Lattice Boltzmann Simulations of Slip Flow of Non-Newtonian Fluids in Microchannels
This paper considers the application of Lattice Boltzmann Method (LBM) to non-Newtonian flow in micro-fluidic devices. 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 non-Newtonian fluids are 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 the different models characterizing the non-Newtonian flow.
Key wordsLattice Boltzmann Method Non-Newtonian Fluid Flows
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