A PLANE INVISCID INCOMPRESSIBLE BUBBLE PLACED WITHIN A CREEPING VISCOUS-FLOW - FORMATION OF A CUSPED BUBBLE

The shape of a plane bubble placed within a creeping viscous flow is a nalysed using complex variable techniques. When the dominant velocity at infinity is a polynomial, a general procedure for construction of e xplicit steady solutions is presented. It is proved that, if a steady solution exists, the conformal mapping of the unit disc of a parametri c plane onto the flow domain must be a rational function with coeffici ents satisfying a system of transcendental equations. Formation of a c usped bubble placed within a straining flow consisting of a combinatio n of linear and cubic velocity fields, is studied. Depending on the cu bic terms, two types of solutions are found which model the regimes of cusping and bursting of a bubble.