Surface roughness and interfacial slip boundary condition for quartz crystal microbalances

MCHALE, G. and NEWTON, M.I., 2004. Surface roughness and interfacial slip boundary condition for quartz crystal microbalances. Journal of Applied Physics, 95 (1), pp. 373-380. ISSN 0021-8979

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Abstract

The response of a quartz crystal microbalance (QCM) is considered using a wave equation for the substrate and the Navier-Stokes equations for a finite liquid layer under a slip boundary condition. It is shown that when the slip length to shear wave penetration depth is small, the first order effect of slip is only present in the frequency response. Importantly, in this approximation the frequency response satisfies an additivity relation with a net response equal to a Kanazawa liquid term plus an additional Sauerbrey "rigid" liquid mass. For the slip length to result in an enhanced frequency decrease compared to a no-slip boundary condition, it is shown that the slip length must be negative so that the slip plane is located on the liquid side of the interface. It is argued that the physical application of such a negative slip length could be to the liquid phase response of a QCM with a completely wetted rough surface. Effectively, the model recovers the starting assumption of additivity used in the trapped mass model for the liquid phase response of a QCM having a rough surface. When applying the slip boundary condition to the rough surface problem, slip is not at a molecular level, but is a formal hydrodynamic boundary condition which relates the response of the QCM to that expected from a QCM with a smooth surface. Finally, possible interpretations of the results in terms of acoustic reflectivity are developed and the potential limitations of the additivity result should vapour trapping occur are discussed.

Item Type: Journal article
Publication Title: Journal of Applied Physics
Creators: McHale, G. and Newton, M.I.
Publisher: American Institute of Physics
Place of Publication: Melville, NY
Date: 2004
Volume: 95
Number: 1
ISSN: 0021-8979
Identifiers:
NumberType
10.1063/1.1630373DOI
Rights: Copyright © 2004 American Institute of Physics
Divisions: Schools > School of Science and Technology
Depositing User: EPrints Services
Date Added: 09 Oct 2015 09:56
Last Modified: 23 Aug 2016 09:07
URI: http://irep.ntu.ac.uk/id/eprint/5210

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