Simulation of multiphase flows with variable surface tension using the Lattice Boltzmann method

Abstract

Methods for implementing variable surface tension on two popular Lattice– Boltzmann models, the original gradient-based chromodynamic model, and the Shan–Chen model, are explored and examined. The experiment, inspired by the work of Greenspan, consists of reducing the surface tension at two poles of a circular droplet due to a diffusive solute (surfactant). Both Lattice Boltzmann models are able to simulate the expected initial deformation where the droplet is stretched along the pole axis, and contracts at the equator. We observed no furrowingto the droplet, which verifies the work of He and Dembo who concluded that variation in surface tension cannot alone account for such furrowing. We were able to simulate the process as the surfactant diffuses over the entire interface and the spatial variation in surface tension vanishes. The droplet reverts back to its original circular shape with the overall surface tension reduced. Variable surface tension is easier to implement with the chromodynamic model. The physically direct Shan–Chen model, which has superior isotropic qualities, can also be used for variable surface tension. However, coordinating the decline of the surface tension with the reduction in the separation forces is a more delicate matter, and the diffusivity of the interface increases if the surface tension is weakened.