A bathtub vortex is usually formed at the axis of a drain. In the presence of such a vortex, gravity separation of solid impurities lighter than the embedding fluid is counteracted by centrifugal separation and viscous resuspension. Both mechanisms are responsible for the agglomeration of impurities at the axis of the vortex. From there the impurities are easily sucked into the outlet.
In the investigated case, a viscous fluid with a given initial rotation is spinning down in a container with endplates both at the bottom and the top. The amount of fluid withdrawn through a circular hole in the center of the vortex is constantly replaced by a radial influx.
The resulting time-dependent flow was solved by means of a finite difference method taking into account the influence of Ekman layers at the bottom and the top. Subsequently, the process of centrifugal separation of particles lighter than the embedding fluid was studied according to the aforementioned flow field. The results were compared with the particle motion in a classical Oseen vortex. For a simplified case an analytical solution was derived and compared with the corresponding numerical solution. Both results were found to be in good agreement.