3 research outputs found
Projection method for droplet dynamics on groove-textured surface with merging and splitting
The geometric motion of small droplets placed on an impermeable textured
substrate is mainly driven by the capillary effect, the competition among
surface tensions of three phases at the moving contact lines, and the
impermeable substrate obstacle. After introducing an infinite dimensional
manifold with an admissible tangent space on the boundary of the manifold, by
Onsager's principle for an obstacle problem, we derive the associated parabolic
variational inequalities. These variational inequalities can be used to
simulate the contact line dynamics with unavoidable merging and splitting of
droplets due to the impermeable obstacle. To efficiently solve the parabolic
variational inequality, we propose an unconditional stable explicit boundary
updating scheme coupled with a projection method. The explicit boundary
updating efficiently decouples the computation of the motion by mean curvature
of the capillary surface and the moving contact lines. Meanwhile, the
projection step efficiently splits the difficulties brought by the obstacle and
the motion by mean curvature of the capillary surface. Furthermore, we prove
the unconditional stability of the scheme and present an accuracy check. The
convergence of the proposed scheme is also proved using a nonlinear
Trotter-Kato's product formula under the pinning contact line assumption. After
incorporating the phase transition information at splitting points, several
challenging examples including splitting and merging of droplets are
demonstrated.Comment: 26 page