Quantitative phase-field modeling for wetting phenomena.

A new phase-field model is developed for studying partial wetting. The introduction of a third phase representing a solid wall allows for the derivation of a new surface tension force that accounts for energy changes at the contact line. In contrast to other multi-phase-field formulations, the present model does not need the introduction of surface energies for the fluid-wall interactions. Instead, all wetting properties are included in a unique parameter known as the equilibrium contact angle θeq. The model requires the solution of a single elliptic phase-field equation, which, coupled to conservation laws for mass and linear momentum, admits the existence of steady and unsteady compact solutions (compactons). The representation of the wall by an additional phase field allows for the study of wetting phenomena on flat, rough, or patterned surfaces in a straightforward manner. The model contains only two free parameters, a measure of interface thickness W and β, which is used in the definition of the mixture viscosity μ=μlϕl+μvϕv+βμlϕw. The former controls the convergence towards the sharp interface limit and the latter the energy dissipation at the contact line. Simulations on rough surfaces show that by taking values for β higher than 1, the model can reproduce, on average, the effects of pinning events of the contact line during its dynamic motion. The model is able to capture, in good agreement with experimental observations, many physical phenomena fundamental to wetting science, such as the wetting transition on micro-structured surfaces and droplet dynamics on solid substrates.