European Journal of Applied Mathematics



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On a model for the motion of a contact line on a smooth solid surface


J. BILLINGHAM a1
a1 School of Mathematical Sciences, University of Nottingham, University Park, Nottingham NG7 2RD, UK email: John.Billingham@Nottingham.ac.uk

Article author query
billingham j   [Google Scholar] 
 

Abstract

In this paper we investigate the model for the motion of a contact line over a smooth solid surface developed by Shikhmurzaev, [24]. We show that the formulation is incomplete as it stands, since the mathematical structure of the model indicates that an additional condition is required at the contact line. Recent work by Bedeaux, [4], provides this missing condition, and we examine the consequences of this for the relationship between the contact angle and contact line speed for Stokes flow, using asymptotic methods to investigate the case of small capillary number, and a boundary integral method to find the solution for general capillary number, which allows us to include the effect of viscous bending. We compare the theory with experimental data from a plunging tape experiment with water/glycerol mixtures of varying viscosities [11]. We find that we are able to obtain a reasonable fit using Shikhmurzaev's model, but that it remains unclear whether the linearized surface thermodynamics that underlies the theory provide an adequate description for the motion of a contact line.

(Received June 8 2005)
(Revised March 28 2006)