Constrained Energy Minimization of a Pinned Droplet on an Inclined Plate

A long standing problem is the prediction of the maximum volume of a droplet that can hang on an inclined plate without rolling off. A key issue in this prediction is to understand the deformation of the droplet. We show that the common assumptions of a fixed droplet base or a shape at global energy minimum result in significant errors. We study droplets on a inline using locally constrained energy minimization. The initial shape of the droplet and maximum and minimum attainable contact angles hereby put constraints on the energy minimization. This results in a history dependence of the droplet behavior before roll-off, but surprisingly, a universal behaviour of the front-to-back baselength of the droplet at roll-off. This universal behavior can be predicted from equilibrium droplet shapes on a horizontal surface and understood from energy landscapes for a 2D droplet.