tact angle, for a static drop, will depend on the previous A method of calculation is introduced that allows the simulahistory of the drop motion, a phenomenon known as contact tion of the time-dependent three-dimensional motion of liquid angle hysteresis. Contact angle hysteresis is believed to be droplets on solid substrates for systems exhibiting finite equilibcaused by substrate heterogeniety which may be either physirium contact angles. The contact angle is a prescribed function cal (i.e., microscopic roughness) or chemical, if the substrate of position on the substrate. An evolution equation is presented, is contaminated by small patches of a solid coating having using the lubrication approximation, that includes viscous, capila different equilibrium contact angle, for example. For a lary, disjoining, and gravitational forces. Motion to and from dry moving drop, observed contact angles also depend on the substrate regions is made possible by use of a thin energetically speed of the motion, and one often refers to dynamic (i.e., stable wetting layer. Axisymmetric spreading on a uniform substrate is calculated, and it is found, in agreement with reported advancing and receding) contact angles (1). Interesting and experiments, that spreading rates are independent of the contact practically important issues arise concerning the relative imangle until the drop has almost stabilized. We simulate motion portance of interface-energetic versus dynamic effects in on a heterogeneous substrate composed of two different materials wetting/dewetting phenomena.
having widely different contact angles. Motion proceeds in an
In this paper we demonstrate the feasibility of time-depenalmost discontinuous fashion as the initial droplet breaks up into dent numerical simulation of droplet spreading on heterogesmaller pieces through the action of the wetting forces. Various neous surfaces. The so-called lubrication or long-wave apforms of the disjoining energy functional are employed; the particproximation is used in the simulations. This approximation ular choice is found to have only a limited quantitative effect of has been shown to be a valid simplication of the Navierthe drop dynamics. Experimental observations confirm the basic Stokes equations of viscous flow when used to model the features of the simulation, although a time-scale correction needs slow motion of liquid layers, provided the liquid free-surface to be applied.