Compressibility Consideration in the Boundary of a Strongly Collapsing Bubble

Abstract

Equations of radial motion of a gas bubble in a compressible viscous liquid have been modified to account for compressibility at the bubble boundary. A new bubble boundary equation has been derived, including a new term resulted from liquid compressibility. The influence of this term has been numerically investigated using isothermal-adiabatic model for the gas inside the bubble. The results clearly indicate that, at the end of the collapse, the new term has a very significant role and its consideration dramatically changes the bubble characteristics. Moreover, the more intense the collapse is, the more significant the effect of the new term is. Also, it has been reasoned out that, the influence of the new term will be established even when the effects of mass (water vapor) exchange, chemical reactions, and gas dynamics inside the bubble are taken into account.