Some Considerations on the Modeling of Disperse Multiphase Flows by Averaged Equations

The first part of the paper addresses some questions concerning the interpretation of averaged-equations descriptions of multiphase flows. A general result on the connection between hyperbolicity and stability is presented and its implications discussed. Exact expressions for the momentum equations applicable to dilute suspensions of spheres in potential flow and in Stokes flow are then presented. These results are only accurate to first order in the disperse-phase volume fraction, but they are nevertheless valuable due to the paucity of exact relations in disperse flows. Finally, the issue of the mixture pressure in a disperse flow is addressed, and some non-dilute results obtained by means of numerical simulations are described. The Appendix contains a summary of a recently developed ensemble-averaging formulation.