A theoretical study is made of the flow behavior of thin Newtonian liquid films being “squeezed” between two flat plates. Solutions to the problem are obtained by using a numerical method, which is found to be stable for all Reynolds numbers, aspect ratios, and grid sizes tested. Particular emphasis is placed on including in the analysis the inertial terms in the Navier-Stokes equations. Comparison of results from the numerical calculation with those from Ishizawa's perturbation solution is made. For the conditions considered here, it is found that the perturbation series is divergent, and that in general one must use a numerical technique to solve this problem.

Squeezing flows of Newtonian liquid films - An analysis including fluid inertia

http://www.ece.uvic.ca/~bctill/papers/numacoust/Beltman_1999a.pdf

Viscothermal wave propagation including acousto-elastic interaction, part I: theory

This research deals with pressure waves in a gas trapped in thin layers or narrow tubes. In these cases viscous and thermal effects can have a significant effect on the propagation of waves. This so-called viscothermal wave propagation is governed by a number of dimensionless parameters. The two most important parameters are the shear wave number and the reduced frequency.

/pdf/viscothermal-wave-propagation-including-acousto-elastic-2pctv9cmef.pdf

Viscothermal wave propagation, including acousto‐elastic interaction

We study the motion which results when a fluid film is squeezed between two parallel plane surfaces in relative motion. Particular attention is given to the special case where one surface is fixed and the other is rapidly accelerated from a state of rest to a state of uniform motion. The analysis is based in part on linear theory and in substance on a finite-difference analysis of the full nonlinear equations of motion.

https://www.cambridge.org/core/services/aop-cambridge-core/content/view/C40828879233D7265590FD7528F06E76/S0022112081000980a.pdf/div-class-title-a-fluid-film-squeezed-between-two-parallel-plane-surfaces-div.pdf

A fluid film squeezed between two parallel plane surfaces

http://iopscience.iop.org/article/10.1016/0169-5983(96)00002-0/pdf

R. M. Terrill

Papers

The Flow Between Two Parallel Circular Disks, One of Which is Subject to a Normal Sinusoidal Oscillation