Theoretical comparison of some models for thermal process inside oscillating multiple bubbles

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Several models have been proposed to describe thermal processes at gas pressure inside bubble. Recently, the comparison of three typical models was performed for the case of single bubble (Sojahrood et al., 2020): Model A approximates the effect of thermal damping by adding an artificial viscosity to the viscosity of liquid surrounding the bubble and is widely used for the case of shell-coated bubbles. Model B is a model that includes the average temperature rise within the bubble and the heat loss at the bubble boundary; this makes it more accurate by taking into account the pressure dependence that was ignored in Model A. Futhermore, Model C is based on the assumption of polytropic process. In this study, we extend the findings of Models A, B, and C from the case of a single bubble to the case of multiple bubbles (i.e., bubbly flow). The nonlinear propagation of ultrasound in bubbly flow is theoretically investigated based on singular perturbation method up to a second order of approximation. As a result, a nonlinear evolution equation is obtained; the differences among Models A, B, and C are summarized in the coefficients. The details of the differences will be explained in a presentation.