Gravitational–centrifugal separation in an axisymmetric source–sink flow with a free surface

The inward source–sink flow of a dilute suspension with an upper free surface, in a cylinder with a horizontal solid bottom rotating about a vertical axis is analysed theoretically. The problem is made unique for the prescribed volume flux and outer radius by the requirement that the height of the interface at the outlet (drain) radius is minimal. A small Ekman number of the global flow and small Taylor and Reynolds numbers for the flow around the dispersed particles are assumed. The steady-state flow-field in the mixture bulk is described by an inviscid shallow water approximation. In addition, the influence of the horizontal shear layer at the bottom is incorporated by an Ekman-layer correlation. It turns out that in the investigated inward flow configuration, around the drain a domain may develop where the entire transport is performed by the Ekman layer. Theoretical predictions for the height of the fluid at the outer wall (position of the source) for various angular velocities are found to agree well with experimental results obtained earlier. The dispersed particles, assumed lighter than the fluid, separate from the main flow as a result of gravitational and centrifugal buoyancy. The numerical solution of the particle transport equation surprisingly shows that the concentration of the particles increases with the radius and, as expected, indicates the formation of a densely packed layer of particles on the top of the suspension.