Modeling of droplet dynamics with soluble surfactant by multi-relaxation-time phase-field lattice Boltzmann method

The multiphase fluid system in the presence of surfactant is frequently encountered in numerous scientific and engineering applications. Developing a model for accurately simulating such complex system is of great significance. In this work, we propose a multi-relaxation-time phase-field lattice Boltzmann model for simulating droplet dynamics with soluble surfactants. The accuracy and validity of the model are verified by benchmark cases including static droplet and Rayleigh-Taylor instability tests. The effects of surfactant, capillary number, and density ratio on single droplet deformation and two-droplet interaction under shear flow are investigated. Simulation results indicate that the Marangoni stress generated by the inhomogeneous distribution of surfactant at the interface plays the roles of promoting droplet deformation and hindering droplet coalescence. Within the studied range, it tends to be much easier for droplets to deform with the decrease of density ratio. The increases of capillary number and surfactant concentration are conducive to promoting the deformation and breakup of droplets. In addition, a higher surfactant concentration is found to result in greater liquid film thickness between droplets, which would hinder the coalescence of the droplets.