[Srh]

Hello all, I have started teaching myself about compressible flow of viscous fluids because I am interested in problems related to pollution/safety of tanks containing viscous liquid. The liquid can overflow tanks from pipes at the top at a range of speeds/Mach numbers (~incompressible to >1). It can be stratified by density. I am interested in what conditions would lead to different layers leaving the tank and the sequence the tank would empty.

I have two questions.
(1) How would I get started finding an appropriate equation of state for a bubbly polymer-type fluid? How would I calculate the contribution of bubbles to the compressibility? Is this just taking the compressibility of the bubbles and liquid and multiplying each by mass fraction? This is probably a very basic question, so advance apologies.

(2) I have not come across much information about this kind of problem, so I don't know how people might approach it or what boundary conditions they might use. Does anyone know of a good resource for this kind of problem?

Most people seem to assume incompressible for viscous liquids, but a bubbly viscous liquid could have a high Mach number. It seems like the best approach would be to use a segregated solver with pressure-velocity coupling because this would work for a range of Mach numbers (but not high Mach numbers). Does anyone know how high? I thought of simplifying the problem by only looking at motion inside the tank, not when the fluid hits the exit pipes and speeds up. This way, the Mach number would stay lower.