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

We study spreading of a droplet, with insoluble surfactant covering its capillary surface, on textured substrate. In this process, the surfactant-dependent surface tension dominates behaviors whole dynamics, particularly moving contact lines. This allows us to derive full dynamics droplets laid by surfactant: (i) lines, (ii) evolution (iii) boundary condition at lines and (iv) incompressible viscous fluids inside droplet. Our derivations base Onsager’s principle Rayleigh dissipation functionals for either flow or motion mean curvature surface. also prove functional case is stronger than one curvature. After incorporating substrate profile, we design numerical scheme based unconditionally stable explicit updates grids, which enable efficient computations many challenging examples showing significant impacts deformation droplets.