A gray lattice Boltzmann model for power-law fluid and its application in the study of slip velocity at porous interface

A gray lattice Boltzmann model (LBM) for the simulation of power-law fluid through porous media is proposed in this paper. The constitutive equation of power-law fluid is introduced into the model by relating the relaxation time of the original gray LBM to the local shear rate, which is calculated using a new scheme to avoid dealing with the derivative of the velocity. The model is validated by simulating the Poiseuille flow of power-law fluid between two infinite parallel plates filled with homogeneous porous media. When the solid volume fraction ns(x) = 0, i.e. the flow degenerates into free flow of power-law fluid (no solid matrix), and when the solid volume fraction ns(x) > 0, the numerical results agree well with the theoretical predictions. Darcy's law of power-law fluid through the homogeneous porous media is confirmed by our numerical results. A power-relation between the drag force induced by the porous matrix and the particle distribution functions is found. Using this model, the slip velocity of power-law fluid at the interface of porous media is studied. The results indicate that the slip velocity of power-law fluid at the porous interface increases as the power index increases for a given porous medium, and increases as the porosity of the porous media increases for a given power-law fluid.