A Two-Phase Model of Bubbly Fluids

We use a continuum theory for multiphase immiscible mixtures whose individual components are separated by infinitesimally thin interfaces. The average balance equations for the different phases, as well as for the mixture, result from a systematic spatial averaging procedure. In addition to equations for mass, momentum, and energy, together with the entropy inequality, the balance equations also include equations for microinertia and microspin tensors. These equations, together with appropriate constitutive equations consistent with the entropy inequality, enable the modeling of immiscible multiphase materials where internal parameters are important. Here, we apply the results to a simple microstretch bubbly fluid. We show that the equations for microspin and microinertia, under a number of simplifying assumptions, combine to yield a general form of the Rayleigh-Plesset equation.