  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.
