Dynamics of surfactant-laden drops in shear flow by lattice Boltzmann method

Abstract

We developed and applied a diffuse interface lattice Boltzmann method for simulating immiscible liquids with soluble surfactants using a modified Ginzburg–Landau free energy functional. We first validated the approach through simulations of planar interfaces and drop equilibration in quiescent fluid. The proposed method accurately captures the phase and surfactant fields with diminishing spurious velocities of 10−6. We systemically examined the effects of capillary number, comparing viscous to surface forces, the combined effect of surfactant and viscosity ratio (λ) of the drop to the continuous phase, and the bulk surfactant load on the deformation and breakage in a shear flow. At a given capillary number (0.05<Ca<0.32), drop behavior is influenced by reduced surface tension, tip-stretching, Marangoni stresses, and surface dilution. These effects either promote (by tip-stretching) or hinder (via Marangoni stresses, surface dilution) the surfactant distribution at the interface, consequently affecting the final drop morphology. As Ca increases, the competition between the viscosity ratio and the presence of surfactant determines drops' topological changes. The presence of surfactants can overcome the effect of viscosity ratio (when 0.05≤λ≤1.7) and promote drop breakup, whereas highly viscous drops (either λ<0.05 or λ>1.7) do not break. Furthermore, high surfactant loads result in higher drop deformation and earlier drop breakup. In brief, our method successfully captures the dynamics of surfactant-laden drops in shear flow, elucidating the complex interplay between flow hydrodynamics and surfactant transport with 3D quantitative phase and surfactant concentration fields.