Modelling the thermal behaviour of gas bubbles

In most cases, the dominant mechanism of energy dissipation for a bubble in volume oscillations is the thermal energy exchanged with the liquid. The process is subtle and its precise description a matter of some complexity. These features have prevented its ready incorporation in many applications, which forcedly have to rely on the rather inaccurate polytropic pressure-volume relation. This paper develops two approximate models of the thermal interaction, formulated in terms of ordinary differential equations, which can be readily added to standard Rayleigh-Plesset-Type formulations at a modest computational cost.