Numerical Algorithm For Complex Flows With Insoluble Surfactants

Multiphase now with insoluble surfactants is widely found in many industries.The mathematical model of this problem is very complicated,so it is a valuable work to propose an efficient and stable numerical algorithm.The main contents are as follows.A high-efficiency numerical algorithm(LS-MLBFS-CN)is proposed.In present method,the level set method is employed to capture the fluid interface,the multi-phase lattice Boltzmann flux solver(MLBFS)is adopted to solve the flow field,and a semi-implicit Crank-Nicholson(CN)scheme is used to discrete the convection-diffusion equation of insoluble surfactant concentration.Firstly,the convergence and stability of the LS-MLBFS-CN are validated by simulating the droplets in the s-hear now with different grid resolutions.Furthermore,different Cappilary numbers(Ca)are considered,and the numerical results show that the larger Ca implies larger deformation.An energy-stable scheme is proposed in the framework of level set method.Firstly,aim at the two-phase now without surfactants,the total energy of the sys-tem is defined as the sum of the kinetic energy of the fluid and the surface free energy.An energy-stable numerical scheme in the framework of level set method is proposed,and its stability is proved by the SAV(Scalar Auxiliary Variable)method.Furthermore,considering the effect of insoluble surfactants on the surface tension coefficient,the energy stable scheme for solving the two-phase now with surfactants is given and proved.