Numerical Simulation of Non-Newtonian Pseudo-Plastic Fluid in a Micro-Channel Using the Lattice Boltzmann Method

In this paper, the power-law model for a non-Newtonian (pseudo-plastic) flow is investigated numerically. The D2Q9 model of Lattice Boltzmann method is used to simulate the micro-channel flow with expansion geometries. This geometry is made by two squared or trapezoid cavities at the bottom and top of the channel which can simulate an artery with local expansion. The cavities are displaced along the channel and the effects of the displacements are investigated for inline structures and staggered ones (anti-symmetric expansion). The method is validated by a Poiseuille flow of the power-law fluid in a duct. Validation is performed for two cases: The Newtonian fluid and the shear thinning fluid (pseudo-plastic) with n = 0.5. The results are discussed in four parts: 1) Pressure drop; It is shown that the pressure drop along the channel for inline cavities is much more than the pressure drop along the staggered structures. 2) Velocity profiles; the velocity profiles are sketched at the centerline of the cavities. The effects of pseudo-plasticity are discussed. 3) Shear stress distribution; the shear stress is computed and shown in the domain. The Newtonian and non-Newto- nian fluids are discussed and the effect of the power n on shear stress is argued. 4) Generated vortices in the cavities are also presented. The shape of the vortices is depicted for various cases. The results for these cases are talked over and it is found that the vortices will be removed for flows with n smaller than 0.5