Lattice Boltzmann simulations of slip flow of Newtonian and non-Newtonian fluids in microgeometries

This paper considers the application of Lattice Boltzmann Method (LBM) to flow in micro-fluidic devices, which requires special consideration because of the variation in Knudsen number as the fluid moves along these devices driven by pressure or acceleration. To set ideas, we first consider the pressure driven gaseous slip flow with small rarefaction through a long micro-channel and formulate the problem in LB framework. The accuracy of the LB solution is checked by comparing it with analytical solution with slip boundary condition and the numerical solutions of Navier-Stokes and augmented Burnett equations without and with slip boundary conditions. We then consider the flow of non-Newtonian fluids characterized by the non-linear stress-strain constitutive models formulated by Casson, Carreau & Yasuda, Herschel, and Cross, and the well known power law model. The formulation of the LBM for slip flow of non-Newtonian flow is presented. For planar constant area micro-channel for power law fluid, it is possible to obtain an analytical solution for both no-slip and slip flow. For other non-Newtonian fluid models, LBM results are compared with the numerical solutions obtained by using the commercial software FLUENT. The LBM results agree well with the analytical solutions and the numerical solutions. Small differences in the results are noticed using different models characterizing the non-Newtonian flow.