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

This is the authors' abstract. We don't add key points for this paper.

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 (Caₑ) and study the effect of Caₑ, viscosity ratio ([STIX]x1D706) and surfactant coverage on the droplet behaviour. Results show that at low Caₑ the droplet eventually reaches steady deformation and a constant moving velocity ud. The presence of surfactants not only increases droplet deformation but also promotes droplet motion. For each [STIX]x1D706, a linear relationship is found between contact-line capillary number and Caₑ, but not between wall stress and ud due to Marangoni effects. As [STIX]x1D706 increases, ud decreases monotonically, but the deformation first increases and then decreases for each Caₑ. Moreover, increasing surfactant coverage enhances droplet deformation and motion, although the surfactant distribution becomes less non-uniform. We then increase Caₑ and study droplet breakup for varying [STIX]x1D706, where the role of surfactants on the critical Caₑ (Cae,c) of droplet breakup is identified by comparing with the clean case. As in the clean case, Cae,c first decreases and then increases with increasing [STIX]x1D706, but its minima occurs at [STIX]x1D706=0.5 instead of [STIX]x1D706=1 in the clean case. The presence of surfactants always decreases Cae,c, and its effect is more pronounced at low [STIX]x1D706. 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 [STIX]x1D706 in the surfactant-covered case.