Spin-up from rest of a mixture: numerical simulation and asymptotic theory

Abstract

Spin-up from rest of a separating fluid–particle mixture is studied. A cylindrical container, filled with a stationary mixture of initially uniform particle volume fraction, is instantaneously set into rapid rotation. The viscous forces.on the walls introduce a secondary Ekman-layer circulation which causes the fluid motion to gradually approach a state of solid-body rotation. While the mixture acquires angular momentum, separation starts under the action of the local centrifugal effects: the dispersed particles – assumed here to be lighter than the fluid – tend to concentrate around the centre, leaving behind a peculiarly shaped domain of pure fluid. This process is simulated by a finite difference version of the ‘mixture model’ equations. The numerical results are in good agreement with previous asymptotical predictions but also illuminate some aspects of the flow field that have been covered by the analytical approach.