Simulation of Droplet Motion on Low-Energy and Heterogeneous Surfaces

Abstract

A method of calculation is introduced that allows the simulation of the time-dependent three-dimensional motion of liquid droplets on solid substrates for systems exhibiting finite equilibrium contact angles. The contact angle is a prescribed function of position on the substrate. An evolution equation is presented, using the lubrication approximation, that includes viscous, capillary, disjoining, and gravitational forces. Motion to and from dry substrate regions is made possible by use of a thin energetically stable wetting layer. Axisymmetric spreading on a uniform substrate is calculated, and it is found, in agreement with reported experiments, that spreading rates are independent of the contact angle until the drop has almost stabilized. We simulate motion on a heterogeneous substrate composed of two different materials having widely different contact angles. Motion proceeds in an almost discontinuous fashion as the initial droplet breaks up into smaller pieces through the action of the wetting forces. Various forms of the disjoining energy functional are employed; the particular choice is found to have only a limited quantitative effect of the drop dynamics. Experimental observations confirm the basic features of the simulation, although a time-scale correction needs to be applied.