Sessile Drops on Heterogeneous Surfaces : Static and Dynamic Behaviour

Abstract

A sessile drop of a pure liquid, L, resting on a perfectly flat, smooth horizontal, isotropic, homogeneous and undeformable solid, S, in the presence of a second fluid, which we shall take to be the vapour V of L for definiteness, should adopt an axisymmetric shape at equilibrium. However, it is an everyday observation that the vast majority of drops on solid surfaces take a form which is anything but axisymmetric. This is related to the phenomenon of wetting hysteresis, or potential variability of the contact angle, θ, (subtended in the liquid phase between the solid surface and the tangent to the liquid/vapour interface) generally caused by inhomogeneity of the surface. A degree of solid heterogeneity may arise from one or several of a host of possible causes including the presence of chemical inhomogeneities, local specific adsorption, surface roughness, molecular orientation and the existence of local solid deformation in the vicinity of the triple line [1-7] Whatever be the essential reason(s) for this contact angle hysteresis, chemical or physical, the fact remains that the simple meniscus shape corresponding to the circular contact line of an axisymmetric drop becomes deformed and solution of Laplace’s capillary equation [8] is then, in general, rather difficult. This relation, describing the equilibrium of the liquid/vapour interface, is a second-order, non-linear partial differential equation which rarely affords an analytical solution (not even in the axisymmetric case if gravitational effects are to be taken into consideration [9]).