  We study spreading of a droplet, with insoluble surfactant covering its
capillary surface, on 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, (iii) the
surfactant dynamics on this moving surface with a boundary condition at the
contact lines and (iv) the incompressible viscous fluids inside the droplet.
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 viscous flow case is stronger than the one for the motion by
mean curvature. After incorporating the textured substrate profile, we design a
numerical scheme based on unconditionally stable explicit boundary updates and
moving grids, which enable efficient computations for many challenging examples
showing significant impacts of the surfactant to the deformation of droplets.
