Modelling a surfactant-covered droplet on a solid surface in three-dimensional shear flow

Abstract

A surfactant-covered droplet on a solid surface subject to a three-dimensional shear flow is studied using a lattice-Boltzmann and finite-difference hybrid method, which allows for the surfactant concentration beyond the critical micelle concentration. We first focus on low values of the effective capillary number ( ) and study the effect of , viscosity ratio ( ) and surfactant coverage on the droplet behaviour. Results show that at low the droplet eventually reaches steady deformation and a constant moving velocity . The presence of surfactants not only increases droplet deformation but also promotes droplet motion. For each , a linear relationship is found between contact-line capillary number and , but not between wall stress and due to Marangoni effects. As increases, decreases monotonically, but the deformation first increases and then decreases for each . Moreover, increasing surfactant coverage enhances droplet deformation and motion, although the surfactant distribution becomes less non-uniform. We then increase and study droplet breakup for varying , where the role of surfactants on the critical ( ) of droplet breakup is identified by comparing with the clean case. As in the clean case, first decreases and then increases with increasing , but its minima occurs at instead of in the clean case. The presence of surfactants always decreases , and its effect is more pronounced at low . Moreover, a decreasing viscosity ratio is found to favour ternary breakup in both clean and surfactant-covered cases, and tip streaming is observed at the lowest in the surfactant-covered case.