Lattice Boltzmann modeling for multiphase viscoplastic fluid flow

We present a lattice Boltzmann model to simulate multiphase viscoplastic fluid flow. It is an extended model based on the free-energy-based lattice Boltzmann method (LBM) for multiphase fluids with possible high-density and high-viscosity ratios by applying the Herschel-Bulkley constitutive relationship to account for the variable viscosity. The model shows good agreements between the simulation results and the corresponding theoretical solutions for different cases. Furthermore, the capability and effectivity of this model is tested by examples, including droplet(s) falling and interaction in Bingham fluid, and sessile viscoplastic droplet motion. The results illustrate that our model is able to catch the yield behavior well, and to distinguish various kinds of viscoplastic fluids effectively.