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On the development of fluid trapping beneath deformable fluid-cell membranes

Published online by Cambridge University Press:  20 April 2006

Randall Wu  and
Sheldon Weinbaum
Randall Wu
Affiliation:
Department of Mechanical Engineering, The City College of The City University of New York, New York, NY 10031 Present address: Union Carbide Corporation, Bound Brook, New Jersey 08805.
Sheldon Weinbaum
Affiliation:
Department of Mechanical Engineering, The City College of The City University of New York, New York, NY 10031
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Abstract

A quantitative theoretical model is developed to describe the time-dependent draining of an initially uniform-thickness fluid squeeze film between an infinitely flexible membrane-bound fluid cell and a planar rigid surface or between two symmetrically loaded cells subject to impulsive loading. The solution of the coupled nonlinear membrane-fluid-film equations shows that two characteristic times and lengthscales are required to describe the membrane deformation and draining behaviour of the fluid film. The early-time behaviour is strikingly different from that predicted by elastohydrodynamic squeeze-film theory (Christensen 1962), where the local elastic deformation of the boundary is not controlled by membrane tension but is pro-portional to the local film pressure. While fluid trapping occurs in both cases, a bidirectional flow is set up during the early-time period in the membrane squeeze film owing to the establishment of an off-axis pressure maximum near the edge of the near-contact area. Fluid is driven radially inward, causing upwelling of the membrane in the central region, and driven radially outward near the edge of the contact area., causing this region to form a narrow fluid gap. After the narrow-edge region hasformed, the off-axis pressure maximum gradually disappears and is replaced by a pressure plateau in the interior and a radial outflow at all locations that is similar to the elasto-hydrodynamic squeeze film. The present problem is closely related to the fluid films studied by Hartland (1967, 1968, 1969), Jones & Wilson (1978) and others when a, small spherical particle or fluid droplet rises or settles under gravity towards a uniform-tension fluid-fluid interface. These studies have theoretically and experimentally examined the long-time drainage of the film after the narrow edge region has formed and the fluid-trapping phenomenon is established. The solutions to the initial-value problem described herein show how this asymptotic quasi-steady drainage state is reached.

A simple experiment has been constructed to confirm qualitatively the theoretically predicted short-time behaviour. Experimental photographs graphically illustrate the gradual thickening of the lubricating layer near the origin and the formation and draining of the edge region as predicted by the membrane squeeze-film theory.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 121 , August 1982 , pp. 315 - 343
Copyright
© 1982 Cambridge University Press

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