*Emily Cook: Pressure-driven flow of a yield-stress fluid in an annular channel with internal torque*
Various industrial problems involve transport of fluids with a yield stress along annular channels driven by an axial pressure gradient, where the inner cylinder can also rotate to aid mobilisation of the material. This problem is considered here for the case of a Bingham fluid, which is undeformed if the applied stress lies below the fluid's yield stress. Unlike for a Newtonian fluid, where the steady-state velocity field is simply a composite of axial Poiseuille flow and azimuthal shear flow, the velocity components for a Bingham fluid are inherently coupled by the rheological non-linearity. The resulting steady behaviour is thus rather more complex, and can take qualitatively different forms, with different regions of the fluid remaining rigid and unyielded. The phase space delineating different flow regimes, and the associated behaviour of the fluxes and flow resistance, are outlined as a function of the applied torque and pressure drop, channel geometry and rheological properties. Flow stability and the possible implications for industrial applications are also discussed.
*Jonathan Watts: 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.