A study on drop and bubble dynamics via a hybrid boundary element-finite element methodology

This dissertation concerns the dynamic behaviour of liquid drops and gas bubbles undergoing shape oscillations. All the interfaces considered are between a gas and a liquid and they are treated as free surfaces. Laplace's equation for the velocity potential is replaced by an integral equation giving the potential anywhere in the domain based on surface quantities. The objective of this study is to develop an efficient and robust numerical scheme that combines the boundary integral formulation for the Laplacian, with the finite element method for the kinematic and dynamic boundary conditions.;Using this methodology we first calculate equilibrium shapes and their stability for a charged conducting drop.;The inviscid oscillations of a liquid drop are studied as a test problem for the efficiency of the hybrid boundary-finite element method, as well as the behaviour of the integral formulation in dynamic simulations.;It has been shown experimentally that water drops with injected air bubbles inside them may be forced dynamically to assume the spherosymmetric shape. Calculations show that besides the fast oscillation of the shell due to the initial disturbance, a slow oscillatory motion of the centres of the bubble and the drop is induced around the concentric configuration.;The attractive or repulsive motion of two pulsating bubbles is studied, depending on whether they oscillate in or out of phase respectively. The same numerical method is used to examine the response of two spherical bubbles to two different initial disturbances. When a step change in the pressure at infinity is applied they are always found to attract each other. As time increases, they develop spherical-cap shapes. They eventually break up through a Rayleigh-Taylor type of instability.;When the pressure at infinity is oscillatory the two bubbles are found to repel each other when the frequency of the pressure variation lies between the two eigen-frequencies. Otherwise the force between them is attractive. (Abstract shortened with permission of author.).