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Stability of a Stokesian Fluid in Couette Flow

dc.contributor.authorGraebel, William Paulen_US
dc.date.accessioned2010-05-06T20:53:55Z
dc.date.available2010-05-06T20:53:55Z
dc.date.issued1961-03en_US
dc.identifier.citationGraebel, William P. (1961). "Stability of a Stokesian Fluid in Couette Flow." Physics of Fluids 4(3): 362-368. <http://hdl.handle.net/2027.42/69631>en_US
dc.identifier.urihttps://hdl.handle.net/2027.42/69631
dc.description.abstractThe stability of a Stokesian fluid (Reiner‐Rivlin fluid) in Couette motion is examined and shown to depend on the Taylor number as well as a further dimensionless parameter which is proportional to the coefficient of cross viscosity. The method of Chandrasekhar is used for small values of this parameter. It is found that for fluids with a positive coefficient of cross viscosity, the critical Taylor number can be appreciably smaller than for the corresponding flow of a Newtonian fluid.en_US
dc.format.extent3102 bytes
dc.format.extent473563 bytes
dc.format.mimetypetext/plain
dc.format.mimetypeapplication/pdf
dc.publisherThe American Institute of Physicsen_US
dc.rights© The American Institute of Physicsen_US
dc.titleStability of a Stokesian Fluid in Couette Flowen_US
dc.typeArticleen_US
dc.subject.hlbsecondlevelPhysicsen_US
dc.subject.hlbtoplevelScienceen_US
dc.description.peerreviewedPeer Revieweden_US
dc.contributor.affiliationumThe University of Michigan, Ann Arbor, Michiganen_US
dc.description.bitstreamurlhttp://deepblue.lib.umich.edu/bitstream/2027.42/69631/2/PFLDAS-4-3-362-1.pdf
dc.identifier.doi10.1063/1.1706334en_US
dc.identifier.sourcePhysics of Fluidsen_US
dc.identifier.citedreferenceSee, for instance, J. G. Oldroyd, Proc. Roy. Soc. (London) A200, 523 (1950); F. H. Garner and A. H. Nissan, Nature 158, 634 (1946); K. Weissenberg, Proc. 1st Intern. Rheological Congr. Amsterdam, I, 29, 46, 1948; ibid. II, 114; J. M. Burgers, Proc. Acad. Sci. Amsterdam 51, 787 (1948); M. Mooney, J. Colloid Sci. 6, 96 (1951), for various constitutive equations, all of which describe fluids exhibiting the normal stress effect described by K. Weissenberg, Nature 159, 310 (1947).en_US
dc.identifier.citedreferenceSee M. Reiner, Handbuch der Physik (Springer‐Verlag, Berlin, 1958), Vol. 6, p. 516, for a brief account of one such controversy.en_US
dc.identifier.citedreferenceM. Reiner, Am. J. Math. 67, 350 (1945).en_US
dc.identifier.citedreferenceJ. L. Ericksen, Quart. Appl. Math. 14, 318 (1956).en_US
dc.identifier.citedreferenceM. K. Jain, J. Sci. and Engr. Research 1, 195 (1957).en_US
dc.identifier.citedreferenceC. Truesdell, J. Ratl. Mech. Anal. 1, 125 (1952), credits Reiner (reference 3) with first stating this law. In deriving Eq. (1) Reiner assumes the stress tensor to be a polynomial in the rate of deformation tensor.The validity of this assumption was first shown by R. S. Rivlin [Proc. Roy. Soc. (London) A193, 260 (1948)], and later by J. Serrin, J. Math. and Mech. 8, 459 (1959), who assume that the stress components are arbitrary functions of the rate of deformation tensor.en_US
dc.identifier.citedreferenceC. Truesdell, reference 6.en_US
dc.identifier.citedreferenceRivlin, Truesdell, and Serrin (references 6) among others have previously presented the solution described in this section.en_US
dc.identifier.citedreferenceS. Chandrasekhar, Mathematika 1, 5 (1954).en_US
dc.owningcollnamePhysics, Department of


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