Two-dimensional modeling of the superhydrophobic behavior of a liquid droplet sliding down a ramp of pillars

We present a two dimensional simulation based on the cellular Potts model of a liquid droplet sliding down a ramp of pillars. For the same critical angle at which a droplet starts to slide with minimal velocity on a smooth ramp in our simulation, we find that for a ramp of pillars the velocity of the droplet depends strongly on the solid fraction of contact (f). The velocity as a function of f has a maximum whose value is about 2.5 times higher than on a smooth surface, this corresponds to low values of the contact angle hysteresis (the difference between the advancing and receding contact angles of droplet measured on the ramp) consistent with superhydrophobic behavior.