Two-Dimensional Analysis of an Elastic Layer Coupled to a Viscous Fluid

Abstract

A two-dimensional elastohydrodynamic analysis is performed on a system consisting of a viscous fluid flowing between a sliding soft layer of finite thickness and a tilted flat plate. The behavior of a soft layer subject to a distributed contact pressure is described in detail. Green’s functions are obtained for each Fourier coefficient of the distributed applied pressure, utilizing the additive property of linear elasticity theory. The resulting equations are numerically evaluated for some typical cases. As a function of the contact dimension, calculations are performed for the critical thickness of the layer beyond which the deformed shape essentially resembles that of the layer having an infinite thickness, in the case of a uniformly applied pressure. We also investigate the effect of layer thickness on the hydrodynamics, which illustrates that conditions in which the infinite half-space assumptions can be justified are highly limited. The findings of this paper have direct application to the modeling of chemical mechanical planarization (CMP).