Cahn-Hilliard Navier-Stokes simulations for design of superhydrophobic surfaces

Self-cleaning is an important feature that is desirable in many applications, such as solar panels. The effect of varying the topography of a surface can aid the ability of droplets, of rainwater for instance, to bead-up, roll down, and pick up dust particles in the process. To this end we consider the motion of a two-dimensional droplet on an inclined substrate and study the effect of varying bottom topography on the motion. The model used to describe the motion is a Navier-Stokes model, incorporating gravity, coupled to a Cahn-Hilliard model for a phase-field. This model is chosen so that the droplet interface is described by an isoline of the phase-field, avoiding posing the problem with a moving boundary, although we still implement an adaptive meshing routine to resolve the interface accurately. The droplet propagation speed in the case of a smooth substrate is compared to the case when the substrate has a sawtooth or triangular pattern, amongst others. The frequency of the patterns is also varied. Results presented will allow provisional conclusions to be drawn on surface designs.