An Energy Approach to the Continuum Surface Tension Method: Application to Droplet Coalescences and Droplet/Wall Interactions

I introduce an energy-based approach to the continuum surface tension method and demonstrate its use in the calculation of large-deformation flows. The energy approach shows that the continuum surface tension method can be understood as a phase field method. Among its advantages are that it 1) allows the introduction of an immiscibility model that can be used for subgrid resolution and reconstruction of interfaces, 2) with the immiscibility model the continuum surface tension method has genuine, locally unique, and repeatable steady states, and 3) variational techniques can be used to find equilibria and set boundary conditions. Calculations are made of droplet coalescence/break-up and of a two-phase driven-cavity flow.