On the viscous flows of leak-out and spherical cap natation

摘要: This paper deals with the hydrodynamics of a viscous liquid passing through hole in deflating hollow sphere. I employ method complementary integrals and calculate closed form pressure streamfunction for axisymmetric, creeping motion coming from changes radius. The resulting flow fields describe deformable spherical cap environment, where deformations include size cap, translation body along axis symmetry. calculations yield explicit expressions jumps resistance coefficients combined deformations. equation force shows that freely suspended is able to propel as an active swimmer. expression contains classic Sampson rate limiting case, but simulations show must also account velocity widening correctly predict outflow rates physiology. Movies based on closed-form solutions visualize pressures part physical processes.