Combined gravity and mean flow effects on agitated slurries in a dead-end filtration set-up

In previous work on dense, agitated particle–fluid mixtures in a dead-end filtration set-up the gravity effects that arise from a mass density contrast between particulate and fluid phase have been neglected. As a consequence the granular temperature theory that leads to a solidosity profile can be scaled by one parameter: the ratio of the mean fluid velocity in the filter to the oscillation velocity amplitude. In the present paper the effects of gravity are included, through a term that contains the mass density contrast. The effective gravity force may be net-buoyant or net-sinking. An extra scaling parameter must be introduced, which represents the ratio of the sedimentation velocity to the dead-end filter velocity. The results of the study are reported in a parameter range (fluid velocity, amplitude of agitation, mass density contrast and particle size) that highlights the relevant physics by looking at limiting cases and is also informed by a practical work environment. The key outcome is the solids volume fraction profile in the filter.