Convective sedimentation of colloidal particles in a bowl

A physical model, which regards a colloidal dispersion as a single fluid continuum, is used to investigate cellular convection accompanying gravitational sedimentation in a hemispherical bowl with a thin cylindrical shaft along its vertical axis of symmetry. We have adapted the stream- function-vorticity form of the Navier-Stokes equations to describe momentum conservation in axially symmetric containers. These hydrodynamic equations have been coupled to the mass balance equation for binary hydrodynamic diffusion in the presence of a vertical gravitational field. Using finite- element software we have solved the equations governing coupled diffusive and hydrodynamic flow. A rapidly intensifying horizontal toroidal vortex develops around the axis of the bowl. This vortex is characterized by downward barycentric flow along the curved surface of the bowl and upward flow in the vicinity of its axis. We find that after a short period of time this large- scale cellular convection associated with the curved boundary of the bowl greatly enhances the rate of sedimentation.