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

by   Yuan Gao, et al.

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


page 27

page 28


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

We study the full dynamics of droplets placed on an inclined groove-text...

Deep Level-set Method for Stefan Problems

We propose a level-set approach to characterize the region occupied by t...

Efficient and Robust Discrete Conformal Equivalence with Boundary

We describe an efficient algorithm to compute a conformally equivalent m...

Sphere tangencies, line incidences, and Lie's line-sphere correspondence

Two spheres with centers p and q and signed radii r and s are said to be...

Please sign up or login with your details

Forgot password? Click here to reset