Bidimensional Fluid-Film Flows of Stokesian Fluids

[+] Author and Article Information
Patrick Bourgin

Laboratoire de Mécanique des Contacts, Institut National des Sciences Appliquées, Villeurbanne, France

Bernard Gay

Centre de Mathématiques, Institut National des Sciences Appliquées, Villeurbanne, France

J. of Lubrication Tech 104(2), 227-233 (Apr 01, 1982) (7 pages) doi:10.1115/1.3253185 History: Received March 06, 1980; Online November 13, 2009


The bidimensional flow equations of a Stokesian fluid are solved for the case of steady, incompressible, and laminar flow between two arbitrary moving surfaces separated by a small gap. The stress T22 and the shearing stress at one of the walls are coupled through nonlinear integro-differential equations, depending on the viscous function only. The form of this differential system is specified for the equations derived from the theory of phenomenological macrorheology, as developed by Reiner and Rivlin. The solution is proved to be unique under certain conditions and for adequate boundary conditions. An example is worked out in the particular case of one single non-Newtonian parameter. The problem is solved in two different ways, using an approximate analytic method and a numerical method. The conception of the latter allows to generalize it by introducing only slight modifications into the program.

Copyright © 1982 by ASME
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