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

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.