Understanding the dynamics of inertial focusing in non-Newtonian fluids is crucial for microfluidic applications such as particle separation and medical diagnostics. This study uses the immersed boundary-lattice Boltzmann method (IB-LBM) to model the inertial focusing of finite-size particles in square and rectangular microchannels. The results demonstrate that reducing the power-law index (n) enhances the focusing efficiency in square channels, while rectangular channels show more complex equilibrium behaviors. A two-step modification of the Newtonian fluid model is proposed to predict the lateral inertial lift force, considering flow field distribution and finite-size effects. The model's accuracy improves significantly, with prediction errors decreasing from 61% to 23% for square channels. These findings provide theoretical insights for optimizing particle manipulation in non-Newtonian fluid systems.

inertial migration, IB-LBM, lift force, non-Newtonian fluids, microchannels