Motion of drops on highly hydrophobic surfaces

We analyse the behaviour of droplets resting on hydrophobic substrates. Such systems have been of significant practical interest in recent years due to their involvement in numerous prototypical problems such as post-rupture. From a theoretical point of view, it presents a curious challenge due to the multi-valuedness of the interface, presenting a stumbling block to typical low-order modelling techniques. The equilibrium problem is solved exactly in terms of elliptic functions and via matched asymptotic expansions showing good agreement. The dynamic problem is computed via an energetic approach that is more accurate and with a broader range of applicability than existing solutions, with validation being performed against direct numerical simulations.