Symmetry breaking due to surface tension and geometry

Multiphase flows occur in an enormous variety of fluid mechanics situations. The influence of surface tension at the fluid-fluid interface can be the driver for symmetry breaking, as has been demonstrated in many cases in the literature. In this talk I give recent examples of our studies of free surface flows where the concepts of symmetry, symmetry breaking, and self-similarity occur and possibly intersect. In particular, I will discuss (1) the manner in which the geometry of an ordinary pressure-driven channel flow can influence, and control,  viscous fingering instabilities, (2) the case of a ``lifted” Hele-Shaw cell, where time-dependent strategies  can either suppress the viscous fingering instability or maintain a series of non-splitting viscous fingers during the displacement process, and (3) a three-dimensional film drainage flow  where an underlying structure of the partial differential equation for the film shape allows a transformation from three independent variables to a single variable, and the solution of the corresponding ordinary differential equation is in excellent agreement with experimental measurements.