Transition between the viscous and the inertial regime in sheared dense suspensions: the effect of wall boundaries

Abstract The transition from the viscous to the inertial regime in dense suspensions remains incompletely understood. Volume-imposed rheometers, with fixed-gap confining walls, provide key insights into this transition by presenting rheology as shear and normal stress versus shear rate. However, the effects of wall boundaries on the rheological response, particularly in narrow-gap systems, which is relevant to many industrial and natural flows, are still not addressed. In this work, we conduct particle-resolved Direct Numerical Simulations (pr-DNS) of dense non-Brownian suspensions sheared between rough walls in a confined volume-imposed cell. Our results reproduce the general trend of the viscous–inertial transition observed in recent experiments. Importantly, consistent with experimental results, we captured a weakening of the effective friction coefficient during the transition. We demonstrate this behavior by introducing different cases changing the wall roughness and flow cell height. Both factors significantly influence stress levels by altering the layering of particles in the sheared suspension. All cases exhibit strong layering, but in the case with the roughest wall and weaker confinement, enhanced inter-layer mixing leads to higher stresses. After large strains, this regime transitions to a more structured, low-mixing regime, reducing stress to levels comparable to other cases. Despite the differences in stress values, all cases followed a consistent viscous–inertial transition trend. Microstructural analysis revealed that the number of contacts reduces during the transition, yet the remaining contacts have larger force magnitudes, causing the transition to the inertial regime. Overall, we show that wall effects strongly influence layering and mixing, thereby shaping the rheological response of confined dense suspensions during the viscous–inertial transition.