Communications in Mathematical Sciences

Volume 9 (2011)

Number 2

Derivation of continuum models for the moving contact line problem based on thermodynamic principles

Pages: 597 – 606

(Fast Communication)



Weiqing Ren (Courant Institute of Mathematical Sciences, New York University, New York)

E. Weinan (Department of Mathematics and PACM, Princeton University)


Contact lines arise as the boundaries of free boundaries in fluids. This problem is interesting and important, not only because it arises in many applications, but also because of the distinct mathematical and physical features it has, such as singularities, hysteresis, instabilities, competing scaling regimes, etc. For a long time, this area of study was plagued with conflicting theories and uncertainties regarding how the problem should be modeled. In the present paper we illustrate how continuum models for the moving contact line problem can be derived using simple thermodynamic considerations. Both the sharp interface models and diffuse interface models are derived.


moving contact lines, molecular dynamics, thermodynamics

2010 Mathematics Subject Classification

76D27, 76D45, 76Txx

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