THE UNIVERSITY OF MICHIGAN INDUSTRY PROGRAM OF THE COLLEGE OF ENGINEERING COUPLED FLOW PHENOMENA IN CLAY-WATER SYSTEMS Donald Ho Gray November, 1966 IP- 736

COUPLED FLOW PHENOMENA IN CLAY-WATER SYSTEMS Donald H. Gray(l) Abstract A thermodynamic account is given of electrokinetic and thermal coupling phenomena. A theoretical equivalence between coupling phenomena (Onsager's principle) is discussed. This equivalence was investigated experimentally for the electrokinetic case and was shown to be generally valid in clay-water systems. This means that streaming potential data on clays can be used to predict their electro-osmotic behavior. The coupled flows of water, heat, and electricity in saturated clays were experimentally evaluated as the water content, exchange capacity, and pore water electrolyte concentration were systematically varied. A linear relationship was observed between the electro-osmotic water transport (in gallons/ampere-hr or moles/Faraday) and the logarithm of the water content. The clay-water systems exhibited characteristic thermoelectric and thermo-osmotic coupling effects. Thermoelectric currents on the order of 1-10 microamperes/~C/cm were measured. Thermo-osmotic pressures were detected, but their importance was secondary compared to electro-osmotic contributions to the flow of water in saturated clays. (1) Assistant Professor of Civil Engineering, University of Michigan, Ann Arbor, Michigan

INTRODUCTION Flows of matter or energy are usually described by simple laws which relate the fluxes directly to their conjugated driving forces. Darcy's and Ohm's Law are typical examples. The former describes the flow of water through the ground under a pressure gradient and the latter, the flow of electricity under an imposed voltage. Coupling or interference effects arise when a driving force of one kind gives rise to a flow of another. A thermocouple, for example, is a device in which an electrical current is induced by an applied temperature gradient. Other lesser known, but perhaps equally interesting coupling effects can also be cited, e.g., electro-osmosis, streaming potential, and diffusion potentials. Conventional flow processes and their coupling or interference effects are schematically illustrated in Table I. The driving forces are listed across the top, and the fluxes vertically down one side. The transport phenomena associated with various force-flux combinations are represented in a matrix in the middle. The diagonal terms running from the top left hand corner to the bottom right corner are the conjugated or conventional flow processes, described by Darcy's, Ohm's Law, etc. The off-diagonal terms are the coupling phenomena such as electro- and thermoosmosis. It is interesting to note from Table I that there are contributions to a given flux from sources other than the conjugated driving force. In many practical or short term applications coupling contributions to a given flux can reasonably be disregarded; in other cases, coupling properly should be taken into account. Consider for example the -1

-2TABLE I COUPLED FLOW PHENOMENA Force. Pressure Temperature Electric Chemical Flow | Gradient Gradient Field Gradient Fluid Darcy's thermo- electro- normal Flow Law osmosis osmosis osmosis hydraulic conductivity Heat isothermal Fourier's Peltier Dufour Flow heat Law effect effect transfer heat conductivity Current thermo- Ohm's diffusion Flow electricity Law and membrane electric potentials conductivity Ion streaming Soret electro- Fick's Flow current effect phoresis Law thermal diffusivity diffusion

-3situation in a geologic basin where thermal, electrical, hydrodynamic, and chemical gradients may co-exist. Coupling effects at first may seem insignificant, but over the immensity of geologic time the contribution of any one of these gradients to, let us say, fluid movement or salt accumulation in the basin may be important. Some specific instances or applications of coupling effects in the earth are worth citing. In electric logging work a so called'self potential' is generated by salt concentration differences between the drilling mud in a borehole and connate water in the surrounding formation. There may be a second contribution to this potential generated by the forced convection of drilling mud filtrate across the mud cake plastered on the walls of the borehole (this is known as a streaming potential). Thermo-electric potentials or currents can be induced if the reference electrode at the surface and the measuring electrodes in the borehole are at two different temperatures as a result of geothermal gradients. Shale formations can act as semi-permeable membranes and hence salt concentration differences across a shale member may produce large osmotic pressure differences. These osmotic pressures have been suggested (Berry and Hanshaw, 1960) as a possible cause of anomalous fluid pressures in the earth, i.e., deviations from the normal hydrostatic gradient with depth. Applied electrical gradients will cause a significant flow of water through certain soils, and this fact has been used successfully by engineers to dewater and stabilize water-logged ground (Cassagrande, 1953). Water movement associated with thermal gradients is important in ice lense formation and frost heaving. Thermo-osmosis has been observed and studied quite extensively in unsaturated soils; a system of particular interest to agronomists.

-4The present study deals with two such coupling phenomena, viz., electrokinetic and thermal coupling in clay-water-electrolyte systems. The experimental investigation reported herein was restricted to fully saturated, sodium clays. The clays varied from slurries to very stiff pastes. Highly consolidated, low water content clays with shale-like properties were not considered in the experimental study, although the same theoretical considerations should still apply. Thermal coupling and electrokinetic effects were experimentally evaluated in several clay-water systems as the exchange capacity, water content, and concentration of pore water electrolyte were systematically varied. Irreversible thermodynamics was used as a theoretical framework for the description of the coupled flows of matter and energy in the present study.

APPLICATION OF IRREVERSIBLE THERMODYNAMICS TO TRANSPORT PHENOMENA General The theory of irreversible or non-equilibrium thermodynamics is a convenient means of analyzing the simultaneous flows of water, heat, and electricity in porous media. A detailed account of the theory is outside the scope of the present paper; furthermore, the subject is treated in depth elsewhere in this symposium. Comprehensive treatises on the thermodynamics of irreversible processes have been written by Denbigh (1951), Prigogine (1961), Fitts (1962), and De Groot and Mazur (1962). These are directed, however, towards students of theoretical physics and chemistry. On the other hand, recent monographs by Katchalsky (1965) and Taylor (1963) deal not only with the fundamentals of the theory, but they also suggest practical applications of direct interest to the scientist or engineer. A unified treatment of mass transport in soils by a simple phenomenalogic approach was suggested quite early by Winterkorn (1947, 1955). He noted a fundamental similarity between osmosis, electro-osmosis, and thermo-osmosis, and suggested a generalization of the Darcy Law to include contributions to mass transport from electrical and thermal gradients. Simultaneous flows in soils have been investigated from a similar standpoint by Taylor and Cary (1960, 1964) and Taylor (1963). These authors reported experiments in which thermal, electrical, and salt concentration gradients were impressed across saturated samples of a silt loam. Each of these gradients caused moisture moisture movement through the soil and they also gave rise to other coupling effects. -5

-6Thermal Coupling Taylor and Cary (1964) have outlined a theoretical analysis based on the thermodynamics of irreversible processes for evaluating coupled flows of heat and water in continuous soil systems. Taylor (1963) also derived the following phenomenalogic equation for describing the simultaneous transfer of water and heat across a discontinuous system, viz., an inert membrane or porous soil plug. Jw = T (A4w)T + Lwq T Jq = (4'w)T + Lqq 2 (2) q T where Jw' Jq = the net fluxes of water and heat respectively Vtw = the specific chemical potential of water T = the absolute temperature L~ww Lqq = direct transfer coefficients, e.g., the hydraulic and Fourier heat conduction coefficients respectively LwqP Lqw = coupled transfer coefficients The following assumptions were made in the derivation of these equations: 1. There is only single component flow of matter, viz., pure water~ 2. The system is inert and no chemical reactions occur within it 3. External force fields are absent or cancel out. 4. The system is never too far from equilibrium, i.e., A4w < < RT and AT < < T. 5. Linearity exists between forces and fluxes.

-7The derived equations are in finite difference form, i.e., they have been integrated over the thickness of the membrane or porous soil plug. This is not as rigorous a formulation as is it when the phenomenalogic equations are left in differential form. In this latter case, the driving forces are usually expressed as gradients and the flows are defined only locally at a point within the system (Taylor and Cary, 1964). The finite difference form is probably more useful for experimental purposes. It assumes, however, that suitable'averages' can be found for the coefficients, Lik, and the temperature, T, within the temperature interval, AT, of interest. The chemical potential of water Abw can be evaluated from the Gibbs potential for water, viz., n w4 = - sw AT + vwzP + Z w _Ack (3) k=l Ck where sw, vw, and kw are the specific entropy, volume, and chemical potential of water; P is the pressure; and ck is the concentration of solute species'k'. However, for pure water at constant temperature, Ack = AT = 0 and Equation (3) simplifies to (A'w)T,ck = Vw P (4) Substitution of (n4w)T from Equation (4) into Equation (1) and (2) yields Jw = Lwwvw + Lwq AT T LswVw +q T (6) AT LqwvwAsP + L - (6)

-8Thus, Equation (5) states that the net flux of water is the sum of two transfer processes than can occur simultaneously. The first is the flow of water that is controlled by the pressure difference, AP, and the hydraulic conductivity of the soil; the second is the flow of water that is induced by a temperature difference, AT. These equations are in fact specific cases of a general relationship in irreversible thermodynamics, viz., the allowable superposition of contributions to a given flux from both conjugated and non-conjugated driving forces like. The principle of linear superposition and the forceflux relationships are expressed in mathematical shorthand by n Ji Z Lik Xk (i,k = 1,2,3... n) (7) k=l where the Ji, and, Xk, are generalized fluxes and forces respectively and the, Lik, are the phenomenalogic transport coefficients previously defined. When an external temperature gradient is applied across a soil plug the system eventually tends toward a steady state condition. If a counter osmotic pressure is allowed to build up in response to a thermally induced flow of water, the net flux of water will vanish at the steady state, i.e., Jw = 0. Under these boundary conditions Equation (5) may be written as ImP1 = Lwq Q*(8) AT| LVWT VT- (8) w 0 where Q* is the so called'heat of transfer'. Equation (8) indicates that the excess of pressure (the thermo-osmotic pressure) that will build up on the hot (or cold side) of a system in response to a unit temperature

-9difference, iAP/AT, depends on the heat of transfer, Q*, the specific volume of water, vw, and the average temperature of the system, T. The heat of transfer in turn is a function of the physical properties of a membrane or porous plug. In general Q* increases with decreasing pore size and increasing temperature. At present there are no a priori grounds for predicting the sign of Q*, in saturated systems, i.e., which direction the thermally induced flow of water will take. The exact mechanism of coupling between matter and heat flows is not well understood. The idea of an energetic separation, i.e., preferential passage of hot or cold molecules has been advanced by Spanner (1954). In unsaturated systems a net flow of water to the cold side has always been observed. This is understandable because of the dominant role of vapour phase transport which occurs towards the cold side. However, a simultaneous return flow of liquid water to the hot side has been observed in some cases (Krischer and Rohnalter, 1940; Taylor and Cavazza, 1954). In experiments with saturated systems using cellophane (Haas and Steinert, 1959) and silty soils (Taylor and Cary, 1960; Habib and Soeiro, 1957) a flow of water to the cold side has been reported. One of the purposes of the present study was to determine not only the magnitude of thermo-osmotic coupling in saturated clay-waterelectrolyte systems but also the direction. A clay-water system is much more complex because one is no longer dealing with an inert, single component system. Applied thermal gradients will now give rise to thermoelectric and secondary electro-osmotic effects. The possibility of thermally induced activity gradients in the pore water should also be

-10considered. Non-equilibrium thermodynamics provides a framework in which to consider all these possibilities, however, a theoretical treatment is omitted here. The interested reader is referred to an earlier study by Gray (1966). In the present paper only the results of experimental tests and a brief interpretation will be given. Phenomenalogic equations which describe thermo-electric coupling effects can likewise be derived (Katchalsky, 1965). Electrical effects associated with thermal gradients become important in charged membranes saturated with electrolyte solutions. Thermoelectric potentials on the order of 0.05 mv/deg0C have been reported by Ikeda (1958) for dilute KC1 solutions and a cation selective collodion membrane. The warmer side had a positive polarity. Thermoelectric potentials with a typical value of 0.3 mv/deg~C for sandstones and shales have been reported by Madden and Marshall (1959). They did not give the polarity of their potentials. Taylor and Cary (1960) and Habib and Soeiro (1957) also detected small currents in their thermal coupling experiments. However, neither of these latter investigators made provision for use of suitable electrodes nor were the test conditions well suited for the detection and evaluation of thermoelectric effects. Electrokinetic Coupling Electrokinetic processes in porous media can also be characterized by phenomenalogic equations. Lorenz (1952, 1953) and Goldshtein (1959) used this approach to describe electro-osmosis in clays under isothermal conditions. Both these investigators postulated that when transport of liquid and electric charge occur simultaneously, both processes combine

-11by simple addition in the following manner Jv = LWAP + LweAE (9) I = LewP + LeeAE (10) where JV = the total volume flux of solution I = electric current AP = pressure drop across membrane of plug ALE = voltage drop across membrane or plug Lik = the phenomenalogic transport coefficients Equations (9) and (10) allow a contribution to either the volume flux or electric current from both a hydraulic gradient and an electric field. Again these equations are but specific cases of the general phenomenalogic relationships stated earlier (Equation 7). Katchalsky (1965) has given a rigorous derivation of the phenomenalogic equations for electrokinetic processes. He starts by analyzing the individual, microscopic flows of anion, cations, and water across a membrane or porous plug. Katchalsky transforms his equations by writing them in terms of macroscopic flows of volume, current, and diffusion flux. This is a permissable and much more practical formulation for experimental purposes. In the classic electrokinetic case it is necessary to assume that no significant ion concentration gradients develop, and therefore that no osmotic counter pressure can develop. This is a critical assumption in the case of electro-osmosis experiments because the prolonged application of a high density D.C. current must inevitably cause electrolyte

-12accumulation on one side of a membrane and depletion on the other (Miller, 1955). Careful attention to experimental detail or at least an awareness of this complication is required to avoid misinterpretation of electro-osmosis data. High current density may also lead to instability in the phenomenalogic coefficients and non linear effects, particularly if the current tends to alter the fabric and flow geometry of the medium. The effect of an applied current on the hydraulic conductivity can be analyzed better by re-arranging Equation (9) is slightly different form. The single action coefficient, Lww, is defined when all forces except the pressure gradient are zero. However, the usual procedure when measuring hydraulic permeability is under open circuit conditions, viz I = 0, ALE / 0. In this case a more convenient phenomenalogic equation can be introduced for the volume flux, Jv ) in terms of a modified electro-osmotic coefficient, P, and a hydraulic filtration coefficient, K, measured under open electrical circuit conditions. Thus Jv KaP + I (11) where K = - P — L O (12) >P= I o ww Lee B Lew (13) I-1AP = 0 Lee Note that K and Lww are equal only if one of the coupling coefficients, Lew or Lwe, is zero. A graphical plot of the generalized flow Equation (11) is shown schematically in Figure 1. All plots are linear and are drawn with the same slope. A constant slope for different current intensities

-13Ld < o K 0 X PES -Z HYDRAULIC PRESSURE - P Figure 1. Graphical Representation of Equation (11) Showing Electrical Contribution to Volume Flow.

-14has an important physical significance, viz., that the passage of a D.C. current is not altering the flow geometry of the porous medium. Prolonged passage of a high intensity D.C. current in one direction will tend to cause physico-chemical changes, at least in a clay-water system, and thus produce non-linear effects. Effects such as these during electro-osmosis experiments in clays have been reported by Casagrande (1949), Goldshtein (1959), and Cambefort (1961). On the other hand, certain experimental precautions (to be outlined later) will eliminate these problems. Olsen (1965), for example, has established the validity of Equation 11 for a kalinite-water system over a wide range of water contents. A very interesting and useful equivalence can be derived for matter flowing in response to an applied electrical field and electric charge flowing in response to an applied pressure gradient. Saxen (1892) first established this relationship experimentally by observing an equivalence between electro-osmosis and streaming potential phenomena in clay diaphragms. This equivalence has subsequently become known as Saxen's Law. However, a much more general proof of Saxen's Law can be established from symmetry relations between coupling coefficients. Symmetry relations between coupling coefficients were derived by Onsager (1931) and they largely form the cornerstone of the modern theory of non-equilibrium thermodynamics. Onsager's fundamental theorem states that provided a proper choice is made of the fluxes, Ji, and forces, Xi, all the coefficients, Lik, with i j k must satisfy the equality Lik = Lki ( ik = 1,23,... n) (14)

-15The equalities expressed in Equation (14) form an important link between the various coupling phenomena. Miller (1960) has reviewed experimental verifications of Onsager's symmetry relations and has shown them to be valid for a wide class of coupling phenomena including electrokinetic coupling. Saxen's Law can thus be proved theoretically by applying Onsager's symmetry relations to the phenomenalogic equations describing electrokinetic phenomena. If the boundary conditions for a hypothetical electro-osmosis and streaming potential experiment are substituted in Equations (9) and (10), the following identities are obtained~ Case i) Streaming Potential Experiment (I = 0) LE Lwe ip I = 0 Lee Case ii) Electro-osmosis Experiment (ZP = 0) (Lx Ja Lewe (16) I ~ ZP = 0 Lee Saxen demonstrated experimentally that the terms on the left hand side of Equations (15) and (16) are equal to one another, i.e.o (sr) = -(JV) (17) 0I = ZIP= 0 However, this equivalence must also follow from the thermodynamic considerations if Onsager's symmetry condition is valid, i.e. if Lew = Lwe (18)

-16The practical utility of this equivalence can be demonstrated for the electrokinetic case. It means, for example, that existing streaming potential data could be used to predict electro-osmotic behavior. This is quite significant in view of the scarcity of extensive electro-osmosis data in clay-water-electrolyte systems and the difficulty in making an electro-osmotic measurement. Furthermore, considerable streaming potential data is already available. Olsen (1961), for example, has measured streaming potentials in homionic and natural clays over a wide range of water contents and external electrolyte concentrations. In principle his data can be used to predict electro-osmosis in clays providing, of course, that the Saxen relations are generally valid in clay-water systems. In practical units the Saxen relation (Equation 17) may be written as Moles of water = Milli volts x 54.5 (18) Faraday equivalent atmosphere This equivalence is examined further as part of the experimental investigation reported herein.

EXPERIMENTAL PROCEDURE General The effects of a systematic variation in certain key parameters on electrokinetic and thermal coupling processes in clay-water systems were studied. The parameters of special interest were the following: 1. Water content 2. Exchange capacity 3. Normality of the external electrolyte Other variables, such as the type of counter-ion and the degree of saturation, were held constant by restricting the investigation to fully saturated, sodium clays. A detailed account of the experimental procedure has been given by Gray (1966); salient features are summarized below. Materials and Apparatus Experimental data were obtained on three types of material: a pure kaolinite (Hydrite UF), and illitic clay (Grundite), and an artificial silty-clay comprised of equal parts by weight of kaolinite and silica flour. These clays and their properties are described in Table II. The clays were made as nearly homoionic to sodium ion as possible by washing batches of clay in concentrated solutions of sodium chloride. The excess salt was then removed by leaching the clays with distilled water. The clays were subsequently dried in an oven at 2300F, lightly pulverized, and stored in sealed jars for further use~ Weighed amounts of each clay were later mixed with the desired electrolyte -17

TABLE II PROPERTIES AND DESCRIPTION OF TEST MATERIALS Descriptive ExchangeO Name of Test Proprietery Size Specific Capacity Material Name Mineralogy Range Gravity Meq/100 gm Supplier Kaolinite Hydrite UF Kaolinite-100% < 2 Micron 2.63 3.8 Georgia Kaolin Co. Q llite - 55% Illinois Clay Kaol. - 10) Products Company Illitic clay Grundite Quartz - 20 <10 Micron 2.78 16.8 Mixed layer - 15 Silty clay None Kaol. - 50% < No. 325 2.65 2o1 Gopher State Silica Silica flour - Mesh Inc. (silica flour 50% only) Notes: 1. Based on X-ray diffraction analysis by Esrig (1964) 2. Fractionated portion of original material 3. Measured by Sanitary Engineering Research Lab., Univ. of Calif.

-19solution into thick slurries prior to their introduction into a specially constructed flow cell. The flow cell itself was designed so that known thermal, electrical, and hydraulic pressure gradients could be applied across the clay samples. Provisions were made to monitor the flows of electricity and water (or solution) that resulted from the application of any one of the gradients. In some cases, it was preferable to pass a known electric current across the system and monitor the voltage drop instead. This capability was provided by a constant current D.C. power supply. A schematic diagram of the test layout is shown in Figure 2 and a general view of the flow cell and test equipment, in Figure 3a. The flow cell was constructed entirely of lucite plastic; nylon fittings and plastic tubing were also used throughout. The sample chamber was cylindrical and had two retractable pistons with recessed porous stones at either end. A exploded view of the flow cell components is shown in Figure 3b. By placing the entire flow assembly in a loading frame as shown in Figure 3a it was possible to consolidate the clay samples and reduce their water content to predetermined levelso Internal heating and cooling coils were installed in the piston heads in order to establish a temperature gradient across the clay sample for thermal coupling tests. The heating and cooling coils in turn were connected to external constant temperature circulators. Temperatures were monitored with thermistor probes and a digital thermometer. The flow cell and test equipment were kept in a constant temperature room maintained at 200C.

CONDUCTIVITY PRESSURE SURE BRIDGE I Iz171 I II. NITROGEN I I HEATING 1 _-i -COOLIG H.P. AIR CYLINDER| CELL-E! - ~ %% / /! CONSTANT CURRENT 0 0 0 i D.C. POWER SUPPLY I I I DIGITAL CONSTANT THEROMETER CONSTANT TEMP. CIRC. TEM. CIRC.j Figure 2. Schematic Diagram of Flow Cell and Test Layout. Figure 2. Schematic Diagram~ of Flow Cell and Test Layout..

-21-. _: _ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~i Ei iii!ii ii inii: Xi i ls ii00iii _ 11 _ s | _ _................................::-:::"::::-:-:-:-~~~~~~~~~~~~~~~~~~~~~~~~~~~~............... t t | Y l l _ -........................................................ _ | ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~............. W.................................................................................................................... t Yt | Y S _ t -. | - - -. — ~~~~~~~~~............................ M, * 11 S | | _:~~~~~~~~ —------------------—: —------ gSS~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~j~~i:lSSSS Z it g- Y.. X X l 11-11 | | _ 1: _ l~ae~i X =E | E | | = = _ g l I ~~I Ill II II _IB I i |~~~ 1. 111-:_:: _1 assss (a) _|_e3 eea ndCoeU iwo Fo eladTs Equipent:

-22Electrokinetic experiments Four transport coefficients were determined in the electrokinetic experiments: the hydraulic permeability, electrical conductivity, electroosmotic coefficient, and the streaming potential coefficient. The last two are equivalent if Saxen's Law or the Onsager symmetry relations are valid. The hydraulic permeability, K, is the conventional filtration coefficient measured under open electrical circuit conditions (I = O). The electrical conductivity was measured under conditons of no hydraulic back pressure (ZlP = O). The electro-osmotic coefficient, (P), is defined in the present study as the water transport per unit charge, e.g. gallons per ampere-hr. or moles per Faraday. The hydraulic permeability was determined by measuring the flow rate through a sample under constant hydraulic head. The pressure drop across the clay sample was determined by monitoring the pressure in the solution at each end of the sample by means of an electrical pressure transducer. The electrical conductivity was measured by passing a known current through the sample from a constant current power source. Separate electrodes were used for application of current and measurement of voltage. Both sets of electrodes were silver-silver chloride; their preparation is described by Gray (1966). The applied currents were limited to a range between 10 and 1000 micro-amps. The current was always passed in two directions through the sample and an average taken of the resulting voltage drops. This procedure tended to cancel out any asymmetry potentials that might have been present. The voltage drops across the sample were measured with a Kiethley Model 610B electrometer which could be used as either a voltmeter or ammeter.

-23Streaming potentials were measured by applying a known hydraulic pressure and recording the electric potential generated across the sample. In order to successfully measure streaming potentials it was necessary to use a very high impedance voltmeter so as to avoid drawing down the voltage source. This requirement is especially critical when measuring very small streaming potentials (on the order of a few millivolts in sorm.e clay samples). The Kiethley electrometer adequately satisfied this requirement because it has an input resistance (if needed) of 1014 ohms. Electro-osmotic transport of water (or solution) was measured by applying a known current from the constant current power source across a clay plug and observing the resulting volume flow rate of solution. The flow rate was determined by timing the movement of an air bubble in a calibrated pipette which formed part of a closed loop between the solution compartments on either side of the clay sample. By-passing of water along the walls of the pipette was prevented by water-proofing the pipette with a commercial hydrophobing agent. This treatment also produced a sharp menicus at the air-water interface in the bubble. Much has been written (Miller, 1955; Cambefort, 1961) about the effects of a prolonged application of a D.C. current across a claywater system with respect to causing electrolysis, ion exchange, gas formation at the electrodes, physico-chemical alteration of the clays, heating, and the build up of concentration gradients across the clay plug. All of these effects were eliminated or suppressed to a negligible level in the present study by the precautions outlined below: a. Use of reversible silver-silver chloride current electrodes. b. Use of homoionic clays and a saturating solution with the same ion as the counter-ion

-24c. Lijitation of the current density to less than 35 microamps/ cm d. Systematic reversal of the current flow direction and limition of the duration of current flow in any one direction to less than 15 minutes. e. Stirring the solution on either side of the clay plug and use of relatively large volumes of solution to swamp concentration changes. Electro-osmosis was always measured by applying the current an equal time in opposite directions and taking an average of the two runs. This procedure cancelled out secondary apparatus effects and prevented accumulation of electrolyte on one side or the other. Because of the highly idealized testing conditions used the electro-osmotic flow rates represented upper bound or limiting values compared to those that would be observed in a field installation when such controls could not be used. Thermo-osmotic and thermo-electric tests Thermo-osmotic pressures were measured in lieu of osmotic flow rates; this procedure was adopted for experimental convenience. The standard procedure was to apply a temperature gradient across a clay sample and observe the build-up in pressure as indicated by the rise or drop of water level in standpipes on either side. The ends of the clay plug were electrically short circuited through an ammeter and the induced thermo-electric current recorded concurrently with the thermo-osmotic pressure. Upon applying a temperature gradient the water level quickly rose in the standpipes because of an initial thermometric expansion, but the two levels equalized because the standpipes were connected by an open

-25bypass valve. Periodic temperature readings were taken to determine how quickly the system approached a steady-state distribution. Five hours proved to be an adequate time interval for temperature stabilization. At the end of five hours, the bypass valve was closed and a temperature-induced pressure difference could develop across the clay plug. The pressure difference was directly proportional to the difference in water level in the two standpipes. The levels were read with the aid of a cathotometer. Periodic readings of the pressure difference were taken until an equilibrium pressure was reached. This was taken as the steady-state condition at which point the volume flow vanishes, Jv = O The pressure difference at this point was the thermo-osmotic pressure of interest. Simultaneous readings of the thermo-electric current were taken also. A continuous and characteristic plot of current vs. time for each clay-water system was obtained in this manner.

RESULTS Electrokinetic Coefficients Experimental electrokinetic coefficients for the clay-waterelectrolyte systems are tabulated in Tables III and IV. They include the hydraulic permeability, electrical conductivity, electro-osmotic transport, and streaming potential coefficient. Each of these coefficients was calculated from the slope of an experimental plot of'flux' vs. appropriate'force'. Typical plots for electro-osmotic transport and streaming potential are shown in Figures 4 and 5 for a kaolinite mixed with O.01N NaCl solution. Also shown in Tables III and IV is a comparison of measured electro-osmotic transport (Column'a') and the calculated equivalent electro-osmotic transport (Column'b'). The latter was calculated from the streaming potential data according to Saxen's Law (Equation 18). Thermo-osmotic and Thermo-electric Tests Steady state thermo-osmotic pressures and thermo-electric currents are tabulated in Table V. Also shown in Table V are the temperature gradient and the mean temperature in the samples after attainment of a steady state temperature distribution. A gradient of approximately 10C/cm and a mean temperature of about 260C were commonly observed. A typical thermo-osmotic pressure build up curve for kaolinite is shown in Figure 6. Steady state thermo-osmotic pressures are shown plotted vs. water content in Figure 7 for the various clay-water-electrolyte systems. Except in two instances, the pressure rise always occurred at the hot side. -26

TABLE III ELECTROKINETIC COEFFICIENTS IN CLAY - 10-3 N SODIUM CHLORIDE SYSTEMS* Test Water Streaming Electro-osmotic Equiv. ElectroNumber Sample Content Permeability Conductivity Potential Transport osmotic Transport** Ratio Percent cm/sec x 107 micromhos/cm mv/atmos moles H20/Faraday moles H20/Faraday b/a a b 1 Silty 50.1 6.55 54 -62.0 3440 3370.98 Clay 41.9 3.71 48 -56.2 3130 3060.98 32.0 1.81 41 -48.4 2620 2640 1.01 23.6 0.44 36 -36.0 1940 1960 1.01 19.3 N.R. N.R. N.R. 1740 2 Kaol. 65.4 6.57 -39.0 2410 2130.88 54.9 2.61 -3.0 2060 2020.98 44.4 0. 7- N.R. -31.5 1850 1720 9 3 34.4 0.34 -25.0 1420 1365.98 30.4 0.26 -21.8 1260 1190.94 3 Illi- 102.0 6.12 1100 - 6.2 410 338.82 tic 84.0 1.27 1110 - 5.1 268 227.85 Clay 59.1 0.27 760 N.R. 204 43.5 | 0.07 930 N.R. 148 37. 3 N.R. 860 - 1.9 120 104.88 Notes: * Experimental coefficients measured at 20~C Calculated from Saxen's Law (Equation 18) N.R. - Not Recorded

TABLE IV ELECTROKINETIC COEFFICIENTS IN CLAY - 10-2 N SODIUM CHLORIDE SYSTEMS* Test Water Streaming Electro-osmotic Equiv. ElectroNumber Sample Content Permeability Conductivity Potential Transport osmotic Transport** Ratio Percent |cm/sec x 107 micromhos/cm mv/atmos moles H20/Faraday moles H20/Faraday b/a a b 4 Silty 74.0 N.R. 497 - 6.7 350 365 1.04 Clay 51.0 11.6 408 - 6.4 325 348 1.07 41.4 N.R. 334 - 6.1 320 332 1.04 32.0 2.31 257 - 5.9 310 332 1.04 26.0 N.R. N.R. - 5.7 305 310 1.02 5 Kaol. 73.7 9 7 602 -14.8 825 806 o.98' 61.7 4.85 563 -13.3 766 725.95 52.2 1.52 504 -12.6 707 686.97 42.7 0.83 436 -12.0 653 654 1.00 33.3 0.39 N.R. -10.1 568 550 0.97 6 Illi- 98.0 N.R. 1810 - 3.06 214 167 0. 8 tic 78.6 1.49 1630 - 2.82 161 154.96 Clay 67.0 N.R. 1400 - 2.60 145 141.97 56.6 0.34 1560 130 43.7 N.R. N.R. - 1.70 107 93.87 Notes: Experimental coefficients measured at 200~C Calculated from Saxen's Law (Equation 18) N.R. - Not Recorded

TABLE V STEADY STATE THERMO-OSMOTIC AND THERMO-ELECTRIC DATA IN CLAY-WATER-ELECTROLYTE SYSTEMS Thermo-2 Thermo-1 Electric Water Osmotic Current Temp. Mean Test Content Pressure Mdicroanp s Grad. Temp. Number Sample Permeant cm H120/0C per OC/cm OC/cm 0( 1 Silty Clay 64.0 1.4 1.5 0.99 26. 41:7.10 1.05 0.92 26.5 33.0.15 0.90* 0.98 26.8 24.4.18 0.85 0.96 27.2 Kaolinite 54.9.20 2.10.92 25.8 8 34.4.46 1.65 1.08 26.1 30.4.51 1.60 1.08 26.8 3 Illitic Clay 84.0.05 2.95 1.00 26.3 59.1 -.18 2.75* 1.03 26.0 43.5 -.08 2.65 1.00 26.1 4 Silty Clay 51.0.03 2.60* 0.94 27.5 31.9.05 2.40 1.04 27.3 5 Koalinite ( 73.7.08 3.85 0.95 26.0 52.2.12 3.45 0.97 26.4 42.7.16 3.20 o.96 26.2 1~~~~~~~~ Notes: Negative sign indicates pressure rise at cold side 2 Polarity: hot side positive * Estimated by interpolation

1.44 1.2 0 O K WATER CONTENT - % C.) I.W COV 0 -J f;.8,~ LL.6 1 C.) cr HI ~ 102 N NaCI W ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ W.2 APPLIED CURRENT - MICROAMPS Figure 4. Electro-osmotic Flow Rate vs. Aplied Currc~ in Kaclinite. u~~~~~~~~~~~~~~~~pie.ure - alii

-31-16 I/A, A) -12 ~WATER CONTENT- ON -12 _3 0 - 10 -8 0 -' 6 z nTEST NO. 5 KAOLINITE ~~~-2 g~~I-0- N NaCI -2 0.5 1.0 1.5 2.0 2.5 PRESSURE DROP ACROSS SAMPLE- KG/SQCM Figure 5. Streaming Potential vs. Pressure in Kaolinite.

~~~-.7 1. V..'... —'7 1.2 26v E I I 0.0 Z.8 2 bJ 24w 0~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~. 0'.4.4222, U) 0 ~AMBIENT TEMP -- 20 0 I.. co Cn w 0:.4 - 0.. PRESSURE 3~ - EQUALIZED TER CONTENT ]4.4 % 0 ~ ~ ~ ~ ~ ~ ~~~~~~~~~~~~~~SATURATING SOLUTION:.00 N NoCI (FLOW TO HOT SIDE) 0'o20 a.1w z:I I0 0 2 4 6 8 10 12 14 16 18 20 22 24 ELAPSED TIME - HRS Figure 6. Thermo-osmotic Pressure Build Up in Kaolinite.

" HOT EXTERNAL.7 SYMBOL SAMPLE ELCTROLYTE I-""'____ CONC.-NORMALITY 0 SILTY CLAY.001 S KAOLINITE.001 O.5 V7 ILLITIC CLAY.001 m|* ~ SILTY CLAY.01 i,.;4 - KAOLINITE.01 (/) C). 0 0 -1 2 w -.2 COLD I I I I I I 0 10 20 30 40 50 60 70 80 90 100 WATER CONTENT - PER CENT Figure 7. Thermo-osmotic Pressure vs. Water Content in Clay-Water Electrolyte Systems.

61 KAOLINITE Or) Cn a, 0.01 N NoCI 24 --:> +CONTENT ~;' -- ---— <9 —-----?~~~~~3.7r- -~ ~~~~~~ L l~~, l"" - l.-O-l-lsl. l o 24 I- z ELAPSED TIME — HRS Fizure 8. lmnermo Electric Current vs. Time in Kaolinite for Various Water Content s and rNormality of Saturating Solution. Average Tenrperature Gradient is 1~C/cm. a:: /AER CONTEN % n,' +.+~ r,)2,.44 +.~~~~~~~~~~~~~001 N NaCl LU 0 2 ~4 6 8 I 0 12 14 16 18 20 22 2 ELAPSED TIME -- HIRS Figure 8. Tem lcrcCretv.Tm nKoiiefrVrosWtrCnet n omaiyo Saturating Solution. Average Temperature Gradient is l~C/cm.

6 SATURATING SOLUTION: 10 N NaCI W"a 5 - ~~~~~~~~~AVE.TEMP. GRADIENT I C/cm 4,. I ILLITIC CLAY KAOLINITE O 0 28 10 12 14 16 1:-:2' 0 4 -,8 6~-?ELAPSED TIME- HRS Figure 9. Comparison of Thermo Electric Curve Envelopes for Three Clays. =.:~Fi ur.........

-36Typical thermo-electric behavior of the clay-water systems is shown in Figures 8 and 9. The induced thermo-electric current is shown plotted as a function of time for various water contents and pore water electrolyte concentrations in Figure 8. The electric current flow was always from hot to cold, i.e., the hot side had the more positive polarity The current tended to increase as either the salinity of the saturating solution or the water content was increased. A comparison of the thermoelectric behavior of the three clay systems is shown by a plot of thermoelectric curve envelopes in Figure 9. For a given saturating solution and temperature gradient, the thermo-electric current increased with increasing exchange capacity of the clay. Linearity between Forces and Fluxes Of considerable interest in this investigation was whether application of a D.C. current or a hydraulic gradient might give nonlinear relationships between forces and fluxes. However, linearity of plots was excellent in nearly ail cases as shown typically in Figures 4 and 5. Miller (1955) and Cambefort (1961) have aptly described difficulties associated with prolonged electro-osmosis experiments. The intent here is not to minimize the difficulties, but merely to show that reasonable precaution and attention to experimental detail lead to consistent linear results. Validity of Saxen's Law Saxen's Law was tested over a wide range of water contents - from slurry to solid paste - for several clay-water-electrolyte systems. The results are summarized in the last columns of Tables III and IV.

-37The equivalence holds quite well in the silty clay and kaolinite but not so well in the illitic clay. In the latter case, however, the deviation occurred mainly at the higher water contents where the clay was still in a slurry form and hence its fabric was more subject to distortion under an applied electrical or hydraulic potential. Olsen (1965) has recently investigated Saxen's relation in sodium kaolinite consolidated over a range of pressures from 05 to 200 kg per sq cm (corresponding roughly to water contents ranging from 60 to 15 per cent). He not only found that the electrokinetic fluxes and forces were strictly linear but also that Saxen's relation was obeyed with a less than one per cent deviation. It thus appears that Saxen's Law is valid in clay-water systems under a wide range of conditions. This means that existing streaming potential data can be used to predict electro-osmosis. Electro-osmotic Transport vs. Water Content Relationship Analysis of existing data revealed an interesting relationship between electro-osmotic transport and water content. This relationship is graphically portrayed in Figures 10-14. Olsen's (1961) streaming potential data on sodium clays was converted to its equivalent electroosmosis form and used to plot these curves. Ballou's (,955) electroosmosis data on sodium kaolinite and Carr's (1962) data on a collodion membrane are also shown for comparison purposes. The consistent parabolic shape of the curves in Figures 10 and 11 suggest a relationship between electro-osmotic water transport and water content of the form W = b(u) (19) /~/

-38where W = electro-osmotic water transport, moles per Faraday w = water content, weight fraction of water b,m = arbitrary constants If a relationship of the form shown in Equation (19) does exist, then the curves in Figures 10 and 11 should plot as straight lines in logarithmic co-ordinates. Such a plot is shown in Figures 12 and 13 for Olsen's, Ballou's and Carr's data. Electro-osmosis data from the present study is shown plotted in this form in Figure 14. Good linearity of plots is shown in nearly all cases. In order to make the relationship given in Equation (19) more useful it would be desirable to relate the arbitrary constants'b' and tmi' to fundamental, easily measured properties of the clay-water-electrolyte system. The constant'b' is the ordinate intercept and'm' is the slope of the curves in Figures 12-14. A preliminary correlation between these two constants and the exchange capacity and concentration of the external electrolyte was attempted by Gray (1966). However, additional experimental work is required to test and establish the working limits of such a correlation.

-394000 SODIUM KAOLINITE N4 NoCI r' L 3000 X Lu C,) LLu n 0 r o 2000 SODIUM KAOLINITE CZ x / NIO3 NNaCI cn X x SODIUM KAOLINITE /4.0X10-3N NaCI o 1000- (BALLOU'S DATA) o/ SODIUM ILLITE I- 10-N NoCI I 0 >~o w SODIUM ILLITE KAOL.-160N NoCI 0 0 10 20 30 40 50 60 70 WATER CONTENT — PER CENT Figure 10. Electro-osmotic Water Transport vs. Water Content for Homoionic Kaolinite and Illite Clays at Various Concentrations of External Electrolyte. (Derived from Streaming Potential Data: Olsen, 1961)

100 90 cr I 80 o cr a. c) w 70 F 60:! DX 60 0 50 0 30 (fe 0,0 U.J POLYSTYRENE SULPHONIC ACID WATER COLLODINTENT - PERCENTLiC Illite Clay and a Polystyrene Collodion Membrane I 0 0 30 20 30 40 50 60 70 Fiue1.EetoomtcWtrTasotv.WtrConet,) Sdu 0 ~~~~Ilt lyadaPlytrn oldo ebae

-S l] - 5000 / 4000 3000 )2500 / o~ 0 2000 SODIUM KAOLINITE 0 W 1500 ( 10'4 N Na CI H i 5 N Na CI / 00oo0 * BALLOU'S (1955) 5 900 0 ELECTRO-OSMOSIS -~=E~~~~~~~~~~,~~DATA 800 700 - 600 0 500 i 0 400 0 Olsen, 1961) rlr" SSODIUM ILLITE U 250 10- N NoCl 200 -l I0 20 30 40 50 60 80 I00 WATER CONTENT - PER CENT Olsen, 1961 )

-42200 150 SODIUM ILLITE /0 10-4N NaCI 0 I'0 IN NaCI 1o00 (derived from streaming g 90O potential data: OLsen,196) 8070 J 60130 | / 0 (30-Ni -25 0 100 30 4 5 O LiCL r (electro- -osmosis data: Carr, 1962) 0 w 10 10 20 30 40 50 60 80 100 WATER CONTENT- PERCENT Figure 13. Electro-osmotic Water Transport vs. Water Content for an Illite Clay and a Cationic Collodion Membrane, Plotted in Logarithmic Co-ordinates.

-435000 4000 - J cy/O 3000 - SILTY CLAY 2500 - OI 13 N NoCl. 1500 -N 23 2000: 800 /KAOLINITE c 3 2 15700 10I N NaC 1- ~ 0 1500 I-f 200 SI0ITY CLAY E / NaC lNC 900 800 KAOLINITE o -2 50 7oo 10 N N NaCI 600 7 j 7 8 o 500 0- 40 S IL oiTY CLAY [ -20 I 10 N NaCe 00I H(~1 ILLITIC CLAY ~ 200N NaCNC,50 ~J 10 20 30 40 50 60 80 100 WATER CONTENT- PERCENT Figure 14. Electro-osmotic Flow vs. Water Content in Clay-WaterElectrolyte Systems, Plotted in Logarithmic Co-ordinates.

DISCUSSION AND CONCLUSIONS Electrokinetic Coupling The results of this study suggest that electrokinetic processes are controlled mainly by the exchange capacity, the water content, and the concentration of the external electrolyte. A more detailed analysis by Gray (1966) showed that electro-osmosis depends fundamentally on ion distribution and ion selectivity within a porous mass. This dependency can be explained by a general thermodynamic analysis - without involving the kinetic models of Schmid (1951) and Helmholtz (1879). An interesting relationship between electro-osmotic transport and water content was also observed. This relationship is empirical, but none the less quite remarkable considering its universality, i.e., the wide variety of test data from independent sources and different materials which it fits. Thermal Coupling Whereas the contribution to hydraulic flow from an applied electrical gradient may be considerable, the same cannot be said of thermal gradients in saturated soils. An analysis by Gray (1966) showed that a temperature gradient of at least 20C/cm would be required under the most favorable circumstances to produce the same hydraulic flow as a unit hydraulic gradient. Naturally occurring temperature gradients of 2~C/cm in the earth are non existent. This would require, for example, a temperature difference of 2000C over a distance one meter. Natural geothermal gradients in the earth rarely exceed 3~C per 100 feet; one of largest -44

-45natural geothermal gradients ever observed is approximately 6~C per 100 geet - the Salton Sea geothermal anomaly, Imperial Valley, California. The thermal coupling phenomenon of greater practical significance is probably the thermo-electric one. Thermo-electric currents on the order of 1-10 micro amps per ~C/cm were detected in the clay-water systems. The thermo-electric currents varied in a consistent manner with the water content, exchange capacity, and salinity of the pore water. These currents possibly are significant in electric logging work. They may also contribute to corrosion problems in the ground when a metal casing traverses a geothermal gradient or when metal sheeting surrounds a buried thermal source.

SUMMARY Coupling effects arise when a thermodynamic force of one kind induces a flow of another. The forced convection of water through a porous medium, for example, may also cause transfer of electric charge (because ions are carried along in the pore water) which in turn manifests itself as a streaming current or electric potential. Alternatively, an electric field applied across a porous medium will induce not only a flow of ions in the pore water (normal electrolytic conduction) but also a flow of water due to the drag exerted by the ions on the water molecules. If the number of cations exceeds the number of anions in the pores (the usual case for negatively charged media, e.g., clays and soils), then a proportionately greater drag will be exerted on the water by the cationso Hence, there will be a net flow of water to the cathode in negatively charged media. This phenomenon is known as electro-osmosis; it has been used successfully to dewater and stabilize saturated clays. Other types of coupling also play an important role in the geologic environment. Temperature and salt concentration gradients across a shale member, for example, may give rise to interesting osmotic and electrical effects. Conventional flow processes and the various coupling effects are summarized in Table I. In the present study both electrokinetic and thermal coupling phenomena in clays were investigated. Equations based on irreversible thermodynamics were presented which relate the contributions to a given flux, e.g., volume flow, electric current, or heat flow, from various thermodynamic driving forces, viz., pressure, temperature, and voltage.

-47A theoretical equivalence between coupling coefficients (Onsager's principle) was discussed. This equivalence was investigated experimentally for the electrokinetic case and was shown to be valid in claywater systems under a wide range of conditions. This means, in effect, that streaming potential data on clay-water systems can also be used to predict the electro-osmotic response of these same systemso The coupled flows of water, heat, and electricity in saturated clays were experimentally evaluated as the exchange capacity, water content, and concentration of the pore water electrolyte were systematically varied. A linear relationship was observed between electro-osmotic water transport and the logarithm of the water content for a given exchange capacity and external electrolyte concentration. This relationship was valid for both clay-water systems and a collodion membraneo Measureable thermoelectric currents on the order of a few micro amperes/~C/cm were detected in the clay-water systems. The thermoelectric current increased consistently with increasing exchange capacity, water content, or external electrolyte concentration. The warmer side always had a more positive polarity. Thermo-osmotic effects in saturated claywater systems were also detected, but they were insignificant compared to electro-osmotic contributions to the flow of water in clayso

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