A Reduced-Order Model of Heat Transfer Effects on the Dynamics of Bubbles

Abstract

The Rayleigh-Plesset equation has been used extensively to model spherical bubble dynamics, yet it has been shown that it cannot correctly capture damping effects due to mass and thermal diffusion. Radial diffusion equations may be solved for a single bubble, but these are too computationally expensive to implement into a continuum model for bubbly cavitating flows since the diffusion equations must be solved at each position in the flow. The goal of the present research is to derive reduced-order models that account for thermal and mass diffusion. We present a model that can capture the damping effects of the diffusion processes in two ODE’s, and gives better results than previous models.

20 years of ultrasound contrast agent modeling

“…Thermal damping is often neglected in the rP equation [57]. For the time-dependent nonlinear oscillations of bubbles, thermal damping requires rigorous treatments that are not easily incorporated (e.g., [58]- [60]), which is one of the reasons it is often neglected or replaced by a thermal viscosity (e.g., [61]). However, it should be noted that this might not always be valid.…”