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.
The Squeezing of a Fluid Between Two Plates
Department of Mathematics, Michigan State University, East Lansing, Mich.
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Wang, C. (December 1, 1976). "The Squeezing of a Fluid Between Two Plates." ASME. J. Appl. Mech. December 1976; 43(4): 579–583. https://doi.org/10.1115/1.3423935
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