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Measurement of Newtonian fluid slip using a torsional ultrasonic oscillator

G. R. Willmott* and J. L. Tallon

  • Industrial Research Limited, 69 Gracefield Road, Lower Hutt, New Zealand

  • *Corresponding author. FAX: (64) (0)4 931 3117. g.willmott@irl.cri.nz
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Phys. Rev. E 76, 066306 – Published 10 December, 2007

DOI: https://doi.org/10.1103/PhysRevE.76.066306

Abstract

The composite torsional ultrasonic oscillator, a versatile experimental system, can be used to investigate slip of a 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 reconsidered 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 nonslip boundary condition 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−1, corresponding to linear displacement amplitudes between 3.2 and 96 nm.

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Phys. Rev. E 76, 066306– Published 10 December, 2007
  • Received 24 May 2007

© 2007 American Physical Society

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