Inertial migration of spherical particle in shear flow of shear-thinning fluids

We investigate inertial migration of a neutrally buoyant spherical particle suspended in an incompressible, shear-thinning fluid undergoing plane Couette flow between two parallel walls, using the smoothed profile–lattice Boltzmann method. Many biological fluids and polymeric liquids exhibit shear-thinning behaviour which is described by the Carreau constitutive model. To assess the influence of shear thinning, we vary the relaxation time of the fluid, the ratio of infinite-shear viscosity to zero-shear viscosity and the power-law index that controls the degree of shear thinning. The results show that the critical Reynolds number for the onset of lateral migration decreases as shear thinning becomes stronger. Further, for a fixed channel Reynolds number, the equilibrium position of the particle shifts away from the centreline toward the walls as shear thinning intensifies. This reduction in the critical Reynolds number is attributed to enhanced local shear gradients near the particle surface, which lower the viscosity and reduce viscous stresses. The resulting increase in the effective local inertial effects promotes an earlier onset of lateral migration. Lift-force profiles are examined to evaluate the stability of equilibrium positions, and the analysis reveals that, in the presence of inertia, shear thinning destabilises the centreline equilibrium, giving rise to symmetric, stable off-centre equilibria. The effect of confinement ratio is also investigated by comparing different particle-to-channel size ratios. A smaller confinement ratio produces further reduction in the critical Reynolds number, indicating that weaker wall interactions enhance the destabilisation of the centreline equilibrium position. These results highlight the intricate interplay between the fluid rheology, inertial and confinement effects in determining particle migration in non-Newtonian flows.