Numerical Simulation on Insoluble Surfactant Mass Transfer on Deformable Bubble Interface in a Couette Flow by Phase-Field Lattice Boltzmann Method–Finite-Difference Method Hybrid Approach

Abstract

Elaborate management on bubble shape and transportations depends on the balance between multiple physical behaviors for two-phase flow with Marangoni stress and the interface mass transfer. In this paper, a new model combining PFLBM (phase-field lattice Boltzmann method) and FDM ( finite-difference method) coupling with the ghost-cell method was built. The PFLBM-FDM was validated for the high accuracy, less computational cost, and low mass loss compared to other methods. Based on the PFLBM-FDM, a surfactant-laden bubble deformed and transported in a laminar Couette flow was investigated. The deformation ratio and transportation velocity were explored with different density ratios, surface tensions, shear velocities, and diffusion coefficients. The numerical results showed that the equilibrium state of the bubble deformation was decided only by the dimensionless numbers when the Sh number was higher than 100. Moreover, the transportation velocity of the bubble can be controlled by the balance between the Marangoni stress and shear velocity. When the Sh is lower than 100, the Marangoni stress from the surfactant is not a long-range force, which only works at the early flow. Otherwise, the Marangoni stress will be a long-range force that provides a persistent force to accelerate the bubble by ∼10%. Increasing Re H will further intensify the effect. Based on all the data, a correlation of the bubble deformation including with the densities of two fluids was obtained and the error range is less 5%.