  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.
