Abstract
Squeeze flow between parallel disks of a Newtonian fluid with variable viscosity is studied using a lubrication approximation. Analytical results are obtained for circumstances in which the viscosity distribution and instantaneous plate velocity and separation are specified. Equations describing the convection of viscosity and the time dependence of the plate separation are developed, although explicit solutions could not be obtained. Our analysis is extended to include two immiscible fluid layers, each having a different but uniform viscosity. As expected, all results reduce to the classical lubrication results for constant viscosity.
Similar content being viewed by others
References
Stephan J. and Sitzungber K., Versuche ber die scheinbare adhesion, Akad. Wiss. Math. Natur. Wien, 69(2), 713–735 (1874).
Scott J.R., Theory and application of the parallel-plate plastometer, part 2, Trans. Inst. Rubber Ind., 10, 418–493 (1935).
Leider P.J. and Bird R.B., Squeezing flow between parallel disks. I. Theoretical analysis, Ind. Eng. Chem., Fundamental, 13(4), 336–341 (1974).
McClelland M.A. and Finlayson B.A., Squeezing flow of highly viscous polymers, J. Rheol., 32(2), 101–133 (1988).
Phan-Thien N. and Low H.T., Squeeze-film flow of a viscoelastic fluid a lubrication model, J. Non-Newtonian Fluid Mech., 28(2), 129–148 (1988).
Winther G., Almdal K. and Kramer O., Determination of polymer melt viscosity by squeezing flow with constant plate velocity, J. Non-Newtonian Fluid Mech., 39(2), 119–136 (1991).
Sus D., Relaxations- und Normalspannungseffekte in der Quetschströmung, Rheol. Acta, 23(5), 489–496 (1984).
Oliver D.R., Influence of fluid inertia, viscosity and extra stress on the load bearing capacity of a squeeze film of oil, Appl. Sci. Res., 35(2–3), 217–235 (1979).
Gordon G.V. and Shaw M.T., Computer Programs for Rheologists (Hanser, Munich, 1994).
Dienes G.J. and Klemm H.F., Theory and application of the parallel plate plastometer, J. Appl. Phys., 17(6), 458–472 (1946).
Leider P.J., Squeezing flow between parallel disks. II. Experimental results, Ind. Eng. Chem, Fundamental, 13(4), 342–346 (1974).
Shaw M.T., Melt characterization of ultra high molecular-weight polyethylene using squeeze flow, Polym. Eng. Sci., 17(4), 266–268 (1977).
Kataoka T., Kitano T. and Nishimura T., Utility of parallel-plate plastometer for rheological study of filled polymer melts, Rheol. Acta, 17(6), 626–631 (1978).
Chatraei S. and Macosko C.W., Lubricated squeezing flow: A new biaxial extensional rheometer, J. Rheol., 25(4), 433–443 (1981).
Lee S.J., Denn M.M., Crochet M.J. and Metzner A.B., Compressive flow between parallel disks: I. Newtonian fluid with a transverse viscosity gradient, J. Non-Newtonian Fluid Mech., 10(1–2), 3–30 (1982).
Zhang W., Silvi N. and Vlachopoulos J., Modeling and experiments of squeezing flow of polymer melts, Int. Polymer Processing, 10(2), 155–164 (1995).
Papanastasiou A.C., Macosko C.W. and Scriven L.E., Analysis of lubricated squeezing flow, Int. J. Num. Meth. Fluids, 6(11), 819–839 (1986).
Laun H.M., Rady M. and Hassager O., Analytical solutions for squeeze flow with partial wall slip, J. Non-Newtonian FluidMech., 81(1–2), 1–15 (1999).
Mavrovouniotis, G.M. and Brenner H., A micromechanical investigation of interfacial transport processes: I. Interfacial conservation equations, Phil. Trans. Roy. Soc., A345(1675), 165–207 (1993).
Mavrovounitious G.M., Brenner H., Edwards D.A. and Ting L., A micromechanical investigation of interfacial transport processes: II. Interfacial constitutive equations, Phil. Trans. Roy. Soc., A345(1675) 209–228 (1993).
Edwards D.A., Brenner H. and Wasan D.T., Interfacial Transport Processes and Rheology (Butterworth-Heinemann, Boston, MA, 1991).
Anderson D.M., McFadden G.B. and Wheeler A.A., Diffuse interface methods in fluid mechanics, Ann. Rev. Fluid Mech., 30, 139–165 (1998).
Landau L.D. and Lifshitz E.M., Fluid Mechanics (Addison-Wesley, London, 1959).
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Gonzalez, L.A., Brenner, H. Squeeze flow of a nonconstant-viscosity fluid. Int J Adv Eng Sci Appl Math 1, 85–97 (2009). https://doi.org/10.1007/s12572-010-0005-8
Published:
Issue Date:
DOI: https://doi.org/10.1007/s12572-010-0005-8