Here is an interesting article (and video) on the shrinking instability of toroidal droplets. Toroidal droplets are inherently unstable due to surface tension and seek to minimise their surface area for a given volume: i.e. they want to transform into spherical droplets. Using PIV, they experimentally determine the internal flow field as the droplets shrink and observe that the cross-sections significantly deviate from circular during the process, flattening in the inside regions of the torus. By measuring the experimental velocities at the droplet boundary, which have both tangential and radial components, these observations are then accounted for by theoretically solving the Stokes equations using the stream function in toroidal coordinates.