A rational extended thermodynamics model for bubble dynamics

  • Brini, Francesca (University of Bologna)
  • Seccia, Leonardo (University of Bologna)

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For more than a century, the mathematical modelling of gas bubbles in a liquid has become a challenging task, with a view to understanding their physical behaviour and improving their practical applications. In order to obtain analytical and numerical models that are not too computationally expensive, one commonly starts from an oversimplification of the description, with particular regard to gas dynamics. However, it is well-known that this can led to incorrect results, unable to provide accurate predictions. A further difficulty is represented by the impossibility of having direct measurements of the physical quantities related to the gas in the bubble, due to the small physical dimensions and the extreme rapidity of the phenomena involved. Usually, what is observable and measurable is the overall effect related to the oscillation of the gas volume inside the bubble or its dissolution under the action of a sound signal. Rational Extended Thermodynamics (RET) theory , as the name itself suggests, is a thermodynamic theory that extends the role of independent field variables to non-equilibrium quantities such as stress tensor, dynamic pressure and heat flux, with the aim of better describing non-equilibrium phenomena. Here, we will refer to the moment equations typical of RET to derive a model that accounts for various physical effects. We will analyse the results for different dynamic regimes related to gas bubble oscillations in liquids in the presence of an acoustic forcing.