2.039'I.96 4.07P 867600 212647 1 100 1] 70^,99 60.920 877600, 223878 1 210.866. 297 3440 120280 3 210.2066.R60 299652 3 210. 866.028 1720 616487 3 210 1018P.905.OP8 511 5807 4 210 11330.905.084 1212 14429 4 210 10140..''4' 9 060 45111 4 210 1 r 40 5.0817982 98543 4 210 1.0300.95.5 9784 115106 4 210 10n 4lt. n5. 5085 1 2369 145412 4 21.0 9949. 5.082 15200 185366 4 210 1 41.005 -089 22620 254157 1 21,0 1.037 0.Q.087 2.2 50 29,0230 1 210 2 0130.933.229 20991?7 4 210 2060.933.213 5295 24859 4 210 202.0.933.236 22319 94534 4 210. 2260 - 933.2233241 145336 1?10 1981.. 33.?224 365? 163036 4 210 20230.933.224 55800 249107 1 210 20260.933.220 69660 63 1663

-127FLU IDT G TEMP. PRESS. DENSITY VISCOSITY SHEAR SHEAR CAPILLARY STRESS RATE NUMBER (DEG. F) (PSIG) (GM/CC) (POISF) (DYN/SQ.CM.) (SFC-1) lo 0 *.904.79o n O 300 13e C.Q9O4(.340). 72 15300o 411290 12 10. n 0 o_4.?6 3440 4873 1.0'.. 4. *6".4 1.81: 29967 3 100 0. 044 *.570 2 qoO n0877 1 100.9"4.512 668 00 130.+69 2 100.9 04.4?23 133000M 314421 2 1A0 ~.9 ~4(.2_). *'.8 I!46 00, 798701 12 100 nI.o04.49 102800 2085.19 1 100 0.9Q4 *46? 192000 41113 1 1"l0 0.904.4 10 32 80On 80000 1 00. 0230.'36 2.740 9612 3508 2 1on 1.97.936 1.6?0 633400 3909o88 1i0 1n 61 I.936 2.760 12290 4453 4 1n 1-?2. *.936 2.480) 15 930 6423 2 1 0 1050 0...936. 750 1.6300 5927 4 0. 10 5:6.93A 2.770?24540 8859 4.....'.......... 6 2*.?40 248? 1.0607 2 1.^)'1031."?.. 0 I' 4308'": 21015 2 10' ^ lOnlI.036 2. 170 47240 21770 1 1! 3.10 3 o3.63. An _ 68?30 28827 2 10". 1 74.936 1. 980 61780 31202 2 1i."" 1^3'.93,6 2.00 6 5 8 3.2465 2 -i'" 1i 13'n... "' 2.0 30 664 71 32744 1.101~ ]3.. *936 2.010o 92240 45891 2 10"' 1nn.9.6 2.020 105700 52327 1 100l'10:.936. 840 143700 78098 1 1n,.0!10?~,. 936 1.. 5O 194000 104865 1 i5 1 165".936 1740 301700 173391 1 on. 1" 65C. 9 6 730 51 4400 297341 10? " E200!. *960 11.600 12400 1069 4 100" 1 450.960 7.610 929800 122181 1 10Q I 96FQO..960. 1.1 l.50 14840 1331 2 10q 2'2?^'".96n 10.5n0 16810 1601 4 100 20140a ~.960 10. 500 23620 2250 1 1en 196b80.60 10.500 3660 2253 2 100 1 96-80.96-'- 9.840 34120 3467 2 100 1 9620.960 9.250 40260 4352 _ 2 110n 19560.960 8.790 67840 7718 2 1"" 109560.960 8.900 75210 8451 2............. _..... _.... _..............................

-128FLUI ) G T EMP..PRESS. DE N.IT T"~ Y.. SHFAR SHEAR CAP[ILLARY ____TRFSS RATE NURMPBE R (DEG. F) (PSIG) (GM/CC) (POISE). IDYN/SQC.) (SEC-1) 10 0 1q53 0.960 8.6. 0 90460 1 519 2 100 19440.q9 60 8.540 12160) 14239 2 100 19440.960 A:.10 17?600 2154 2 100 19340.960 6 7. 8990 b6400t 2365 2 100 19880.960 8.620 23. 500Ii 26740 1 100 19880.96: 8.260 34620?' 41913 100 1 957' -.9,60 8.73n.47550' ) 54467 1 100 19570:.960 1.',o.77650 1 21 0.866 ".1?2 2 I0 15 210.Ov. 866.09? 36000) 392585 2 210 0.866. 1 7200 71287 2 210'..866.095 181. 0 1.89727 2 210 9950.905.282 44350 15426 2 210 1 00090.960..61 18440 70651 1 210 10'.95.3004613 15377 4 210 9961.905.248 696? 28,73 2 210 9945.o239 927 38787 2 210 10250,.9I5.26?6'.9943 3786 4 210 9945.905.236 1].010 45A 9 3 210 1. 250.9. 264 11 6 414 4 210 1037n,.267 13170 49324 4 210 1 009o.06.249 7228 37.060 1 210]. 96 2.Q63.685 5367 78.5 210 19820.0933.388 15203921 i 21 2001 033 648 1 246 1228 4 210 19650.933.9 12650 21441 2 210 19820.933.h35 1481?23323 1 210 19620.933. 47 1-92 5'' 31.2I? 2 21.0 1 962 Z 933 509 227 60 44 715 2 210. 19680 n.933.4 381 3'080 6 53f 2 210 1 9940 9,033.5'03 3696) 73479 1 210 19880.9o 3.484 4908. 10.1405 1 21 0) 1 9880.9 3. 4' 8 970. - 223209 1 300 99 881.131 517 3947 4 300 2?0390.91.3.242 1.51. 71. 626R6 4 306' 9936.881.134 1007 7515 4 300 10050.881.127 2109 17315 4 300 10410.881.103. 6317 61 330 4 300 10410io.881.1P3 7016 68117 4

-129FLI.'IT G TEMP. PRESS. DENSITY VISCOSITY SHEAR SHEAR CAPTLLAPY STRESS RATE NUMBER (DEG. F) (PSIG) (GM/CC) (POISE) (OYN/SQ.CM.) (SFC-1) 300 10410.,881,.100 16210 162100 4 300 20200. 913.296 1907 6443 4 300 20390 913.296 3032 10243 4 300 0.835.053 0 0 150

-130FLUID H TEMP. PRESS. CENSITY VISCCSITY S'-EAR SHEAR CAPILLARY STRESS RATE NUMBER (DEG. F) (PSIG) (GC/CC) (POISE) (CYh/SC.CM.) (SEC-1) 100 0.836.907 0 C 3CO 210 0.796.084 I 1CC 300 0.736.031 0 C 150 100 O.836.881 6680 7809 3 100 0.836.890 73750 82865 1 100 0.836.9C5 2C5COC 226519 1 100 10220 869 7.250 4449 614 4 100 10260.869 6.900 6454 935 4 100 1C300.869 6.68C 13650 2043 4 100 1C220.869 6.64C 453E0 6902 4 100 1C220.869 6.71C 46290 6899 4 100 1C260.869 7.040 49CO0 6960 4 100 1 9690S.4 37.40C 6725 180 4 100 19630.894 39.900 15C60 377 4 10( 19500.894 37.600 27130 722 4 100 1 s9C.894 39.000 35sC S910 4 100 19380.894 38.700 43C70 1113 4 100 19 70.894 38.30C SfCO0 2480 1 100 19870.894 39.00C 114800 2944 1 100 19870.894 38.9 C 138COO 3548 1 100 19870.894 38.6CC 17440C 4518 1 100 19570.894 34.90C 8161CC 23384 1 100 29470.911 182 2CC90 111 4 100 29240.911 188 38COO 202 4 10C 2S280.911 191 39210 206 4 100 29780.911 196 51690 263 4 102 29919.911 190 ICCCOO 526 1 102 2c840.911 181 250COC 1378 1 102 29840.911 174 340C00 1954 1 102 295SC.911 160 S3C700 5824 1 100 39740.933 1142 26E100 252 1 100 38810.930 1163 957C00 823 1 100 39430.930 1C58 1C17COO 961 1 210.796.87 3340 38391 3 210 C.796.C82 7240 88293 2 210 0.796,C89 18100 203371 2 210 0.796.088 36200 411364 2 210 1C220.837.339 4975 14676 4 210 1C140.837.341 9843 2886' 4 210 1C140.837.333 11960 35916 4

-131FLUID H TEMP. PRESS. DENSITY VISCCSITY SHEAR SHEAR CAPILLARY STRESS RATE NUMBER (DEG. F) (PSIG) (GM/CC) (PCISE) (CYN/SQ.CM.) (SEC-1) 210 1S870.853 1.20C 4170 3475 4 210 199S40 -853 1. 200 5178 4315 4 210 19870.853 1.230 i490 5276 4 210'1r0- *8-53 T.T51 - 459 6 4.86 4 210 19870.853 1.170 13160 11248 4 210 19870.853 1.100 14700 13364 4 210 29530."876 3'380 629 5 1862 4 210 29590.876 3.40C 7505 2207 4 2T.. 270 — 876 3. 260 -'T- 36E0- - 34847 4 ~210 29470.876 3.340 125300 37515 4 210 29470.876 3.300 145E00 44182 4 210 2-95400. 876- 3-'2-60- 1-E54 00 50 736 6 4 210 39270.900 9,800 12800 1306 4 21- 3S350.0g9O 10.000 1 4700 - 47- -4 210 39270.900 9 90C 18060 1824 4 210 3S430.900 10.500 23800 2267 4 210 39430-.900- 1500. 26360 2510 4 210 3S430.900 10.400 28f20 2752 4 21- 39430. 0 10. 600 31 800 3000 4

-132FLUID I TEMP. PRESS. DENSITY VISCGSITY SItEAR SHEAR CAFILLARY STRESS RATE NMLBER (DEG. F (PSIG) (GM/CC) (POISE) (C N/SC.CM.) (SEC-1) 100 0.957.792 i^CO 210 0. 96. 306 0 200 300 O.864.157 ~ 1C 100 0.957.832 6880 8269 3 100 O.957.814 14460 17789 2 100 0.957.800 43400 5425C 2 100 0.957.837 496C0 59259 2 100 1C430 1.020 2.57C 3056 1189 4 100 1C390 1.020 2. 529 4662 1850 4 100 10390 1.020 2.60C 5704 2194 4 100 10300 1.C20 2.52C 7305 2899 4 100 1C260 1 C.20 2.51C 15480 6167 4 100 1C220 1,C20 2.380 16750 7038 4 100 10350 1.C20 2.48C 52130 21020 1 100 1C350 1.020 2.37C 6E60 4 40C69 1 100 1C35C 1.020 2.38C 1Ce5CC 44748 1 100 10350 1.020 2.28C 11 500 519 74 1 100 20220 1.050 5.59C 4C05 716 4 100 20220 1.050 5.36C 4365 814 4 100 20220 1.050 5.55C 5 30 960 4 100 20160 1.050 5.34C 11240 2105 4 100 20090 1.050 5.41C 15840 2928 4 100 2C090 1.050 5.13C 121300 23645 1 100 20090 1.050 5.18C 2C140 3888 1 100 2CC90 1.050 5.32C 2 1890 4115 1 100 3C370 1.C8C 12,COC 114C00 9500 1 100 30400 1.080 11.600 163500 14095 1 100 3C24C 1.080 10.60C 281400 26547 1 100 30370 1.080 11.200 3CCICO 26795 1 100 40420 1.110 26.400 5127 194 4 100 40420 1.110 25.5CC CE65 387 4 100 40420 1.110 25.80C 12700 492 4 100 4C420 1.110 26.200 16370 625 4 100 4C590 1.110 26.200 27560 1C52 4 100 40130 1.110 25.20C 147200 5841 1 100 4C130 1.110 23.50C 1525CC 6489 1 100 40130 1.110 23.400 320000 13675 1 100 51350 1.140 58.3CC 16660C 2858 1 100 51510 1.140 61.30C 215900 3522 1 100 51350 1.140 59.C00 265500 4500 1

-133FLUID I TEMP. PRESS. OENSITY VISCGSITY S- E R SHEAR CAPILLARY STRESS RATE NUMBER (DEG. F) (PSIG) (GI/CC) (POISE) (CYN/SC.CM.) (SEC-i) 100 51350 1.140 57.20C 31490 5505 1 10C 59970 1.160 124 170900 1380 1 100 59810 1.160 112 271300 2429 1 100 59730 1.160 108 361600 3348 1 100 5965 1.16 1 6 1 369600 3197 1 100 71370 1.180 371 20f61O 556 1 100 71370 1.180 368 259800 705 1 100 71200 1.180 375 52CECO 1389 1 100 71370 1.180 365 705COP 1929 1 100 81430 1.200 992 29E200 301 1 100 81270 1.200 949 380200 401 1 100 81430 1.200 965 418900 434 1 210 0.906.312 18100 58013 2 210 0.906 28'8 36 2 00 12 5694 2 210 0.906.312 54000 173077 2 210 1C430.976 1.020 2238 2194 4 210 10470.976 1.08C 4004 3707 4 210 1C470.976 1.05C 4435 4224 4 210 1C470.976.a 1 o 5169 -5 16- 4 210 1C550.976.98C 1C670 10888 4 210 1C510.976.940 14320 15234 4 210 2C290 1.C20 2.13C 3992 1874 4 210 20290 1.020 2. CC 6105 2921 4 210 2C290 i.20 2.'-0C-r7-09' 8595 4 210 2C290 1.020 1.5SC 17600 9026 4 210 2C350 1.020 1.870 19580 1C471 4 210 51350 1.110 11.60C 10070 868 4 210 51350 1.110 11.60C 15350 1323 4 210 51350- 1.10 11.70C 18220 1557 4 210 51190 1.110 11.60C 37510 3234 4 210 51190 1.110 11.800 38730 3282 4 210 51350 1.110 12.100 4C190 3321 4 210 71600 1.160 33.40C 6909 207 4 210 7 143. 160 32.4- 011770 363 210 71430 1.160 30.700 12460 406 4 210 71430 1.160 32.50C 21110 650 4

-134FLUID J TEMP. PRESS. DENSITY VISCOSITY ShEAR SHEAR CAPILLARY STRESS RATE NUMBER (DEG. F) (PSIG) (GM/CC) (POISE) (DY~/SC.CM.) (SEC-1) 100 0 1.230.950 0 0 300 210 0 1.170 169 0 0 150 100 0 1.230.968 3440 3554 3 100 0 1.230.998 8600 8617 3 100 0 1.230 1.040 36200 34808 2 100 0 1.230 1.060 5400 5094 2 100 0 1.230 1*020 71800 70392 2 100 10360 1.290 4.46C 5870 1316 4 100 10340 1.290 4.37C 6600 1510 4 100 10160 1.290 4.290 604 2239 4 100 10160 1.290 4.220 9844 2333 4 100 10320 1.290 4.100 9952 2427 4 100 9962 1.290 4.100 13730 3349 4 100 10120 1.290 4.270 19020 4454 4 100 10430 1.290 4.630 38560 8328 1 100 10470 1.290 4.51C 53360 11831 1 100 10470 1.290 4*430 86300 19481 1 100 10470 1.290 4,220 1C0500 23815 1 100 20080 1.330 16.500 4524 274 4 100 20080 1.330 16.700 5700 341 4 100 20170 1.330 16.400 27350 1668 4 100 20210 1*330 17.200 36760 2137 4 100 20220 1.330 15,200 54750 3602 1 100 20280 1.330 16.COO 86800 5425 1 100 20220 1.330 15.40C 117100 7604 1 100 19710 1*330 15.40C 152000 9870 1 100 20410 1.330 14.500 253900 17510 1 100__O o 20380 1.330 14,400 3.16500 21979 1 100 20350 1.330 14.100 400000 28369 1 100 30010 1.360 53.800 10170 189 4 100 30070 1.360 52.600 13540 257 4 100 29940 1.360 51.700 17080 330 4..1 29940 1.360 52.600 18770 357 4 100 30560 1.360 55.70C 116000 2083 1 100 30500 1.360 50.400 153900 3054 1 100 30460 1*360 49.300 242000 4909 1 100 30430 1.360 52.800 354800 6720 1 _100 40290 1. 380...182.31430 1727 1 100 40130 1.380 182 364500 2005 1 100 40210 1.380 178 39600 222 1

-135FLUID J TEMP. PRESS. DENSITY VISCCSITY SHEAR SHEAR CAFILLARY STRFSS RATE NUMBER (DEG. F) (PSIG) (GM/CC (POISE) (DYN/SC.CM.) ISEC-I1) 100 40290 1.380 180 442600 2459 1 100 40290 1*380 184 722300 3926 1 100 40130 1.380 176 107700 612 1 100 51190 1.410 720 267700 372 1 100 51350 1.410 722 310400 430 1 210 0 1.170 173 3440 19884 3 210 0 1 170.157 8600 54777 3 210 10390 1.260.686 4075 5940 4 210 10350 1.260.691 6040 8741 4 210 10.430 1 260.675 1002-0 14844 4 210 10430 1.260.648 13100 20216 4 210 20730 1.290 1.840 4066 2210 4 210 20480 1.290 1.690 5e66 3471 4 210 20800 1.290 1 720 12730 7401 4 210 20730 1.290 1.750 12900 7371 4 210 30240 1.320 3.560 9806 2754 4 210 30240 1.320 3.650 13250 3630 4 210 30270 1.320 3*640 15240 4187 4 210 40260 1.360 8.900 21940 2465 4 210 40260 l.360 8 820 22200 2517 4 210 40780 1,_360 8. 890 26100 2936 4 210 40940 1.360 8.860 29820 3366 4 2_10 40780 1 360 8.730 31070 3559 4 210 51350 1.390 18.200 11840 651 4 210 51350 1.39.0.. 8 100 12100 669 4 210 51680 1.390 18.100 14520 _ 802 4 210 51510 1.390 19.000 24840 1307 4 210 51510 1.390 19*000 32740 1723 4 210 62120 1.410 37.000 11000 297 4 210 62120 1..4.0 38.100 _12030 316 4. 210 62.1.20. 1.410 36.900...27340. 741.. 4

CHAPTER V CONCLUSIONS AND RECOMMENDATIONS The conclusions and recommendations are presented in two sections. The first section considers the experimental equipment while the second considers fluid behavior. Both of these sections summarize the discussion in previous chapters and then recommendations are made concerning future work. A. Experimental Equipment A unique two-way high pressure capillary viscometer was proven to produce accurate viscosity measurements at pressures from 10,000 to 80,000 psig, temperatures from 100 to 300~F, and over a shear stress range from 300 to 1.2 x 106 dynes/cm2. The system accuracy was verified by comparing measured low shear viscosity-pressure data with previously reported data on a chemically well defined fluid (bis-2-ethyl hexyl sebacate). The two sets of viscosity data differed by less than 2 percent. As a result of this research, a useful system has been developed which can measure viscosities from 1.0 to 100,000 centipoise. The equipment is designed for a maximum pressure of 100,000 psi and is presently capable of producing viscosity measurements at this pressure provided the viscosity. is less than 100,000 centipoise at this pressure and room temperature. Higher viscosities could be measured if the system is modified such that shear rates less than 100 sec-1 could be measured. The minimum measurable shear rate could be reduced if the period of steady flow through the capillary could be increased by increasing the duration of constant pressure in the low pressure hydraulic -136

-137system. In order to achieve long conatant pressure periods (greater than thirty seconds) in the hydraulic system, some mechanical system should replace the present hand-actuated pumps. The temperature of the experimental fluid in the capillary section can presently be varied from approximately -50 to 450~F. The temperature of the fluid in the high pressure reservoirs, however, cannot be adequately controlled at this time. This inability led to premature gelation of the petroleum oils examined. As a result, the maximum pressure was limited to 50,000 psig for the paraffinic based fluids and to 20,000 psig for the naphthenic based fluids. Since gelation occurs when some constituents in the fluid solidify at certain combinations of temperature and pressure, it can be prevented by controlling the temperature of the experimental fluid outside the constant temperature bath. An attempt was made to prevent gelation by heating the appropriate sections with electrical heaters. This effort was unsuccessful because of inadequate instrumentation. An automatic temperature sensing and control system could be designed which would solve the gelation problemo Considerable effort was expended in an unsuccessful attempt to evaluate the elastic energy stored in the petroleum oils at elevated pressures. The two major reasons for the inability to obtain the necessary data were (1) equipment limitations and (2) the small magnitude of the elastic energy. In order to evaluate the elastic energy (recoverable shear strain) it is necessary to obtain constant shear rate viscosity data from capillaries with different length-to-diameter ratioso The existing system is capable of measuring large elastic energies, Sr > 5.0, at elevated pressures.

-138Even though constant shear rate data are reguired, the experimental shear stress range for each capillary is the limiting factor. Thus the maximum shear stress obtainable for the longer of the two capillaries must be increased, and similarly, the minimum shear stress obtainable for the shorter capillary must be decreased. The corrected shear stress at the capillary wall, Tcorr, as defined by Equation (14) in Chapter II is AP-KEC (14) corr 4 L/D where AP is the measured pressure differential across the capillary, KEC is the kinetic energy correction, and L/D is the capillary lengthto-diameter ratio. Since the maximum AP is used when the maximum shear stress is sought, the only way to increase the shear stress is to use a capillary with a analler length-to-diameter ratio. Thus the maximum shear stress for the longer of the two capillaries can only be increased by using a capillary with a smaller length-to-diameter ratio than the one previously employed. The minimum measurable shear stress for the shorter capillary can be decreased by either decreasing the minimum measurable pressure differential or by increasing the capillary lengthto-diameter ratio. This latter suggestion is not desireable because it is advantageous to use capillaries with as large a difference in their length-to-diameter ratios as possible. Thus decreasing the minimum measurable shear stress is the best method. This decrease can be achieved if the sensitivity of the differential pressure measurements is increased by increasing the amplifier gain settings or by increasing the differential pressure transducer excitation voltages from six to

-139twelve, or even twenty-four, voltso Therefore, by using capillaries with length-to-diameter ratios of 25 and 11, instead of the ratios of 50 and 11 used in this work, and by also increasing the sensitivity of the differential pressure measurements, it should be possible to evaluate the recoverable shear strain at elevated pressures in the fluids examined. The noise level in the differential pressure transducers was acceptable but could possibly have been reduced further. The following three measures may or may not accomplish the desired results: 1. twist all pairs of wires where possible, 2. obtain a better ground, 3. ground cable shields, avoiding ground loops. This first item may reduce the noise level because twisting pairs of wires tends to cancel the induced voltages. The existing common electrical ground in the laboratory is sufficient from a safety viewpoint, but inadequate for noise suppression. Therefore, a ground point as close as possible to the equipment should reduce the noise level by significantly reducing the path resistance from the equipment to groundo All the transducer cables are shielded but the shields are not groundedo Grounding the shields should also reduce the noise level, if done properlyo The major difficulty in achieving noise reduction via this method is the very high probability of ground-loops which may increase the noise levelo The major objective in grounding the complete system is to start from a common ground and work radially outward.

-140B. Fluid Behavior The viscosity of ten well defined fluids was measured in a capillary-type viscometer at pressures up to 80,000 psig, temperatures of 100, 210, and 300~F and shear stresses from 300 to 1.2 x 106 dynes/cm. In addition to the fluid used to verify the accuracy of the system, the nine additional fluids were: (1) a paraffinic base oil (A), (2) A plus four percent polyalkylmethacrylate (5.6 x 105 weight average molecular weight), (3) A plus eight percent polyalkylmethacrylate, (4) A plus four percent polytertiarybutylstyrene (3.9 x 105 weight average molecular weight), (5) Naphthenic base oil (B), (6) B plus four percent polyalkylmethacrylate, (7) polybutene (409 Number average molecular weight), (8) dimethylsiloxane (82.6 cp. at 100~F), and (9) trifluoropropylmethylsiloxane'(81o3 cs. at 100~F). Data correlation and presentation techniques were also investigated in order to facilitate comprehension of the significant trends and interrelations among the fluids examined. The experimental data indicate the following general trends~ 1. The flow curves show that the basic behavior of a fluid is not affected by temperature or pressure unless gelation occurso Six of the fluids exhibit a Newtonian behavior at all temperatures and pressures examined. The other four fluids are non-Newtonian at all temperatures and pressures. 2o Straight line relations are obtained on the ASTM viscositytemperature charts for all fluids when pressure and shear stress are constants

-1413. The viscosity-pressure relations for the silicones are basically different than the viscosity-pressure relations of the other fluids examined. The viscosity-pressure curves for the silicones possess inflection points while similar curves for the other fluids do not. 4. The flow curves for the non-Newtonian fluids show that the viscosity is constant in a low shear stress range (initial Newtonian region) and then begins to decrease with increasing shear stress. The shear stress value at which this temporary viscosity loss begins seems to be independent of pressure and temperature. This temporary viscosity loss also seems to begin near a line of constant energy input, i.e. a line of constant shear-stress shear-rate product. No permanent viscosity loss was observed in these fluids. The various amounts of polyalkylmethacrylate (PAMA) added to the paraffinic base oil resulted in the following effects being observedo 1. The slopes of the viscosity-pressure curves (or viscositypressure coefficient*, C) decreased with polymer content at atmospheric pressure while they increased with polymer content at 50,000 psig. Thus the viscosity-pressure curves approached straight lines with increasing polymer content. 2. The viscosity of the polymer blends decreased less with increasing temperature than the viscosity of the base oil. 3. The elastic energy stored in the fluids at high shear stress increased with polymer content. A measure of the elastic energy is the recoverable shear strain which was negligible, or nonexistent, * all 4 AP T

-142for the base oils at atmospheric pressure, 100~F, and the shear stress range examinedo For the same temperature and pressure, the recoverable shear strain was also negligible for the polymer blends at shear stresses less than 105 dynes/cm2. However, the recoverable shear strain was measurable in the polymer blends for higher shear stresses. The four percent PAMA blend had a recoverable shear strain of 7.2 at a shear stress of 3.0 x 105 dynes/cm2 and a shear rate of 7.6 x 105 sec1, while the corresponding value for the eight percent PAMA blend was 10.1 at a shear stress of 4.4 x 105 dynes/cm2 and a shear rate of 5.9 x 105 sec-1o It is not possible to evaluate the recoverable shear strain at elevated pressures with the existing data. But these high pressure data do indicate that the recoverable shear strain is negligible (i.e. Sr < 4) at shear stresses less than 105 dynes/cm2. 4. Some of the constituents in these paraffinic based fluids solidified at room temperature and pressures above 50,000 psig and thus gelation prevented viscosity measurements above this pressure. The following differences were noted between the data for the paraffinic base oil blended with four percent polyalkylmethacrylate (PAMA) and the data for the same base oil blended with four percent polyalkylstyrene (PAS). 1. The slopes of the viscosity-temperature and the viscositypressure curves for the four percent PAS blend are greater than the corresponding slopes for the four percent PAMA blendo 2. The recoverable shear strain is 6.5 for both the PAS and the PAMA blends at atmospheric pressure, 100~F and a shear stress of 2.6 x 105 dynes/cm2.

-1433. Gelation also occurred in these fluids at room temperature and pressures above 50,000 psig thus limiting the viscosity measurements to pressures of 50,000 psig or lower. A comparison of the data for the paraffinic and naphthenic base oils and the data for these oils blended with four percent polyalkylmethacrylate (PAMA) indicates the following trends. 1. Gelation of the naphthenic based fluids occurs at pressures greater than 20,000 psig at room temperature while gelation does not occur in the paraffinic based fluids at room temperature until the pressure exceeds 50,000 psig. 2. At atmospheric pressure, the viscosity of the naphthenic based fluids is less than the viscosity of the corresponding paraffinic based fluids and the viscosity of the former also decreases more with temperature than the corresponding paraffinic based fluids. 3. The viscosity-pressure coefficients for the naphthenic based fluids are greater than their paraffinic based counterparts. 4. The recoverable shear strain is greater for the naphthenic blend (15.5 at a shear stress of 2.5 x 105 dynes/cm2) than for the paraffinic blend (7.2 at 3.0 x 105 dynes/cm ). The experimental data for the four synthetic fluids indicate the following behavior. 1. Gelation did not occur in any of these fluids and therefore the maximum pressure at which viscosity measurements were made was limited by the smallest measurable shear rate. 2. The diester (bis-2-ethyl hexyl sebacate) has the lowest viscosity-pressure coefficient of the ten fluids examined while the polybutene has the largest viscosity-pressure coefficient.

-1443. The polybutene also has the largest viscosity-temperature coefficient, VTC, of the ten fluids and therefore has the largest change in viscosity with temperatureo 4o The dimethylsiloxane has the smallest viscosity-temperature coefficient and hence the smallest change in viscosity with temperature. 5. The viscosity-pressure curves for the two siloxane fluids are basically different than similar curves for the other eight fluids because the curves for these two fluids possess inflection points while similar curves for the other eight fluids do not. The viscosity data for the Newtonian fluids can be adequately presented by constant temperature lines on viscosity-pressure curves. The viscosity data for the non-Newtonian fluids cannot be adequately presented on a single curve. The analytical correlation methods surveyed for Newtonian fluids were unsatisfactory because they were either difficult to employ or were only applicable to relatively low pressure data. The generalized (30) non-Newtonian technique as presented by Wright was shown to be applicable to high pressure viscosity data but it could not be generalized to include the effects of temperature and pressure. The reduced variables (14) technique presented by Philippoff( could not be successfully applied to the data obtained in this research.. The high pressure data for the petroleum oil-polymer blends examined indicate that the temporary viscosity loss is not large for the shear stress range investigated. The polymers used in this research were in the relatively low to medium molecular weight range. Therefore, *VTC - (1 - 210/10o)P

-145if subsequent data prove that the elastic energy is not large at shear stresses outside the range examined, there is a possibility that it may be more desirable to use a larger quantity of low molecular weight polymer to obtain a given low shear reference viscosity than to use a smaller quantity of high molecular weight polymer.

APPENDIX A FLUID DESCRIPTIONS The following table summarizes the experimental fluids used in this research. The remaining pages in this appendix contain the descriptive data supplied with the fluidso EXPERIMENTAL FLUIDS Letter Description A Diester-Plexol 201 bis-2-ethyl hexyl sebacate B Paraffinic Base Oil R-620-12 C B + 4% polyalkylmethacrylate D B + 8% polyalkylmethacrylate E B + 4% polyalkylstyrene F Naphthenic Base Oil R-620-15 G F + 4% polyalkylmethacrylate H Polybutene LF-5193 I Dimethylsiloxane J Trifluoropropylmethylsiloxane -146

-147FLUID CHARACTERIZATION Symbol: A Type: bis-2-ethyl hexyl sebacate Source: Rohm and Haas Company Property Viscosity at 210~F, cs 3.32 Viscosity at 100~F, cs 12.75 Viscosity at -65~F, cs 7988 Viscosity Index (ASTM D-974) 150 Neutralization Number (ASTM D-974) 0.02 Cloud Point (ASTM D-2500)~F below -65

-148Symbol: B and F Types: Paraffinic (B) and Naphthenic (F) Base Oils Source: Sun Oil Company Fluid B F Viscosity at 100~F (cs) 33.33 24.06 Viscosity at 210F(cs) 5.336 3.728 SUS/100 156.2 115.2 SUS/210 43.74 38.59 Viscosity Index (ASTM D-2270) 102 -13 Flash Point (~F) 410 315 Fire Point (~F) 470 365 Pour Point (~F) 5 -45 Refractive Index 1.4754 1.5085 Density at 68~F (gm/cc).8596.9157 Molecular Weight 401 305 2 Percentage of Carbon atoms in aromatic rings 4.0 21.5 2 Percentage of Carbon atoms in naphthenic rings 28.0 36.0 Percentage of Carbon atoms in paraffinic rings2 68.0 42.5 Percentage of Carbon atoms in aromatic rings3 4.0 20.3 Percentage of Carbon atoms in naphthenic rings3 27.4 34.5 Percentage of Carbon atoms in paraffinic rings3 68.8 45.2 Average number of aromatic rings per molecule3 0.20 0.77 Average number of naphthenic rings per molecule3 1.59 1.74 Average number of total rings per molecule3 1.79 2.51 1 Calculated from viscosity data using the method of A. E. Hirschler, J. Inst. Petroleum, 32, 133-61, 1946. 2 Obtained using the Viscosity-Gravity Constant and the Refractivity Intercept using the method of S.S. Kurtz, Jr., R.W.King, W.J. Stout, and D.J. Gilbert, from a paper, "Relationship between Carbon Type Composition Viscosity-Gravity Constant and Refractivity Intercept", presented before the Petroleum Div., ACS, Sept., 1955. 3 Calculated using the n-d-M method of structural group analysis of of mineral oil fractions of Van Nes and Van Westen, "Aspects of the Constitution of Mineral Oils", Elsevier Publishing Co., Inc. 1951.

-149Symbol: (None; used as additive in C, D, G) Type: Polyalkylmethacrylate Source: Rohm and Haas Company The polymer had a viscosity average molecular weight of 560,000 and was in solution with a paraffinic hydrocarbon very similar to fluid B in this investigation. The solution contained 36.1 percent polymer and had a viscosity of 796 cs at 2100F. The percent additive reported in Table III (ie. 4 or 8%) was the percent polymer in the final solution. Symbol: (None; used as additive in E) Type: Polytertiarybutylstyrene Source: Dow Chemical Company The polymer had a weight average molecular weight of 375,000 as determined by an ultracentrifuge method. The polymer was supplied in solution with a paraffinic hydrocarbon similar to Fluid B. The solution contained 25% polymer. Fluid E contained 4% polytertiarybutylstyrene polymer

-150Symbol: H Type: Polybutene Source: American Oil Company Figure Al shows the molecular weight distribution of this fluid as determined by a gel-permeation chromatograph. Viscosity: 0~F, cs/SSU 18836/86740 100QF, cs/SSU 109/505 210~F, cs/SSU 10.6/61.6 Viscosity Index (ASTM D-2270) 87 Flash Point, COC, ~F 300 Unsaturation by Hydrogenation, % 91 Density at 25~C, gm/cc. 0.8443 Molecular Weight (No. average). 409 Symbol: I and J Types: Dimethylsiloxane (I) and Trifluoropropylmethylsiloxane (J) Source: Dow Corning Corporation Fluid I J Viscosity: 100~F, cs 82.6 81.3 210~F, cs 33.1 14.3 Flash Point, ~F 575 500 Freeze Point, ~F -67 -55 Density at 25~C, gm/cc 0.968 1.23 Molecular Weight 7000 4000

0: crI S CH \ Wj *B lv a D3 3 / I X/ 8 ~ a ^ N ^33B~i in i KMi LCi

APPENDIX B EXPERIMENTAL EQUIPMENT B.l Operating Procedure The following list briefly outlines the steps necessary to operate the high pressure viscometer and associated electronics used in this research. Explanations of the steps follow when necessary. Operating Procedure Check List I. Clean and Fill Viscometer Test Section and Reservoirs II. Calibration A. Pressure Level Transducer (at atmospheric pressure) 1. Excite transducer and turn on galvanometer No. 3. 2. Null output signal by balancing wheatstone bridge circuit. 3. Select sensitivity and calibration switch positions. 4. Record zero position. 5. Push red calibration button and record calibration signal (Table B3). B. Differential Pressure Transducers (at each elevated pressure level) 1. Excite transducers and null output signals by balancing wheatstone bridge circuits. 2. Select sensitivity and calibration switch positions. 3. Turn on galvanometers No. 1 and No. 2. 4. Record zero position. 5. Push red calibration buttons and record calibration signal (Table B2). C. Displacement Transducer Step II A. automatically calibrates this transducer. -152

-153III. Data Acquisition A. Obtaining Pressure Level 1. Turn off galvanometers No. 1 and No. 2 and battary excitation switches for the differential pressure transducerso 2. Increase static pressure to desired level with by-pass level open. B. Viscosity Data 1. Set visicorder timing switch to desired position and select visicorder paper speed. 2. Set displacement transducer sensitivity switch (SS4) to desired position and set galvanometer No. 4 signal at a convenient position by adjusting micrometer head. 3. Close by-pass valve. 4. Excite differential pressure transducer No, 1 and null output as before. 5. Repeat step 4 for pressure transducer No. 2. 6. Turn on visicorder paper drive. 7. Record zero position of pressure transducer No. 3 by temporarily pushing the black zero button. 8. Move traversing piston. C. Reset procedure 1. Turn off paper drive and galvanometers No. 1 and No. 2. 2. Open by-pass valve until the deviation amplifiers are almost saturated. 3. Reposition galvanometer No. 4 (displacement signal). 4. Repeat steps B3 through B8. The preceeding list shows that there are only two basic steps in using the existing electronic control box. The first step is calibration of the transducers and the second is adjustment of the transducer outputs at elevated pressures to obtain data.

-154Calibration is accomplished in two parts. The first part calibrates the pressure level transducer as well as the displacement, transducer and the second part calibrates the differential pressure transducerso The first part, which determines the voltage of the battery used to excite both the pressure level transducer (No. 3) and the displacement transducer, is accomplished by nulling the output signal from the pressure level transducer at atmospheric pressure. Next the sensitivity and calibration switches (SS3 and CS3) are set at the desired positions. Finally the zero position and calibration signal are recordedo These latter signals are obtained by pushing the red calibration button for pressure transducer No. 3. The second part of the calibration procedure determines the coefficients for the differential pressure transducers which are a function of the amplifier gain settings and the excitation battery voltages. This calibration procedure is identical to that for the calibration of the pressure level transducer except that it should be followed at each pressure level to insure that the gain of the amplifiers has not changed with time. The positions of the sensitivity switches, (SS1 and SS3), the positions calibration switches, (CS1 and CS3), and the calibration signals (deflections of galvanometers No. 1, 2 and 3) are used as input data to the data reduction computer program (See appendix C1). The data reduction computer program is written such that there is no need to calibrate any of the pressure transducers at more than one position of the sensitivity switch. The program only needs the displacement transducer excitation voltage and output signal in order to calculate the translating piston displacement. Since the voltage of the battery

-155which excites both the pressure level transducer and the displacement transducer is determined in the pressure level calibration, there is no need to calibrate the displacement transducer. Once the calibration data has been obtained, the collection of viscosity data can begin. It is important to turn off galvanometers No. 1 and No. 2 before the pressure level is increased because of their extreme sensitivity. Permanent damage to the galvanometers may result if this step is omitted. The excitation voltage to pressure transducers No. 1 and No. 2 should also be removed before the pressure level is increased, otherwise the amplifiers will become saturated. The pressure level should be set at a value slightly less than desired because the pressure will increase when the by-pass valve is closed. The rest of the operating procedure is straight-forward and only one step requires additional comments. The translating piston is moved in step B8. This motion should be made in such a manner that the pressure drop (galvanometer signals No. 1 and No. 2) across the capillary remain constant. Care must be exercised not to saturate the deviation amplifiers when a large pressure drop is sought. B.2 Instrumentation B.2.a Measurement Error The error analysis section, (Chapter III, Section E), discussed the major possible error in the measurement of the galvanometer signals. In this section other less important error sources are discussed as well as the accuracy of the pressure transducer calibration data and the accuracy of the calibration constants.

-156The measurement of the transducer signals were made from the edges of the galvanometer traces. This method eliminated the necessity of accurately locating the center of the 0.050 inch wide trace. Other possible errors inherent in this method were (1) measurements made from opposite edges of the galvanometer trace, and (2) measurements made from the wrong reference line. These minor errors were obviously eliminated by exercising sufficient care. The position of the reference lines for the differential pressure signals could be affected by variations in the amplifier characteristics. The amplifier gain and zero drift were the two characteristics which had to be closely watched. The gain was checked by recalibrating the amplifier signals after every series of runs at a given pressure level. The zero drift was minimized by allowing at least one hour warm up time and only using short time intervals for data collection. The following discussion of the equivalent pressure values for the calibration resistors assumes that the pressures produced by the Ruska Model 2400 dead weight gage were exact. This assumption is acceptable because, as mentioned in Chapter III, the possible error in the pressure, approximately 0.2 psi, could not be accurately detected by the existing instrumentation at normal gain settings. With the above assumption, the equivalent pressure values for the calibration resistors were evaluated and recorded in Table B2 of the next section. The accuracy of these values only depended upon the accuracy of the galvanometer displacement measurement. From Figure B1 it is seen that the equivalent pressure, Peq' is: eq

-157CALIBRATION PRESSURE p ) UPPER BOUND (P ) eq max pF EQUIBLIRIUM PRESSURE eq (P ) LOWER BOUND eq min 6c= CALIBRATION PRESSURE W SIGNAL 0I:: n //6e = CALIBRATION RESISTOR C) SIGNAL w 0 E = POSSIBLE ERROR IN MEASUREMENT E E ~- ~ E~t ^~~~~~ L 6e 6c GALVANOMETER DEFLECTION Figure Bl. Typical Pressure Transducer Calibration Curve.

-158(be) P = P Peq c (5c)' (Se+E) (Peq)max Pc (c, E ~~and (P ~, (be-E) and k(Peq)min = c where ( eq)max = upper bound of Peq' (Peq)min = lower bound of Peq Pc = calibration pressure, (psi), 5c = galvanometer signal produced by Pc' (inches), be = galvanometer signal produced by the calibration resistor, (inches), and c = possible error in any displacement measurement, (inches). Thus it can be shown that the true equivalent pressure is less than [1 + be/bc] 100 (e/b)(l - /c) % above Peq and less than C[1 + be/bc] 100 (be/bc)(1 + C/6b) below Peq Table Bl shows that the possible error in the equivalent pressure values for all pressure transducers is less than one percent. It should be noted that the estimated possible error of the displacement measurements was 0.01 inch instead of the 0.02 inch value mentioned previously. The reason for the increased accuracy is that C = 0.02 inch is a maximum estimated value for normal data acquisition. For the calibration measurements however, the reference points were constantly checked, thus eliminating one possible source of error.

-159TABLE Bl PRESSURE TRANSDUCER CALIBRATION DATA Pressure Transducer No. 1 No. 2 No. 3 Transducer Function Differential Pressure Pressure Level Sensitivity Switch Position 4 4 4 Calibration Switch Position 3 3 5 Calibration Resistor* (ohms) 20 M 20 M 75 K Calibration Pressure, Pc (psi) 150.0 150.0* 12,000 Calibration Pressure Signal, 6c (inch) 3.72 3.98 3~50 Calibration Resistor Signal, 6e (inch) 1.33 1.51 3.37 Estimated Possible Error, (inch) 0.01 0.01 Oo01 Possible Error in 6e Measurement (%) + 0.75 + 0.66 + 0.296 Equivalent Pressure, Pe (psi) 53.6 56.9 11,500 x Upper Bound, (Pq)max psi) 54.1 57.4 11,600. Lower Bound, (Peq)min (psi) 53.1 56.4 11,500~ Possible Equivalent Pressure Error (5) + 0.93 + Oo88 ~ 0.43 * Resistors most frequently used for calibration ** The reference pressure level was 10,030 psi and the calibration pressure difference was obtained by increasing the pressure level to 10,180 psi. This transducer is not linear over the complete calibration range. Therefore derived equations are not correct, but they do give an adequate approximation of the error bounds.

-160Now that the error in the equivalent pressures has been evaluated, the accuracy of the calibration constants can be determined. For the three pressure transducers, these three constants converted the galvanometer deflections to voltages, which were then used with the manufacturers calibration data to obtain the desired information. In the case of the displacement transducer, the calibration constant was used to convert the galvanometer displacement directly to the displacement of the translating piston. For the three pressure transducers, the accuracy of this method was checked by using the galvanometer deflections, obtained from the calibration pressure signals, as computer input data. The calculated values were then compared with the values of the calibration pressure. In all cases, the error in the calculated values was within the measurement error of the galvanometer calibration signals. Since this checking procedure verified the accuracy of calibration constants, it was assumed that for the three pressure transducers the accuracy of the galvanometer signals were equal to the accuracy of the equivalent pressure values. These calibrations constants for the differential pressure transducers were a function of the excitation voltage, amplifier gain, and attenuation resistor magnitude. Therefore, these constants were recalculated frequently. The constant for the pressure level transducer was only a function of the excitation voltage and attenuation resistor. Therefore, only the excitation voltage had to be determined. This was accomplished using the calibration resistor signal. This method of determine the excitation voltage was verified by a vacuum tube voltmeter which was calibrated with a standard cell.

-161The calibration constant for the displacement transducer was only a function of the excitation voltage and attenuation resistor. Since the same battery was used to excite both the pressure level transducer and the displacement transducer, it was not necessary to recalculate this constant. This method was verified by comparing the calculated displacements with the known displacement of the micrometer head. The calculated values were within the possible error of the calibration signal measurements. Thus for the displacement transducer, the accuracy of the galvanometer signal was equal to the accuracy of the excitation voltage calculationo B.2,b Transducer Details and Calibration Data i. Pressure Transducers The three strain gage pressure transducers were manufactured by the Advanced Technology Division of American-Standardo The following four pages contain a technical data sheet for a typical transducer and the manufacturer's calibration data for the three transducers. As mentioned in Chapter III, Section C, the two goals of the calibration procedure were (1) to check the accuracy of the manufacturer's data where possible and (2) to determine equivalent pressures for the calibration resistors. The pressure source was a Ruska Model 2400 dead weight gage which has an upper limit of 12140 psi. A Heise bourdon tube gauge was used to extend the calibration range of the pressure level transducer because it was not accurate enough to calibrate the differential pressure transducers.

-16234 -114 PERFORMANCE> BRIDGE Four active arms RESONANT FREQUENCY Approx. 45,000 cps COMBINED NON- Less than 1.0% of full scale by best straight PRESSURE LIMIT 150% F.S. for static pressures LINEARITY AND line drawn through calibration curve Full scale for dynamic pressures HYSTERESIS —----- NEGATIVE PRESSURE Usable to full vacuum REPEATABILITY Within 0.1% of F.S. BURST PRESSURE Above 200% F.S. RESOLUTION Infinite EXCITATION Recommended 10 volts DC or AC ACCELERATION EFFECT Less than 0.1% of F.S. per "G", all planes Maximum 17 volts DC or AC VIBRATION EFFECT Insensitive from 50 to 2000 cps to 100 "G", 3 COOLING AIR 2 cfm at 15 to 20 psig clean, dry air planes MATERIAL 347 stainless steel diaphragm and TEMPERATURE RANGE - 65~ to 300~F. uncooled; 2000~F. (gases) 17-4 PH stainless steel body cooled ----------— cooled ---- 34 BRIDGE Uncompensated. Maximum voltage output ZERO PRESSURE OUTPUT Less than _ 2% of F.S. ZERO PRESSURE OUTPUT Less than 2% of- 35 BRIDGE Voltage compensated. Single shunt calibration THREAD TEMPERATURE 300~F. maximum resistor: 280,700 ohms, 10% F.S. 112,200 ohms, 25% F.S. THERMAL ZERO SHIFT Less than 0.02% F.S./ ~F. change 56,000 ohms, 50% F.S. (0~ to 200~F.) - 36 BRIDGE Voltage compensated. Bridge input symmetrical. THERMAL SENSITIVITY Less than 0.02% F.S./ F. change External calibration resistor values not speciSHIFT (0O to 200~F.) fied. ORDERING CATALOG NUMBER SELECTION TABLE BRIDGE MOUNTING THREADS TYPE MAXIMUM IMPEDANCE F.S. OUTPUT BASIC COOLING PRESSURE INPUT AT 10 V. MOUNTING DIAPHRAGM MODEL ORDER (psig) ORDER AS SHOWN EXCITATION ORDER TORQUE ORDER NO. NO. ORDER NO. NO. OUTPUT ~ 10% (MV) NO. DESCRIPTION (FT.-LB.) NO. 114 - 1 20,000 -34 350 ~ 10% 32 minimum -13 1-1/16-16 42 -61 air-cooled 30,000 - 35 350 ~ 2% 30 ~ 2% UN-2A (347 SS or 50,000 - 36 350 ~ 2% 30 ~ 2% welded) - 3 60,000 uncooled - 3 100,000 uncooled!r — N -- 114 — 3 -50,000 -34 -13 -61 EXAMPLE ORDER NUMBER AS SELECTED FROM TABLE EXAMPLE AS WRITTEN: 114-3-50,000-34-13-61 It is requested that the full six-part catalog number be used when ordering PIN IDENTIFICATION ACCESSORY EQUIPMENT CABLES (12 FT.) AND CONNECTORS Vn/14 A^^ \C0 0CABLE NUMBER / 0 0 A = Signal (+) BRIDGE CONNECTOR AD CF B = Signal (-) TYPE COOLED UNCOOLED NUMBER Bridge C = Excitation (-) |l 0 C =D Excitation 1-34 192-2 191-2 51009-2 B \^ y <.. D = Excitation +)3 E EE External Shunt - 35 - 35 192-1 191-1 51009-1 Extr nal Shunt Bridge - 36 192-2 191-2 51009-2 I ---------- >c-A faoxnly _ A/ER CAN-.$tandard ADVANCED TECHNOLOGY DIVISION MONROVIA INSTRUMENTS DEPARTMENT 1401 SO. SHAMROCK AVENUE MONROVIA. CALIFORNIA Phone (213) 359-9317

-1653^AMERrcaiAtnd andawd a ADVANCED TECHNOLOGY DIVISION MONROVIA INSTRUMENT DEPARTMENT 1401 SOUTH SHAMROCK AVENUE * MONROVIA, CALIFORNIA 91016 AREA CODE 213 359-9317 CALIBRATION RECORD Model No.: 114-1-100,000-34-13-61 Serial No.: 8458 Sensitivity: 8.159 MV/V Excitation: 10V AC/DC Input Resistance: 349.0 Pressure Range: 0-100,000 PSI Mounting Torque: 42 Ft. Lbs. Coolant Inlet Pressure: 20 PSIG Flowing Non-Linearity and Hysteresis Combined B. S. L.:.76 % F. S. Input PSI Output in % %Rated Pressure Increasing Decreasing 0% 0__ _ 0 -.07 10% _.8.80 8.48 20% __ 18.85 18.55 40%A _40% _ 39.12 38.70 60.% 959.37 59.16 80% 80% _ T79.87 79.79 100% 99.95 --- PIN IDENTIFICATION -c^ C >*A^ PiA = Signal (+) -3q o/ B = Signal ( —) |Br dg' n -) Calibrated by: Litt Zeeve o, E D = Excitation (+) ~? —I^edL^ = External Shunt -35 Inspected by: __.EIA RAI O: Sita NDF = External Shunt Bridge only Date: 3-23-66 AMERICAN RADIATOR & STANDARD SANITARY CORPORATION

-164DVACE TEH ADVANCED TECHNOLOGY DIVISION MONROVIA INSTRUMENT DEPARTMENT 1401 SOUTH SHAMROCK AVENUE * MONROVIA, CALIFORNIA 91016 AREA CODE 213 359-9317 CALIBRATION RECORD Model No.: 114-1-100,00-34-13-61 Serial No.: 8481 Sensitivity: 8.080 MV/V Excitation: 10V AC/DC Input Resistance: 350.1 Pre3sure Range: 0-100.000 PSI Mounting Torque: 42 Ft. Lbs. Coolant Inlet Pressure: 20 PSIG Flowing Non-Linearity and Hysteresis Combined B. S. L.:.49 % F.S. Input PSI Output in % %Rated Pressure Increasing Decreasing 0% 0 -.10 I 10i%_ 9.53_ 9.15 20% 19.20 19.13 40o ~40~~% 39.03 39.24 60% _ _59.15 59.49 80% _ 79.14 79.72 " 100%O 100.02 ___PIN IDENTIFICATION.-ed A FC C.' ( ) A = Signal (+).e F *;~. I'~ ~OB = Signal (-I ol C = Excitation (-)Calibrated by: Davenport & ittle |, o Y ~'t-D E D = Excitation (+) AMERIC. E = External Shunt -35 Inspected by: R ___-A F = External Shunt Bridge /led only Date: 4-1-66 AMERICAN RADIATOR & STANDARD SANITARY CORPORATION

-165W*. AN/ w ADVANCEO TECHNOLOGY LABORATORIIS DIVISION OATA INSTRUMENT DSPARTMINT 3e0 WHISMAN ROAD * MOUNTAIN VIIW. CALI'ORNIA SUNfNYVAL.t LANT PHONK: 415 6e0-4401 TWXt 40?7a7-o0s3 CALIBRATION RECORD #3 Model No.: 114-1-100,000-34-13-61 Serial No.: 7627 Sensitivity: 9.240 ~MV/V Excitation: 10VQy Input Reslstance: 351. 8 ohms Pressure Range: 100,000 PSIG Mounting Torque: 42 ft. lbs. Coolant Inlet Pressure: 20 PSIG Non-Linearity and Hysteresis Combined B. S. L.: 1.02 % F.8. Input PSIOu t in % %Rated Pressure Increasin Decreasin 0% 0 -.03 10% 11.94 11.94 41 20% 22.05 21.44 ~40% _ _ 41.90 41. 55 _____ 61.40 61. 30 80% _= 80.60 80.40 100% 100. 000 - PIN IDENTIICATION 1^ 9^ r 0 A c Signal -(+), C: t E1cittiaon (-) Calibrated by: Nicolai & Little = Excitation I iy>c. ~ =^ = _erl Shunt - 35 Inspected by: f = ExtMnol Shunt Brid-e FoEn o Date: May 24, 1965 AMERICAN RADIATOR & STANDARD SANITARY CORPORATION

-166The differential pressure transducers, No. 1 and No. 2, were each calibrated at five different pressure levels, 3030, 4930, 5030, 10030, and 12030 psi. Table B2 contains a summary of the calibration data. Figure 9, Chapter III, shows that the assumption of a constant slope for the pressure-output curve between 10,000 and 12,000 psi is correct. TABLE B2 DIFFERENTIAL PRESSURE TRANSDUCER CALIBRATION SUMMARY Transducer No. 1 Calibration Switch Position (CS1) 1 2 3 4 5 6 Calibration Resistor 80M 40M 20M 10M 5M 2.5M Pressure level (psi) Equivalent Pressure Difference (psi) 3030 15.75 31.5 62.4 4930 14.75 29.25 58.5 5030 14.50 29.2 58.3 115. 225. 463. 10030 13.2 26.5 53.6 106. 218. 432. 12030 13.2 26.5 53.5 Transducer No. 2 Calibration Switch Position (CS1) 1 2 3 4 5 6 Calibration Resistor 80M 40M M 2 0 M M 5M 2.5M Pressure level (psi) Equivalent Pressure Difference (psi) 3030 15.75 31.75 64.75 4930 14.75 29.75 60.3 5030 14.7 29.75 60.0 120. 248. 496. 10030 14.4 28.8 56.9 114. 222. 443. 12030 14.4 28.8 56.8

-167Table B3 contains a summary of the calibration data for the pressure level transducer while Figure B2 contains the pressure versus galvanometer deflection curve for the maximum instrumentation sensitivity (SS3 = 4). Figure B2 contains the pressure versus galvanometer deflection curves for all four instrumentation sensitivities. TABLE B3 PRESSURE LEVEL TRANSDUCER CALIBRATION SUMMARY Calibration Switch Position (CS3) 1 2 3 4 5 6 Calibration Resistor 1M 301K 150K 100K 75K 30.1K Equivalent Pressure 750 2800 5630 8500 11500 (psi) ii. Displacement Transducers The two displacement transducers were manufactured by the Sanborn Division of the Hewlett-Packard Company. Calibration was achieved by plotting the galvanometer deflection versus core deflection. Figures B4 is a typical calibration curve. This figure shows that the output signal becomes non-linear for large core displacements. The problems associated with non-linearity were avoided by only operating in the linear range.

-16814 12 ~12 ~ ~ 75 K=11,500 psi 10 - gO so 8 - A r 8 —__ 100 K = 8500 psi / 301 K=2800 psi 6 15- I M = 750 psi i 0. 4I M 750 psi 0 1.0 2.0 3.0 4.0 GALVANOMETER DEFLECTION (inches) Figure B2. Pressure Level Transducer Calibration Curve.

-1b950 It 8/ w 30 -i I0 -/'00 w 20 a: I0 0 I.O 2.0 3.0 4.0 5.0 GALVANOMETER DEFLECTION (inches) Figure B3. Pressure Level Transducer Output Signal Curve. w / //r

-170Q: t-/ w z LrJ Z/ t- wl w 2/ 00 Z < < _1/ E(-J > a. (9Q: MICROMETER DISPLACEMENT Figure B4. Typical Displacement TransducEr Calibration Curve.

-171B.2.c Electronic Circuits This section contains schematic circuit diagrams for the instrumentation control box and equivalent circuits for all transducers. The following is a list of figures presented in this section. LIST OF FIGURES IN SECTION -B.2.b Figure Title B5 Instrumentation Block Diagram B6 Instrumentation Control Box Panel B7 Transducer Cables —Schematic Diagrams B8 Deviation Amplifier Cables —Schematic Diagrams B9 Visicorder and Battery Cables —Schematic Diagrams B10 Control Box Schematic —Differential Pressure Transducer Circuits Bl1 Control Box Schematic —Differential Pressure Transducer Circuits (Continued). B12 Control Box Schematic —Pressure Level and Displacement Transducer Circuits. B13 Equivalent Circuit for Differential Pressure Transducers B14 Equivalent Circuit for Pressure level Transducer B15 Equivalent Circuit for Displacement Transducer Figure B5 shows the general block diagram for the instrumentation. The transducer connectors are not numbered, but all connectors on the control box and visicorder are numbered. Figure B5 should be

-172— I. ~' —--- -I.7^1 DC PT I [E....= AMP I2 D 1 i an=====^ ~ ^TI I O VA 6o 110 VAC (3)6V BATT'S m LLI-I --- AMP va ~~o 10 o: QI I I -- I2 a: 100 10V PT 3 <: (D 7 DCDT ^^"-" 110 VAC INDICATOR TO LIGHT REMOTE 110 VAC LIGHT 6 VAC CIRCUIT CONTROL POWER Fge SUPPLY Figure B5. Instrumentation Block Diagram.

-173referred to when studying figures B6 through B12 in detail because the control box connector numbers are consistent in all figures. Figure B6 is a photograph of the control panel and shows the position of all control knobs, switches, and lights. Tables B2 and B3 summarize the values of resistors and their corresponding equivalent pressure signals for the two calibration switches CS1 and CS3. Figures B7, B8, and B9 are self explanatory and require no further comments. Figures B10 and Bll are the schematic diagrams for the differential pressure transducer circuits in the instrumentation control box. These circuits have been divided into two figures for clarity. When studying these figures, it should be kept in mind that the circuits for both differential pressure transducers are identical, but physically and electrically isolated. Figure B10 contains the portion of the circuits from the transducer cable connections (No. 1 and No.2) to the DC amplifier input connectors (No. 9 and No. 10). The balance potentiometers, excitation voltage connector (No. 5) and the calibration resistors are also included. Figure Bll contains the portion of the circuits from the DC amplifier output signals (connectors No. 9 and No. 10) to the visicorder connector (No. 6). The attenuation resistors and filter capacitors are also included. Figures B10, Bll, and B12 all contain indicator light circuits. A single transformer provides the six volt AC source. The red lights indicate when the excitation voltage is applied to each transducer. The white warning lights indicate when the galvanometers are activated. Figure B12 contains the complete circuits for both the pressure level transducer and the displacement transducer.

0 fol S.4 C) 4103.4..).4) 051 ~:~ 4..t. 4 S.{ t:, tt —

-175AArd AAr C ArdA Ard B B B D Co_ - bk bB- B bk DC C bk C- _> D<>8Ewh - IC wh _ D gn 9 rD -D Y E E F F PRESSURE I -TRANSDUCER 1,2,3 TRANSDUCERS CABLES CONTROL I iD2,# 3 A A BOX CONNECTOR D C =- ~ D0 EEXITATION A-C OUTPUT B-D BALANCE ADC B C CALIBRATION A-B DCDT ] C-D rd-A -— A rd rdlA A rd bkB Bbk bk B B bk I ci UTPUT D Figure TndcCae-Sm4 EXCITATION A B I OUTPUT D E i-t "^ g~ DEMODU- I OSCILLA- LATOR & TOR FILTER INPUT i T O RFILTER'OUTPUT iLr ____________________________ Figure B7. Transducer Cables - Schematic Diagrams.

-l7obkA -A A INPUT HIGH rd B B INPUT LOW C C-__ D D.~~a m-wt E E OUTPUT HIGH F F INPUTy A -- rd INPUT bk B B bk OUTPUT Y D D gn OUTPUT bk E — w _K K SHIELD bk L L GROUND Mn M M OUTPUT LOW DEVIATION AMPLIFIER CABLES NI N__ rd 0 0 IIOVAC NEUTRAL P -P_ Figure B8. Deviation Amplier Cables - Schematic Diagrams.

-17TbkA A r- - A d o bk B -B bk er —— ^ — ^ cbkB Blbk0 B~red 7, rdbkF A oa BATTERY# white Kt- wi D D bkEe A rd bkFATTe I Fbkt bk k G "~G n~G G bkFigure B9. Visicorder and Battery Cables - Schematic Diagrams. bkL I) bkM1- -L- I-MbkB B k 0 bk K ) — nK z co bk L L!- wt E' E bk bkN -M r VISICORDER CABLE BATTERY CABLE red rd A A rd BATTERY# I wie wtE B Bwt B red... C Crd m BATTERY#2 white tD Dw red r —-- ErdBATTERYf/3 white, Jwt F _G-,G ~ Figure B9. Visicorder and Battery Cables - Schematic Diagrams.

-1781B ^AL. BAL. I0 K~':35 K 6M o5K 1i mbk —----,E (red) S IbkEO (r XITATIO. 0 AM C- 20UTPUT - D, 4 5M,. BALANCE A-DD 0C ~ S+_Er <!A/ ^ "/NO L?^40R40M', - 6'rd 2.5M 6 — wt 9 )", I 2 OM VACB 5 CALIBRATION RESISTORS A rd ----------—'DFigure. Control x Schematic - Differential 2 ^ ^ 6M su 5K a.Tra r FINE COARSE BAL. \:BAL. E IOK 5 K 5 K 10 EXITATION A-C OUTPUT B- D BALANCE A-D-C o CALIBRATION A-B C-B Figure B10. Control Box Schematic - Differential Pressure Transducer Circuits.

-179nO6VAC o'. (white) 6 VAC Fii I A INPUT bk IB yDD 60 2bk or,Af d J- ^ 15 K 9 _K100 K2 63 80 T~301 K 4I 80 C0 bkif il P e T r Ciri 5L__ > IE 15Js K 6 120n| 42 K 49 2 y A 60 J ^ 100 K _\________INPUT bk80T C 012 -— ^ 10 6VAC'N. 0,) Figure Bll. Control Bo'x Schematic - Differential Pressure Transducer Circuits.

-1 80F E CONNECTOR 5 I — ~ —a. 1200t1 Rs3 __(red) 6VAC 600 ATTENUATION ----— 2 3 -I 230n RESISTORS A.rd, rBlbk t C t ~~ 7Z —^I M o 30) 1K cn E w5 150 uJ 3 3.6K 3 o 00R^ V 0-o -- 62 5 75K z N.. N.O. Rc363 35K -jK c lA sy_ —---— |- - 6VAC (white) < a B bk 4:r 450< Q B )- (red) V A og C- 6O I —---— VAC NR CONNECSISTOR 5 Figure B12 Control Box Schematic - Pressure Level and D(white) (Transducer Circu 1 ----- 6 VAC ATTENUATION o RESISTOR'3'-! 1 J I00 K o _ 0- 5350xt Ibk 4, Figure B12. Control Box Schematic - Pressure Level and Displacement Transducer Circuits.

-181Figures B13, B14, and B15 are the equivalent circuits for the transducers. For the differential pressure transducers, the relation between the transducer output, (% of total), AEo and the galvanometer deflection 6 is: AE, - I1 k+ls2+ fl+ 1 103 + Rsl 1 } Eo= {[a + 18.2(- + 1)(12s + 120 - +sv where K = f(V, Ra, Ri, G) (determined from calibration data) V = excitation voltage Ra = attenuation resistor Ri = amplifier input impedance G = amplifier gain Sv = galvanometer voltage sensitivity (in/mv) Si = galvanometer current sensitivity (in/ka) For this circuit, S. = (.125) 12000/12028.6 =.124703 (in/mv) and S,= _1(4.37) 12000. (28.6 + 136) 4.070098 (in/la) 12000 (28.6 + 119.6 + 18.2) + 28.6 (18.2 + 119.6) The relation between the transducer output E03 and the galvanometer deflection 6 for the pressure level transducer can be reduced to E03 = 100 K3 6/(9.24 V) % where K3 = f(Ra) (determined from calibration data) Ra = attenuation resistor V = excitation voltage (volts)

-182C{ N'I CT Q" I 0 0 c' E-H 0 0 N N 0o (( C:N~~~ C9~~pH 0 0 0rr t0 OI h0 _..

-183Ob~~~~~ rd U) CM~~~~~~~~~C 0> I i N — I I - I I~~~ ~v I_ SL ~~~~~~~~~C) C)) (U Cr U) In ~ ~ I 33 CO U)?-< -H 0r ~ I~~~~~~= g ^~~~~h ^ ^~~~~~~~r C)~~~ d~~~~~~~~P rr,~~~~~~~~~~(,r~~~~~~~~~~i ^ ~ o $ r~ ^

-i-84Ra Rg 65.4n 350-a Figure B15. Equivalent Circuit for Displacement Transducer.

-185For the displacement transducer, the relation between the core displacement and the galvanometer deflection is: d = K4 V 5 where: d = core displacement (inches) K4 = f(Ra) (determined from calibration data) Ra = attenuation resistor V = excitation voltage (volts) 6 = galvanometer deflection (inches) B.2,d. Visicorder Oscillograph A Honeywell visicorder oscillograph Model 906C was used to simultaneously record the signals from all for transducers. This model can record up to 14 channels of data at frequencies from DC up to 5000 cps. It contains a high-pressure mercury vapor light source, mirror galvanometers, timing light, an optical system and a paper transport system. Table B4 contains a summary of the galvanometer data.

-186TABLE B.4 GALVANOMETER INFORMATION Channel* 1 2 3 4 Galvanometer M40-120A M40-120A M40-350A M100-350 Nominal Undamped Natural Freq. (cps) 40 40 40 100 Flat Frequency 0-24 0-24 0-24 0-60 Response (cps) Required External Damping Resistance 120 120 350 350 (ohms) Nominal Coil Resistance (ohms) 28.6 28.6 61.o 65.4 Current Sensitivity (in/4a).125.125.243.158 Voltage Sensitivity (in/mv) 4.37 4.37 4.00 2.41 Channel Transducer 1 differential pressure 2 differential pressure 3 pressure level 4 displacement

APPENDIX C DATA REDUCTION COMPUTER PROGRAM C.1 Program Objectives This program was written to convert the raw experimental data to useful quantities such as test fluid pressure, pressure difference across the capillary, shear stress, shear rate, kinetic energy correction, Reynolds number, entrance length, and finally the viscosity. C.2 Program Description and Equations The first data card read into the computer was a remark card which could contain any comment punched between columns 1 and 72, inclusiveo This had to be the first data card and no additional comment cards were allowed. The second data card contained the capillary dimensions and transducer calibration data in the following manner. D =.xxxx, L x.xxxx, CALI(O) = x.x,xx, CALF(O) = x.xxx.xxx.xx where D and L were the capillary diameter and length respectively. The first two quantities in the CALI vector were the integers SS1 and CS1 which were the sensitivity and calibration switch positions for the differential pressure transducers. The third and fourth quantities in the CALI vector were the integers SS3 and CS3 which were the sensitivity and calibration switch positions for the pressure level transducer. The quantities in the CALF vector were the floating point numbers DEL1, DEL2, and DEL3 which were the calibration signals from the three pressure transducers. The computer used this information to calculate the transducer excitation voltage V3 and the coefficients K1 and K20 -187

-188The next data card was repeated for each data run until new calibration data was to be read. DATAI(O) = x,x,x, DATAF(O) = x.xx,x.xx,x.xx,x.xx,x.xx, -1.0w RUN NUMBER The variables in the DATAI vector were the integers SS1, SS3, and SS4, the sensitivity switch position for the displacement transducer. The variables in the DATAF vector were the floating point numbers DEL1, DEL2, DEL3, DEL4, TIME and CALDAT. The first four elements were the galvanometer deflections which represented the output signal of the various transducers. The fifth element, TIME, was the time interval in seconds, during which the displacement transducer signal, DEL4, was obtained. The last element in the DATAF vector, CALDAT, was a dummy variable which signaled whether or not the next data card contained calibration data. If new calibration was to be read, this variable was set equal to 1.0, otherwise it could be omitted from the list, or could contain any number less than zero. The fluid density RHO was also included in this list if the assumption of RHO = 50 lbm/ft3 was not sufficient. The last item on this card, RUN NUMBER, was any desired identification in columns 61 and 72, inclusive. After the calibration data had been used to calculate the necessary coefficients and the experimental data had been read, the computer calculated the desired quantities. First the pressure level, P3, was calculated. P3 = PRESS.(V3) (psi) The internal function PRESS used three variables to determine the

-189percent output of the pressure level transducer, E03. E03 = 100 * K3(SS3) * DEL3/(9.24 * V3) (%) This value was used with appropriate constants given by the manufacturer's calibration data to determine the pressure level, P3 - P3 = PI3 + DPDE3 * (E03 - EI3) (psi) The displacement of the translating piston, DISPL, was DISPL = SENS4(SS4) * V3 * DEL4 (in) The flow rate through the capillary was Q = PI *.49 * ~49/4. * DISPL/TIME (in3/sec) The average velocity in the capillary, V, was V Q/(PI * D * D/4.) (in/sec) The kinetic energy correction, KEC, was KEC = RHO * V * V/(32.2 * 144. * 144o) (psi) As mentioned previously, the program assumed a density RHO of 50 lbm/ft3 unless RHO was included in the input data. Next the pressure drop across the capillary was calculatedo The pressure levle determined the slope of the Pressure-Output curves for the differential pressure transducers. The output of each transducer, DE1 and DE2, was then calculated and finally the corrected pressure drop across the capillary, DELTAP.

-190DELTAP =.ABS. (DPDE1 * DE1 - DPDE2 * DE2) - KEC (psi) The pressure drop and capillary geometry were then used to determine the shear stress at the capillary wall. TAU = DELTAP/(4. * L/D) (psi) TAUDYN = 68950. * TAU (dyn/cm2) The Newtonian shear rate, or apparent shear rate, at the capillary wall was NSRATE = 32. * Q/(PI * D.P.3) (sec-1) Thus the apparent viscosity was VISC - TAU/NSRATE (Lbf.sec/in ) VISCP = 68950. * VISC (poise) The Reynolds number was REYN = RHO * V * D/VISC The Boussenesq relation was used to determine the ratio of entrance length —to capillary length. LEOL =.065 * REYN * D/L Then the results were printed. Finally, the next data card was read and the necessary calculations repeated.

-191C.3 MAD Symbol Definitions Symbol Definition CALDAT Dummy variable = 1.0 if next data card contains calibration data. Otherwise, it can be omitted. CALF Vector containing the floating point calibration data DEL1, DEL2, DEL3. CALI Vector containing the integer calibration data SS1, CS1, SS3, CS3. CS1 Position of calibration switch No. 1, input data. CS3 Position of calibration switch No. 3, input data. DATAF Vector containing the floating point input data DEL1, DEL2, DEL3, DEL4, TIME, CALDAT. DATAI Vector containing the integer input data SS1, SS3, SS4, DE1 Output of Pressure Transducer No. 1 (TO) DE2 Output of Pressure Transducer Noo 2 (%) DELl Deflection of Galvanometer No 1, Pressure Transducer No, 1 output signal. input data (in) DEL2 Deflection of Galvanometer No. 2, Pressure Transducer Noo 2 output signal input data (in) DEL3 Deflection of Galvanometer Noo 3, Pressure Transducer No. 3 output signal. input data (in) DEL4 Deflection of Galvanometer No. 4, Displacement Transducer output signal. input data (in) DELPC1 Vector containing calibration data for Pressure Transducer No. 1. DELPC2 Vector containing calibration data for Pressure Transducer No. 2. DELTAP Pressure drop across capillary. (psi) DISPL Displacement of transversing piston (inches) DPDE1 Slope of Pressure-Output curve for pressure transducer No. 1 (psi/%)

-192Symbol Definition DPDE2 Slope of Pressure-Output curve for pressure transducer No. 2 (psi/%) DPDE3 Slope of pressure-output curve for pressure transducer No. 3 (psi/%) D Capillary diameter, input data (inches) E3C Vector containing calibration data for pressure transducer No. 3 EI3 Output of pressure transducer No. 3 corresponding to pressure values on manufacturer's calibration data (%) E03 Calculated output of pressure transducer No. 3 (%) HEAD Vector used to contain information on remark card. Kl Quantity used to calculate DE1 K2 Quantity used to calculate DE K3 Vector containing coefficients for E03 calculation. KEC Kinetic Energy Correction (psi) LEOL Ratio of entrance length-to-capillary length. (in/in) L Capillary Length, input data (inches) NSRATE Newtonian shear rate at capillary wall (sec.-1) P3 Pressure Level (psi) PI3 Pressure values given on manufacturer's calibration data for pressure transducer No. 3. (psi) PI Program constant = 3.1415926 PUNCH Boolean variable = 1B if punched card output is desired. input data Ql Integer used for list TAUSAV Q2 Integer used for list VISAVE Q Volumetric flowrate (in3/sec.) REYN Reynolds Number

-193Symbol Definition RHO Fluid Density (lbm/ft3) RS1 Vector containing values of series resistors in pressure transducers No. 1 and No. 2 electrical circuit (ohms) RUN Vector containing identification in columns 60 through 72 inclusive SENS4 Vector containing coefficients for displacement transducer, SI1 Current sensitivities for galvanometers No. 1 and No. 2 (in/a) SS1 Position of sensitivity switch No. 1, input data SS3 Position of sensitivity switch No. 3, input data SV1 Voltage sensitivity of galvanometers No. 1 and No.2 (in/mv) 2 TAUDYN Wall shear stress (dyn/cm ) TAU Wall shear stress (psi) TAUSAV List contain values of TAUDYN TIME Time obtained from visicorder trace. (Sec) V3 Excitation voltage for pressure transducer No. 3 and displacement transducer (volts) VISAVE List containing values of VISCP VISCP Apparent viscosity (poises) VISC Apparent viscosity (lbf sec/in2) V Average fluid velocity in capillary (in/sec)

-194C.4 Program Listing.....HIGH PRESSURE VISCOSITY PROGRAM.. REFERENCES ON PARAMETER PI (3.1415S26),5Il(.124703), SV1(4.C700c8) EQUIVALENCE (CALF(0 ) OATAF(C ),DEL).(CALF( 1.DEL2) (CALF(2)I 1 DEL3),(DATAF(3),DEL4), (DATAF(4),TIME),(CATAF(5),CALDAT ) 1 (QlTAUSAV),(Q2,VISAVE),(DATAI(0),SS1) (DATAI(1 )SS3), (OATAI(2),SS4) DIMENSION CALF(2),DATAF(5),TAUSAV(300),VISAVE(300) INTEGER CALI(3) DATAI(2),PUN( 1) tQl1Q2SSl~SS3,SS4,CS1,CS3,HEAD(12 1 ) BOOLEAN PUNCH VECTOR VALUES RS1(1i)=301CCC *100000.,4200C. 5COC. VECTOR VALUES DELPC1( 1)13.2,26.5253.2,1C6..218.,432. VECTOR VALUES DELPC2( 1)=14.4,28.E,56.6,114.,222..443. VECTOR VALUES SENS4()1 =0.001398.0.03S353.026. C.00899,0.0C253. 1 C.C005 EO.CC629,0.004CE,C. C0128,0. C0C238 VECTOR VALUES E3C(1)=.86,3.3,6.83,1C.15,13.53,33.2 VECTOR VALUES K3(1)=8.65,5.42,3.50 2.25 *....INTERNAL FUNCTION, PRESSURE CALCULATICN..... INTERNAL FUNCTION PRESS.(\V) E03 = 100. *K3(SS3)*DEL3/(S.24*VV) WHENEVER EG3.GE.8C.6 E13=E0.6 PI3=6000C. DPDE3=2000C. / (OC.-80.6) OR WHENEVER EC3.GE.61.4 E13=61.4 P13=00OC. DPDE3=20000./(80.60-61.4C) OR WHENEVER E03.GE.41.5 EI3=41.9 PI3=4000C. DPDE3=20000./ (61.40-41.90) OR WHENEVER E03.GE.22.C5 EI3=22.05 PI3=2000C. DPDE3=2000C./(41.9C-22.05) OR WHENEVER E03.GE.11o.4 EI3=11.94 PI3=1000C. DPDE3=10GOC./(22.C5- 11594) OTHERWISE EI3=O.0 PI3=C.O DPDE3 = 10COO./11.94 END OF CONDITIONAL P3=PI3+PFDE3*( E.3-EI3) FUNCTION RETURN P3

-195 - END OF FUNCTICN RHO=50. SETEF. (PLOT) PUNCH=08 Ql=0 Q2=C READ FORMAT $12C6*$,HEAC(1)...HEAD(12) PRINT FORMAT $1HI,SO,12C6//*$,HEAD(1).. -EAC(12) *.. TRANSDUCER CALIBRATI C..........PRESSURE LEVEL TRANSOtCER (NC.3)..... NEWCAL READ DATA PUNCHD,L,CAL I(C)=SSI,CS1,SS3,CS3tCALF ()=D EL1, DEL2,DEL3* CAL AT=-1,0 SS1=CALI(0) CS1=CALI(1) SS3=CAL I (2) CS3=CAL I(3) V3 = 100.*K 3(SS3)*DEL3/( 9.24*E3C(CS3)).....DIFFERENTIAL PRESSURE TRANSDUCERS(NO.1 ANh 2)..... P3=PRESS.(V3) DEI ='0.001005 * DELPCI(CS1) DE2 = C.000967 * CELPC2(CS1) K1l=((RSI(SSI)4+18.2*(RS1(SS1S) /120.+1.) )*(.*C8333/SV1+ 1/SII1 )* I.C01 +(RS1(SS1)/120.+1.)/SV1) * DELl/DEl K2 = Kl * DEl/DELl * DEL2/DE2 PRINT FORMAT ENE.SS3,CS3,CtEL3 V3tSSltCSlCEL I DEL2,K1,K2,P3L, CD,L/D, 1 RHO.....VISCOSITY CALCULAT IChS..... NEWDAT LOOK AT FORMAT $S60,2C6*$,FtJh(C)RUN(1) READ DATA DATAI(0)=SS1,S S3SS44 DATAF(O)=DEL1,DEL2,DEL3, 1 3O DEL4,T IME, CALDAT* RUN NO. SS4 = DATAI(2) P3=PRESS. IV3) WHENEVER P3.GE.8000C. DPDE1=20COC./( S.95-7S.87) DPDE2=2000C. / (100.02-79.14) OR WHENEVER P3.GE.600CC. DPOE1=2000C./( 7S.E7-59.37) DPDE2=20000./(79. 14-59.15) OR WHENEVER P3.GE.4COCC. POE1=2000C./( 5S.37-39.12) DPDE2=2CCC. /(59.15-39.C3) OR WHENEVER P3.GE.200CC. OPDEl=20C00./(39.12-18.85) OPOE2=20CO0./( 39(.C2-1920) OR WHENEVER P3.GE.973C. DPDEl=10COC./ (18E.5-8.8C) DPDE2=10OC./( 19.20-9.53) OR WHENEVER P3.GE. 490C..ANC. P3.LE. 51C0. OPDE1=1 1*10030./ { 18.85-8.80 ) DPDE2=1.032*1OCCC. / 19.20-9.53)

-196OTHER ISE PRINT COMMENT $ DIFFERENTIAL PRESSURE TRANSCUCERS AR I E NCT CALIBRATED AT THIS LEVELS PRIN1 RESULTS P3 TRANSFER TC NEWCAT END OF CONDITIONAL DISPL = SENS 4SS4 *V3*DEL4 C=P *. 4S*.49/4.*0 ISPL/TIME NSRATE = 32.*C/(PI*C.P.3) V=Q/ (P I*DD/4. KEC=RHO*V*V/( 32.2*144.* 144) DE1=1.0/K1*( RS1(SSI)+18.2*(RSI(SS1)/120.*+.))*(.08333/SV1+ 1 1./SI )*.001+(RSI(SS1)/12C.+. )/SVI)*OELI DE2=1.0/K2*( (RSl(SSI)+18.2*(RSIlSSi)/120.*+. )*(*08333/SVlI+ 1 1./SI 1)*.001+(RS1(SS1)/12C.+1.)/SV1)*OEL2 DELTAP =.ABS.(DPOCEIDE1 - CPDE2*Dt:2)-KEC TAU=DELTAP/(4.*L/D) TAUOYN=68950. *TA SET LIST TO TAUSAV,300 SAVE DATA TAUCYN VI SC=TAU/NS RATE VISCP=66950.*\I SC SET LIST TO VISAVE,300 SAVE DATA VISCP REYN= fHC*V*C/ (VISC*32.2*144 *.144). LEOL=. 65*REYN*D/L PRINT FORMAT TWORUN(O),R UN(1) SS,l SS.SS4CAIAF( 0)..CATAF(3),TIME, I P3,VISCPTAUDYNNSRATE CELl AP KECV ISCTAUtREYNtLEOL WHENEVER PUNCHPUKNCh FCRIAWT THREERUN(O).RUN(1),VISCPTAUDYN, i NSRATE WHENEVER CALCAT.G.O.O,TRAhSFER TC NEWCAL TRANSFER TO NEWDAT PLOT PRINT CCMMENT $1$ EXECUTE SETPLT.(1,'TAUSAV(1),VISAVE(1),Cl,$*$S33,CRC ) PRINT COMMENT $ TAU IN DYNES/(Cl).P.2$ EXECUTE SYSTEM. VECTOR VALUES ORD=$ VISCOSITY IN POISE*$ VECTOR VALUES ONE=$S36,h*CALI RATIUN CATA*//S5 H*SS3*S2S H*CS3*S2 1 H*DEL3*S4,H*V3*S3,H*S SIS*2, H*CS1*S2,H*ELl*S2, H*DEL2*S4, 1 H*Kl*S7,H*K2*S8,H*P3*/S5,I2,S3,I2,S2,F5.2,SlF6.3,S2, 1 I2,S3,I2,S2,F5.2,S1,F5*.2 E9.3, ES.3, ElO.4///S36, 1 H*VISCOSITY DATA*//S12,h*L =*F6.3,S8,H*O =*,F5.3, S8,H*L/D = 1 *F6.1,S8,H*RHC =*F6.1////4$ VECTOR VALUES TWC=$S5,2CtS3,H*SS1*S3,H*SS3*S2,H*SS4*S3,H*DEL1*S3, 1 H*DEL2*S3,H*DEL3*S3tH*CEL4*53,H*TIME*/S20,I2,S4,I2,S4,I2, 1 S3,F5.2,S2,F5.2,S2tF5.2,S2 F5.*2S2,F6.2//S24,HtP3*,S5, 1 H*VISCP*,S6,H*TAUOYN**S 6,H*NSRATE*,S6, *OELTAP*/S19, 1 5 (E O4, S2 )//S23,H*KEC* S9 H*VI SC*,S8,H*TAU, S,H*REYN*, 1 SQ.H*LE/L*/S19,5(EIC.4,SP2////*$ VECTOR VALUES THREE=$2C6,3(S, E1O.4 )*$ END GF PROGRAM

-197C.5 Typical Input-Output DATA REDUCTION PROGRAM-INPUT DATA Card No. 1 ANY COMMENTS BETWEEN COLUMNS 1 AND 72 INCLUSIVE 2 PUNCH=1B.RHO=., = L., L=.,CALI(0)=,_ (SS1) (CS1) (SS3) (CS3) CALF(O)=, (DELl) (DEL2)'(DEL3) 3 DATAI(O)=,,,DATAF(0)=.,, *,, (SS1) (SS3) (SS) (DEL) (DEL2) (DEL3) (DEL2) (DL3)(DEL4) (TIM) CALDAT=1.0 (Col. 60-72 inclusive) if next card is new calibration data, otherwise omit. COMMENTS: Card #1: must be the first data card, no additional comment cards are allowed. This card is printed before any calculations are made. Card #2: if the previous card #3 contains CALDAT=1.0, only the CALI and CALF vectors need to be punched if other quantities are unchanged. Card #3: CALDAT=1.0 is included only when new calibration data are to be used. Then card #2 must be the next data card. Columns 61 to 72 inclusive can contain any comment. When CALDAT is omitted the next data card is also #3. If decimal points are omitted, the quantity is an integer. * An cannot be preceded by a comma.

-198SEPT. 18, 1967, FLUID A, CAPILLARY NO. 4, 100 F CALIBRATION DATA SS3 CS3 DEL3 V3 SS1 CS1 DELl OEL2 Kl K2 P3 4 5 3.43 6.173 4 3 4.30 4.35.137E+05.135E+05.1157E+05 VISCOSITY DATA L = 2.933 0 =.010 L/D = 280.0 RHO = 58.6 A4.10.1 SS1 SS3 SS4 DELl DEL2 DEL3 DEL4 TIME 4 4 10 -.79.65 2.97.59 40 P3 VISCP TAUDYN NSRATE DELTAP.9812E+04.3099E+00.1122E+04.3622E+04.1823E+02 KEC VISC TAU REYN LE/L.1973E-02.4494E-05.1628E-01.9700E+00.2252E-03 A4.10.2 SS1 SS3 SS4 DELl DEL2 DEL3 DEL4 TIME 4 4 9 -1.51 1.24 2.95.61 1.10 P3 VI SCP TAUDYN NSRATE DELTAP.9746E+04.2926E+00.2143E+04.7323E+04.3481E+02 KEC VISC TAU REYN LE/L.8069E-02.4244E-05.3108E-01.2077E+01.4821E-03 A4.10.3 SS1 SS3 SS4 DELI DEL2 DEL3 DEL4 TIME 4 4 9 -2.36 2.83 3.00.65.60 P3 VI SCP TAUDYN NSRATE OELTAP.9911E+04.2840E+00.4063E+04.1431E+05.6599E+02 KEC VISC TAU REYN LE/L.3079E-01.4119E-05.5892E-01.4181E+01.9706E-03

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