Beyond Bagnold: Rheological measurements of inertial suspensions

Since the seminal study by Bagnold in 1954, which was inspired by sand movement in the desert and sediment transport in rivers, researchers have continued to investigate inertial and collisional effects in flows of non-Brownian suspensions. This paper overviews several post-Bagnold experimental studies on neutrally-buoyant suspensions that focused on measuring the suspension effective viscosity for conditions in which the particle Reynolds number was greater than 1, Re-p > 1. Similar to what was found with Bagnold's experiments, secondary flows and end-wall vortices impact the rheological measurements especially as the rotational speed is increased. Recent experiments using a specialized rheometer that decreases the effect of end vortices demonstrate that the inertial contribution to the effective viscosity increases with a Reynolds number based linearly on particle diameter, Re-d. The magnitude of the increase, however, is modest with a doubling in the inertial viscosity as Re-d increases from 1 to 500. Larger contributions from inertial and collisional stresses are expected for the flows originally considered by Bagnold - inertial flows involving particles denser than the surrounding fluid.