Lattice Boltzmann Model And Application Of Multiphase Flows With Soluble Surfactant

The multiphase fluid system in the presence of surfactants can be frequently encountered in numerous scientific and engineering applications,such as enhanced oil recovery,coating,biomedical field,and droplet manipulation in microfluidic devices.With great advances in computer technology,numerical modeling has become an increasingly popular approach for studying such interfacial flows with surfactant.Several research studies have made great efforts to construct some effective numerical approaches for simulating multiphase flows with surfactants,while some challenges still remain.Different from these conventional Navier-Stokes solvers,the mesoscopic lattice Boltzmann(LB)method has some advantages over the traditional numerical methods in terms of the algorithmic simplicity,parallelization,complex boundary implementation and describing the micro-interactions between fluid components and surfactant components.Based on the phase-field theory,we present an improved lattice Boltzmann(LB)method for simulating droplet dynamics with soluble surfactant.This method takes advantage of three sets of particle distribution functions for solving the coupled system of two Cahn-Hilliard-like equations and incompressible Navier-Stokes equations.The phase field model is formulated from the perspective of the Ginzburg-Landau free energy functional,where some modifications introduced circumvent unphysical behavior of the interfacial layer and improve the well-posedness of the model.We also give a comprehensive review on the existing surface tension force formulations and demonstrated that the popular potential form is artificial,instead an alternative potential surface tension force is deduced.The equation of state accounting for the influence of the surfactant concentration on interfacial tension can be directly incorporated into the present approach,further improving the flexibility of the method.Besides,a linear equilibrium distribution function and proper source term are introduced into the LB method for surfactant such that it can recover the correct physical formulations for a surfactant-laden multiphase system through Chapman-Enskog theoretical analysis.An abundant of numerical experiments are carried out to validate the LB method and the numerical performances of the tensor and potential surface tension forces are also evaluated.It is reported that the new potential scheme achieves a better accuracy in solving interfacial dynamics at low surfactant concentrations and also is favor of lower spurious velocities near the interface.In addition,the numerical predictions of surfactantladen droplet dynamics show good agreements with the literature data.