Eur. Phys. J. Special Topics 197, 37-46 (2011)
https://doi.org/10.1140/epjst/e2011-01434-y

Regular Article

Can diffuse-interface models quantitatively describe moving contact lines?

¹ Department of Mathematics, Virginia Polytechnic Institute and State University, Blacksburg, VA 24061-0123, USA
² Department of Chemical and Biological Engineering, University of British Columbia, Vancouver, BC V6T 1Z3, Canada
³ Department of Mathematics, University of British Columbia, Vancouver, BC V6T 1Z2, Canada

^a e-mail: ptyue@math.vt.edu

Received: 2 June 2011
Revised: 15 June 2011
Published online: 30 August 2011

Abstract

The three-phase contact line is a long-standing problem in the physics and hydrodynamics of interfaces. The traditional sharp-interface Navier-Stokes formulation encounters a non-integrable stress singularity, which is commonly avoided by introducing slip at the contact line. In recent years, diffuse-interface models have emerged as an alternative method. They are attractive in regularizing the singularity in a more rational manner, and in the meantime supplying a means for describing the interfacial motion on the large scale. Although a number of groups have carried out diffuse-interface computations of moving contact lines, a closer inspection shows that some fundamental questions remain to be answered. For example, how can a sharp-interface limit be realized to produce a solution that is independent of the interfacial thickness? How to determine model parameters so as to match a specific experiment? Finally, is it possible to make quantitatively accurate predictions of the moving contact line using diffuse-interface models? Using the Cahn-Hilliard model as an example, we describe these issues and suggest solutions.