Analytical solution of Taylor circulation in a prolate ellipsoid droplet in the frame of 2D Stokes equations. (2nd November 2019) - Makeev, Ilya V.; Popov, Igor Yu.; Abiev, Rufat Sh.
Graphical abstract: Analytical solution of Taylor circulation in microchannel in a prolate ellipsoid droplet for the case of one pair of vortices (left) and three pairs of vortices (right). Highlights: Additional vortices are formed near both ends of the droplet in Taylor flow. 2D Analytical solutions can be used as a benchmark for Taylor flow model testing. Streamlines of 2D analytical solution are similar to the 3D numerical solution. Abstract: Exact solutions for the biharmonic Stokes equation for the stream function of the Stokes flow were obtained for the prolate ellipsoid which mimics the shape of an elongated Taylor bubble or droplet in two-phase gas-liquid or liquid-liquid flow in microchannels. The Obtained results demonstrate good qualitative agreement with data available in the published papers: two main vortices along the droplet plus two secondary vortices near both ends of the droplet.