| In this thesis we present the solutions of six different free boundary problems. Five deal with the shape of a gas bubble or liquid drop. The sixth concerns the collapse of an infinite wedge of water.;The four equilibrium problems to which we apply this method are: an axisymmetric bubble or drop in a uniform flow, an axisymmetric bubble or drop in a uniform flow with gravity, a bubble in an axially symmetric shear flow and a drop in an electric field.;The fifth problem is the collapse of a wedge of water due to surface tension. By changing to similarity variables we are able to formulate the problem in the manner of the previous problems. We solve it numerically and show the existence of surface waves on the collapsing wedge.;The last problem is the radial oscillation of a bubble in an incident sound field. We derive an equation for the oscillations which includes the effects of acoustic radiation, viscosity and surface tension. An analysis of this equation is then presented.;The first four are equilibrium free boundary problems for a harmonic potential. The potential is defined either interior to, or exterior to, a boundary on which it satisfies a nonlinear boundary condition. Each problem will be formulated as a nonlinear integro-differential system of equations for the free boundary and the potential function on it. This system will be discretized and then solved by Newton's method. When possible, analytical solutions for limiting values of the parameters will be obtained. |
