Contact line dynamics for merging and splitting of droplets: gradient flow formulation and computations

Abstract: The capillary effects caused by the interfacial energy dominates the dynamics of small droplets and takes the form of mean curvature flow of the capillary surface coupled with contact line dynamics. For the volume preserving motion, this is modeled by a free boundary incompressible potential flow. A gradient flow on a Hilbert manifold is used for effective numerical methods. We propose unconditionally stable first/second order numerical schemes based on explicit moving boundary updates and a semi-Lagrangian method. To enforce impermeable obstacle constraint, a projection method for a variational inequality is further adapted to simulate the unavoidable merging and splitting of droplets. The phase transition for the emerged contact lines are detected and equipped with contact line mechanism. We also compare the purely geometric droplet dynamics with hydrodynamic models.

Mathematics

Audience: researchers in the topic

ICCM 2020