A hybrid lattice Boltzmann model for surfactant-covered droplets

Abstract

This paper proposes a hybrid model for the study of the droplet flow behavior in an immiscible medium with insoluble nonionic surfactant adhering to its interface. The evolution of the surfactant concentration on the interface is modeled by the time-dependent surfactant convection-diffusion equation and solved by a finite difference scheme. The fluid velocity field, the pressure and the interface curvature are calculated using the lattice Boltzmann method (LBM) for binary fluid mixtures. The coupling between the LBM and the finite difference scheme is achieved through the LBM variables and the surfactant equation of state. The Gunstensen LBM is used here because it provides local and independent application of a distinct interfacial tension on the individual nodes of the droplet interface. The hybrid model was developed and successfully applied to droplet deformations under a variety of flow conditions.