An Analysis of the Flow of a Viscoelastic Fluid Between Arbitrary Two-Dimensional Surfaces Subject to Normal High Frequency Oscillations

Abstract

An analytic solution is presented for the flow of a viscoelastic fluid between arbitrary but sufficiently smooth two-dimensional surfaces, one of which is subjected to small high frequency oscillations normal to the other. The results are presented in terms of the complex viscosity parameters of linear viscoelasticity, and are valid for any simple viscoelastic fluid, provided the oscillation amplitude is sufficiently small. Fluid inertia effects are included although convective inertia terms are shown to be negligible through order-of-magnitude considerations. The resulting linearized equations of motion can be solved through conventional means by techniques established in earlier works. Solutions for the velocity field, pressure distribution, and load are presented in terms of the Reynolds and Deborah numbers. Two illustrative cases are demonstrated—the tapered thrust bearing and the partial journal bearing. Unusual resonance effects in pressure and load are exhibited as the oscillation frequency (or Reynolds number) is increased for a particular fluid.