Inertial migration of soft particle pairs: vortex-induced abrupt spacing changes in power-law fluids

We numerically investigate the inertial migration of two soft particles in power-law fluids. A notable finding is a distinct regime in which the axial equilibrium spacing between particle pairs increases linearly with the Reynolds number. Outside this linear region, the spacing undergoes a sharp escalation, and the Reynolds number interval supporting linear behavior widens as the power-law exponent rises. This sudden jump in spacing likely results from the formation of two vortices in the gap between particles, whose intensity grows with Reynolds number. Once the Reynolds number surpasses a critical threshold, these vortices occupy the entire interstitial volume, triggering a dramatic expansion of the axial equilibrium spacing. In shear-thinning fluids, increasing the blockage ratio yields a non-monotonic trend in axial spacing, which first increases and then decreases. Furthermore, higher capillary numbers or larger power-law exponents drive the particles toward the channel center, while an increase in Reynolds number initially pushes the particles outward before they migrate back inward. These results highlight vortex-induced transitions as the key mechanism governing spacing changes and provide new insights into soft-particle dynamics in confined power-law flows.