Quantifying the shear-induced migration of rigid and deformable particles in a power-law suspending fluid

Shear-induced migration (SIM), namely, the migration of particles from areas of high shear stress to low shear-stress ones, plays a pivotal role in several critical applications, such as drug delivery in the microvascular system. We have recently presented [Polykarpou et al., Phys. Fluids37, 083365 (2025)], a modification of the diffusive flux model, which accounts for the SIM of deformable particles in Newtonian suspensions. In this work, we further generalize the model by considering the suspending fluid to be described by a power-law model. We find that the shear-thinning behavior of the suspending fluid greatly influences SIM, as seen from the resulting particle concentration profiles. It is observed that irrespective of the flow considered (tube or cylindrical Couette), fluids that shear-thin extensively (small power-law exponents) result in reversing the direction of migration for both rigid and deformable particles. In the tube flow, the centerline velocity when using deformable particles is larger than when using rigid particles, which is reminiscent of the case of Newtonian suspending fluids. Furthermore, the increase of the suspending fluid characteristic time intensifies the SIM, in some cases, leaving the centerline devoid of particles. We demonstrate that the revised diffusive flux model aligns with existing experimental literature data. We believe that using this model in numerical simulations of more complex geometries will enhance our understanding of the migration of rigid and deformable particles suspended in non-Newtonian fluids, which is significant in a plethora of technological applications.