Viscous flows with time-dependent free boundaries in a non-planar Hele-Shaw cell

The dynamics of blobs of viscous fluid in a non-planar Hele-Shaw cell is considered. The general approach developed by Richardson and some of the resulting analytic techniques are extended to flows in non-planar cells, including ce:ils shaped as surfaces of revolution and helical surfaces. An example related to the development and coalescence of two initially separated blobs in a cell on a spherical surface is presented. Some applications to mathematically equivalent problems dealing with planar Hele-Shaw cells with a non-uniform gap and flows through porous media are also discussed.