Journal of Fluid Mechanics

Papers

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

PENGTAO YUEa1 c1, CHUNFENG ZHOUa2 and JAMES J. FENGa2a3

a1 Department of Mathematics, Virginia Polytechnic Institute and State University, Blacksburg, VA 24061-0123, USA

a2 Department of Chemical and Biological Engineering, University of British Columbia, Vancouver, BC V6T 1Z3, Canada

a3 Department of Mathematics, University of British Columbia, Vancouver, BC V6T 1Z2, Canada

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.

(Received October 07 2008)

(Revised October 09 2009)

(Accepted October 09 2009)

Correspondence:

c1 Email address for correspondence: ptyue@math.vt.edu

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