An improved phase-field-based lattice Boltzmann model for droplet dynamics with soluble surfactant

We present an improved phase-field model in the lattice Boltzmann scheme to investigate the droplet dynamics in the presence of soluble surfactant. The phase-field model based on the Ginzburg–Landau free energy is developed in which the immiscible binary fluid interfacial profile is independent of the surfactant concentration. The improved model is validated and then employed to study the surfactant effect on single droplet deformation, two droplets interactions and interactions among four droplets in the shear flow. The results show that the increase of surfactant concentration promotes droplet deformation, droplet breakup and more complex droplet-droplet interaction compared to the clean droplet. Moreover, the effects of capillary number, viscosity ratio, as well as peclet number on the behavior of surfactant-covered droplets in the shear flow are investigated. The results indicate that the droplet Taylor deformation parameter increases with the increase of capillary number but the decrease of viscosity ratio. The minimum distance between two interacting droplets enlarges with both capillary number and peclet number.