The equations of motion of a one-velocity, one-temperature bubbly fluid (revisited)

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Abstract
We present a continuum model for a non-dilute suspension of spheres with variable radius. To simplify the resulting equations and to stress the expansion dynamics only, we leave aside the problems of relative motion and temperature difference between the spheres and the surrounding liquid. It is shown that the state variable associated with the expansion degree of freedom is the scalar moment of momentum of the whole mixture, which is somewhat the analog of the usual angular momentum for the rotational degree of freedom. The equation of motion of this new variable leads to a non-dilute form of the Rayleigh-Plesset equation. Our simplified description of bubbly fluids involves six phenomenological functions of the bubble volume fraction. One of them is linked to the bubble resonant frequency and is attainable by sound velocity measurements. Among the five remaining functions are four viscosities. We detail their respective roles and correct a long-lived erroneous statement concerning the bulk or second viscosity of the bubbly fluid

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