Equilibrium Drop Shapes on a Tilted Substrate with a Chemical Step

We calculate the equilibrium shape of a droplet sitting on a tilted substrate with a "chemical step", that is, different lypophilicity at the two sides of the step. This problem can be generalized to that of a droplet experiencing a body force, pushing it from the lyophilic part to the lyophobic part of the substrate. We present phase diagrams, in which we show for which droplet sizes there are dynamically inaccessible equilibrium shapes. We also identify what determines the threshold volume. While this given system was studied previously in the literature using contact angle hysteresis laws, we present the full static thermodynamical solution of the interfacial energy including the contact energy, while omitting the hysteresis effects from the contact line.