The Squeezing of a Fluid Between Two Plates

[+] Author and Article Information
C.-Y. Wang

Department of Mathematics, Michigan State University, East Lansing, Mich.

J. Appl. Mech 43(4), 579-583 (Dec 01, 1976) (5 pages) doi:10.1115/1.3423935 History: Received September 01, 1975; Revised April 01, 1976; Online July 12, 2010


A viscous fluid lies between two parallel plates which are being squeezed or separated. If the normal velocity is proportional to (1 − αt)−1/2 the unsteady Navier-Stokes equations admit similarity solutions. The resulting nonlinear ordinary differential equation is governed by a parameter S which characterizes unsteadiness. Asymptotic solutions for small S and for large positive S are found which compare well with those obtained by numerical integration. It is found that the resistance is proportional to (1 − αt)−2 but is not necessarily opposite to the direction of motion.

Copyright © 1976 by ASME
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