Modelling contact angle hysteresis on chemically patterned and superhydrophobic surfaces

We investigate contact angle hysteresis on chemically patterned and superhydrophobic surfaces, as the drop volume is quasi-statically increased and decreased. We consider both two, and three, dimensions using analytical and numerical approaches to minimise the free energy of the drop. In two dimensions we find, in agreement with other authors, a slip, jump, stick motion of the contact line. In three dimensions this behaviour persists, but the position and magnitude of the contact line jumps are sensitive to the details of the surface patterning. In two dimensions we identify analytically the advancing and receding contact angles on the different surfaces and we use numerical insights to argue that these provide bounds for the three dimensional cases. We present explicit simulations to show that a simple average over the disorder is not sufficient to predict the details of the contact angle hysteresis, and to support an explanation for the low contact angle hysteresis of suspended drops on superhydrophobic surfaces.