Projection method for droplet dynamics on groove-textured surface with merging and splitting

Abstract

We study the full dynamics of droplets placed on an inclined groove-textured surface with merging and splitting. The motion of droplets can be determined by the contact line dynamics and motion by mean curvature, which are driven by the competition between surfaces tensions of three phases and gravitational effect. We reformulate the dynamics as a gradient flow on a Hilbert manifold with boundary, which can be further reduced to a parabolic variational inequality under some differentiable assumptions. To efficiently solve the parabolic variational inequality, the convergence and stability of projection method for obstacle problem in Hilbert space is revisited using Trotter-Kato's product formula. Based on this, we proposed a projection scheme for the droplets dynamics, which incorporates both the obstacle information and the phase transition information when merging and splitting happen. Several challenging examples including splitting and merging of droplets are demonstrated.

Surfactant-dependent contact line dynamics and droplet spreading on textured substrates: derivations and computations

“…We remark that the second order numerical scheme developed in [11] can be adapted here. When there are topological changes of droplets such as splitting and merging due to an impermeable textured substrate, the projection method for solving variational inequalities developed in [12] can also be adapted.…”