Simulation of sedimentation of bidisperse suspensions

Abstract The batch sedimentation behaviour of monodisperse suspensions can be predicted from the flux plot, but this approach is unavailable for polydisperse suspensions. However, computer simulations and shock-capturing numerical solutions are still useful. The Masliyah–Lockett–Bassoon equation, which predicts particle velocities in polydisperse suspensions, is ideally suited to computer simulations. The concentrations of the various species in each thin layer determine the mean velocity of each species there. Using these values, a deterministic simulation involving one million spheres moves each sphere a short distance in a small time-step. When all particles in each layer have been moved, concentrations are recalculated and the process continues until all particles have settled into the packed bed. These simulations mirror the features captured by sophisticated numerical solutions. Shocks are clearly visible and the upper level of the suspension contains only small spheres. Their concentration there is increased beyond its initial value (Smith effect). In reality, identical spheres do not behave identically. Their velocities vary from sphere to sphere and from time to time even when the solids concentration is constant. Thus, we use a stochastic model to incorporate the spatial and continuous temporal variability of particle velocities. This variability produces a hydrodynamic diffusion that replaces shocks by concentration gradients: both the lower and the upper interfaces are diffuse. There is an “induction period” during which the interfaces gradually form. The basic shape of the solids profile is established during this induction period and changes only slightly as the spheres move downward.

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