Dense suspensions in ducts: μ(J) beyond simple shear

Accurately capturing the rheology of dense non-Brownian suspensions is a problem with widespread applications in biological, geophysical and industrial settings. There has been some success in modelling their behaviour under steady simple shear using the family of "μ(J)" models, but the predictions of these models in inhomogeneous flows have been relatively unexplored. We present a model for the pressure-driven flow of a suspension of dense particles down a duct oriented perpendicular to the direction of gravity. This problem gives rise to a range of possible flows, ranging from percolation of fluid through a static granular packing, to partially mobilised particulate flow in some of the duct, and finally to fully mobile suspension flow. We explore the predictions of the model, characterise the solutions across a range of parameters, and make comparison with experimental results. We also discuss known inadequacies of the μ(J) models in describing some suspension flow phenomena, in particular the observed flow of dense suspensions below their apparent yield stress, and consider the possibility of a nonlocal dense suspension theory, by analogy with existing nonlocal models for granular flows.