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The motion of a contact line is examined, and comparisons drawn, for avariety of models proposed in the literature. Pressure and stress behaviours atthe contact line are examined in the prototype system of quasistatic spreadingof a thin two-dimensional droplet on a planar substrate. The models analysedinclude three disjoining pressure models based on van der Waals interactions, amodel introduced for polar fluids, and a liquid-gas diffuse-interface model;Navier-slip and two non-linear slip models are investigated, with threemicroscopic contact angle boundary conditions imposed (two of these contactangle conditions having a contact line velocity dependence); and the interfaceformation model is also considered. In certain parameter regimes it is shownthat all of the models predict the same quasistatic droplet spreadingbehaviour.

journal of engineering mathematics

A comparison of slip, disjoining pressure, and interface formation  models for contact line motion through asymptotic analysis of thin  two-dimensional droplet spreading