Continuum modelling of dense granular suspensions in a duct: bold italic mu bold left parenthesis bold italic upper J bold right parenthesis μ ( J ) μ (J) beyond simple shear

We present a theoretical and experimental study of the pressure-driven flow of a suspension of non-Brownian, negatively buoyant particles through a tall horizontal rectangular duct. We address two limits of the flow, namely the cases of smooth and rough side walls, corresponding to traction-free and no-slip boundary conditions on the suspension, respectively. In both cases, any solution to the system can be fully classified by the dimensionless fluid pressure gradient and the average solid fraction in the duct. In the case of smooth side walls, the flow becomes horizontally uniform, and admits semi-analytical solutions, which we compute and find asymptotic expressions for in the limits of large and small pressure gradient. We investigate the results of modifying this system with a Coulomb friction condition on the side walls. With rough side walls, the flow adopts both cross-duct and vertical dependence. We study the limit in which cross-duct shear stress dominates, and the solid fraction is nearly uniform across the duct, to avoid cross-duct buoyancy gradients, classifying all solutions. We carry out laboratory experiments with suspensions of glass beads to compare with the two models, and find more favourable qualitative agreement with the smooth-side-wall model, modified by a Coulomb friction condition.