Measurement of Newtonian fluid slip using a torsional ultrasonic oscillator

TL;DR

This study uses a torsional ultrasonic oscillator to measure slip in Newtonian fluids at smooth surfaces, clarifying slip length definitions and verifying non-slip conditions with experimental data.

Contribution

It introduces a rigorous analysis of slip-dependent damping in oscillating flows and applies it to experimental measurements of slip length at a solid-liquid interface.

Findings

Non-slip boundary condition verified within ~60 nm for hydrophobic water surface

Slip length b is generally a complex number in oscillating flows

Experimental measurements conducted at shear rates up to 6800 /s

Abstract

The composite torsional ultrasonic oscillator, a versatile experimental system, can be used to investigate slip of Newtonian fluid at a smooth surface. A rigorous analysis of slip-dependent damping for the oscillator is presented. Initially, the phenomenon of finite surface slip and the slip length are considered for a half-space of Newtonian fluid in contact with a smooth, oscillating solid surface. Definitions are revisited and clarified in light of inconsistencies in the literature. We point out that, in general oscillating flows, Navier's slip length b is a complex number. An intuitive 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 preliminary experimental work for a 40 kHz oscillator is presented. The Non-Slip Boundary Condition (NSBC) has been verified for a hydrophobic surface in water to within ~60 nm of |b|=0 nm. Experiments were carried out at shear rate amplitudes between 230 and 6800 /s, corresponding to linear displacement amplitudes between 3.2 and 96 nm.