Modeling the deformation and breakup of a surfactant-coated droplet on a roughness solid surface in shear flow

A surfactant-coated droplet attached to a rough wall subjected to shear flow is investigated using a coupled lattice Boltzmann with the finite difference method, where a contact angle hysteresis model is introduced into the method to characterize the surface roughness. The method is first verified by the equilibrium contact angle of a semi-circular droplet setting on the bottom plane. It is then adopted to explore the surfactant role on the droplet motion and deformation on a rough wall with two representative hysteresis windows. For the hysteresis window of (0°, 180°), i.e., the contact line remains pinned, the addition of surfactants first promotes droplet deformation and then hinders droplet deformation with increasing effective capillary number. However, for the hysteresis window of (70°, 110°), the addition of surfactants always promotes droplet motion and deformation. Finally, the surfactant role on droplet breakup is presented. For the hysteresis window of (0°, 180°), the addition of surfactants hinders droplet breakup. However, for the hysteresis window of (70°, 110°), the addition of surfactants promotes droplet breakup.