Analysis of slip of a Newtonian fluid applied to a torsional ultrasonic oscillator

A rigorous analysis of slip-dependent damping for an ultrasonic torsional composite oscillator is presented. This versatile experimental system has recently been used to measure surface slip of a Newtonian fluid. Initially, the phenomenon of finite surface slip and the slip length is considered for a half-space of Newtonian fluid in contact with a smooth, oscillating solid surface. Definitions are revisited and clarified in light of previous inconsistencies in the literature. We point out that, in general oscillating flows, the slip length is a complex number. An intuitive and versatile velocity discontinuity parameter of unrestricted phase is used to describe the effect of slip on measurement of viscous shear damping. The analysis is applied to the composite oscillator and the interpretation of experimental slip measurements is reviewed.