Bubble dynamics in a compressible liquid. Part 1. First-order theory

Abstract

The radial dynamics of a spherical bubble in a compressible liquid is studied by means of a simplified singular-perturbation method to first order in the bubble-wall Mach number. It is shown that, at this order, a one-parameter family of approximate equations for the bubble radius exists, which includes those previously derived by Herring and Keller as special cases. The relative merits of these and other equations of the family are judged by comparison with numerical results obtained from the complete partial-differential-equation formulation by the method of characteristics. It is concluded that an equation close to the Keller form, but written in terms of the enthalpy of the liquid at the bubble wall, rather than the pressure, is most accurate, at least for the cases considered of collapse in a constant-pressure field and collapse driven by a Gaussian pressure pulse. A physical discussion of the magnitude and nature of compressibility effects is also given.

A reduced-order model of diffusive effects on the dynamics of bubbles

“…Several assumptions are made at the outset: ͑i͒ The liquid is incompressible; ͑ii͒ the gas-vapor mixture is a perfect gas; ͑iii͒ Fourier's law for heat conduction in liquid and gas; ͑iv͒ Fick's law of mass diffusion for the noncondensible gas in the liquid and for the interdiffusion of vapor and gas inside the bubble; ͑v͒ constant transport properties, liquid density, and surface tension; ͑vi͒ constant transport properties for the gas; ͑vii͒ thermal equilibrium at the gas-liquid interface; and ͑viii͒ Henry's law at the gas-liquid interface. We note that there are alternatives to some of these assumptions, for example the first-order correction for liquid compressibility 5 and van der Waals equation of state for the gas. 6 However, we neglect these higher-order effects, since the focus of this paper is on modeling the impact of heat and mass transfer on bubble dynamics, rather than all possible competing effects.…”

Enhancement of heat and mass transfer by cavitation

“…Keller and Miksis [11] further considered the retarded time in the equations. Prosperetti and Lezzi [12,13] explored the connections between various models and built a more sophiscated model for bubble motion. This equation of bubble motion coupled with heat and mass transfer equation around bubbles are the main equations to be solved for bubble dynamics.…”

Nonlinear oscillations following the Rayleigh collapse of a gas bubble in a linear viscoelastic (tissue-like) medium

“…The dynamics of a single spherical gas bubble in an infinite body of compressible viscoelastic material are considered based on the Keller-Miksis equation [31][32][33] …”