A new formulation and analysis of a collapsing bubble with different content in a liquid induced during acoustic cavitation

Abstract

Purpose – The purpose of this paper is to present numerical investigation of the gas/vapor bubble dynamics under the influence of an ultrasonic field to give a more comprehensive understanding of the phenomenon and present new results Design/methodology/approach – In order to formulate the mathematical model, a set of governing equations for the gas inside the bubble and the liquid surrounding it are used. All hydrodynamics forces acting on the bubble are considered in the typical solution. The systems of equations required to be solved consist of ordinary and partial differential equations, which are both nonlinear and time dependent equations. A fourth order Runge-Kutta method is applied to solve the ordinary differential equations. On the other hand, the finite difference method is employed to solve the partial differential equations and a time-marching technique is applied. Findings – The numerical model which is developed in the current study permits a correct prediction of the bubble behavior and its characteristics in an acoustic field generated at this occasion. Originality/value – Previous studies considering numerical simulations of an acoustic bubble were performed based on the polytropic approximation or pressure uniformity models of the contents inside the bubble. In this study, an enhanced numerical model is developed to study the acoustic cavitation phenomenon and the enhancement concerns taking into account both the pressure and temperature gradients inside the bubble as well as heat transfer through the bubble surface into account which is very important to obtain the temperature of the liquid surrounding the bubble surface.