Concentration evolution of gas species within a collapsing bubble in a liquid medium

Abstract

In this study numerical methods are used to investigate the relationship between chemical concentration of gas species within a cavitating bubble, equilibrium radius of the gas bubble and pressure variations in the ambient liquid. For this purpose, governing equations are developed to describe the dynamic equilibrium of a bubble in a flowing fluid and mass transfer between gas and liquid phases, where it was assumed that gases undergo isothermal compression, obey the ideal gas law, Henry law. It is further assumed that the concentration of each phase within the bubble is uniform. The resulting nonlinear equations are solved using implicit Trapezoidal method with Newton iteration. Four gas species are modeled under various initial and ambient pressure variation conditions. These conditions maybe considered to represent typical cavitation events. The numerical results obtained are presented in terms of dimensionless numbers. These results indicate that chemical damage maybe an important component of cavitation surface damage, since high concentration profiles may develop within a collapsing bubble. Proposed formulation and numerical solutions are simple and cost effective to implement. The results presented in this study maybe used to benchmark experimental investigations or other more complex solutions, which are outside the scope of this study.