Hysteretic Effects in Droplet Motions on Heterogeneous Substrates: Direct Numerical Simulation

Amethodof calculation is introduced that allows the simulation of the time-dependent three-dimensional motion of liquid droplets on solid substrates for systems with finite equilibrium contact angles. The contact angle is a prescribed function of position on the substrate. An evolution equation is given, using the lubrication assumption, that includes viscous, capillary, and disjoining forces. Motion to and from dry substrate regions is made possible by use of a thin energetically stable wetting layer. We simulate motion on heterogeneous substrates with periodic arrays of high-contact-angle patches. For a homogeneous substrate, calculated droplet spreading rates are compared to published experimental results, revealing the need for a time-scale correction. Two different problems are treated. The first is spontaneous motion driven only by wetting forces. If the contact-angle difference is sufficiently high, the droplet can find several different stable positions, depending on the previous history of the motion. A second simulation treats a forced cyclical motion. Energy dissipation per cycle for a heterogeneous substrate is found to be larger than that for a uniform substrate with the same total energy. Comparison is made with simple quasi-static theories.