A multicomponent pseudopotential lattice Boltzmann model for liquid–liquid systems with soluble surfactants

The intermolecular interactions in the pseudo-potential lattice Boltzmann (PPLB) method can readily be
extended to more than two components. We report about a three-component PPLB approach to explore whether
the effect of a surfactant could be included in describing droplet behaviour in (liquid–liquid) emulsions.
The two main liquid components are taken to follow the Carnahan-Starling equation of state (EoS), while
the surfactant obeys an ideal EoS. We investigate the nature of the phases present at equilibrium and the
dependence of the interfacial tension between the two liquid phases on the amount of surfactant. The response
of a droplet subjected to simple shear is investigated in the absence and the presence of a surfactant. Our
exploratory simulations show how during droplet deformation the surfactant re-distributes itself due to the
action of the shear and flows towards the far ends of the deformed droplet, up to the moment the droplet
breaks up. This inhomogeneous surfactant distribution along the interface increases the shear rate that is
needed for droplet breakup such that the critical capillary number for breakup increases and the breakup
process is delayed. The simulations also reveal the detailed flow fields inside and outside the deforming droplet.