Resolved immersed-boundary simulation of fluid–solid interaction in non-Newtonian fluids

A resolved immersed boundary–computational fluid dynamics–discrete element method framework is developed for rigid-particle fluid–solid interaction in incompressible non-Newtonian fluids. Power-law, Bingham, and Herschel–Bulkley rheology are incorporated through an apparent-viscosity formulation, and a semi-implicit viscous treatment is used to reduce the severe time step restriction caused by large apparent viscosities. Benchmark tests for lid-driven cavity flow, confined cylinder flow, and particle sedimentation show good agreement with reference solutions in velocity profiles, hydrodynamic forces, yielded/unyielded regions, and particle trajectories. The explicit–semi-implicit comparison shows that the semi-implicit treatment permits larger stable time steps and reduces the total central processing unit time required to reach the same physical time in stiff low-Reynolds-number and high-Bingham-number cases. Two-dimensional sedimentation simulations show that shear-thinning fluids promote faster collective settling through low-viscosity pathways, whereas shear-thickening fluids suppress particle rearrangement through enhanced local viscous damping. The collective sedimentation results further indicate that drafting–kissing–tumbling-like overtaking can occur beyond isolated particle pairs under the considered rheological conditions, while in yield-stress fluids the evolution of yielded and weakly sheared regions delays particle approach and weakens this overtaking behavior. These results demonstrate the capability of the proposed resolved framework to capture rheology-dependent particle-scale dynamics in non-Newtonian fluid–solid interaction.