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Sharp-interface limit of the Cahn–Hilliard model for moving contact lines

Published online by Cambridge University Press:  22 February 2010

PENGTAO YUE ,
CHUNFENG ZHOU  and
JAMES J. FENG
PENGTAO YUE*
Affiliation:
Department of Mathematics, Virginia Polytechnic Institute and State University, Blacksburg, VA 24061-0123, USA
CHUNFENG ZHOU
Affiliation:
Department of Chemical and Biological Engineering, University of British Columbia, Vancouver, BC V6T 1Z3, Canada
JAMES J. FENG
Affiliation:
Department of Chemical and Biological Engineering, University of British Columbia, Vancouver, BC V6T 1Z3, Canada Department of Mathematics, University of British Columbia, Vancouver, BC V6T 1Z2, Canada
*
†Email address for correspondence: ptyue@math.vt.edu
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Abstract

Diffuse-interface models may be used to compute moving contact lines because the Cahn–Hilliard diffusion regularizes the singularity at the contact line. This paper investigates the basic questions underlying this approach. Through scaling arguments and numerical computations, we demonstrate that the Cahn–Hilliard model approaches a sharp-interface limit when the interfacial thickness is reduced below a threshold while other parameters are fixed. In this limit, the contact line has a diffusion length that is related to the slip length in sharp-interface models. Based on the numerical results, we propose a criterion for attaining the sharp-interface limit in computing moving contact lines.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 645 , 25 February 2010 , pp. 279 - 294
Copyright
Copyright © Cambridge University Press 2010

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