MULTISCALE ANALYSIS FOR DYNAMIC CONTACT ANGLE HYSTERESIS ON ROUGH SURFACES

Dynamic contact angle hysteresis is of critical importance for many two-phase flow problems with moving contact lines. It is induced by inhomogeneity or roughness of the substrates. In this paper, we present theoretical studies on the time averaging of a reduced model for wetting on rough surfaces and also the analysis on the effect of stochastic thermal forces. We derive equations for the averaged dynamics and show that the apparent contact angle depends on the harmonic averaging of the geometric and chemical properties of the substrates as well as the contact line velocity. The contact angle hysteresis can be determined quantitatively by the equations. The averaging results are proved rigorously by multi-scale analysis and verified by some numerical examples.