Lattice Boltzmann simulation of two-phase flow involving non-Newtonian fluid in rough channels

In the present work, a lattice Boltzmann model for two-phase flow involving non-Newtonian fluid is proposed by incorporating the rheological equation into the LBM method for two-phase flow with large density ratio based on the phase field theory. In order to guarantee the continuity of velocity and stress at the interface, the viscosity variation of a power-law fluid at the interface is obtained by using an inverse linear interpolation scheme. The validation of current model is performed by modeling single bubble rising in power-law fluids. Then, the displacement of Newtonian fluid by power-law fluids in rough channel characterized by rectangular roughness element is simulated in the absence of gravity effects. The influences of power-law index and geometric parameters of roughness element including relative roughness and element spacing on the displacement process are analyzed. With the help of shape evolution plots, the differences in the behavior of displaced fluid are compared. By means of velocity profiles, the variations of displacement velocity are discussed. These results demonstrate the reliability and suitability of the current two-phase LBM model for non-Newtonian flow simulations.