Some considerations on the modeling of disperse multiphase flows by averaged equations

The first part of the paper addresses some questions concerning the interpr etation of averaged-equations descriptions of multiphase flows. A general r esult on the connection between hyperbolicity and stability is presented an d 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 ill disperse flows. Finally, the issue, of the mixture pressure in a disperse,flow is addressed, and some nondilute results obtained by means of numerical simulations are described, The Appe ndix contains a summary of a recently developed ensemble-averaging formulat ion.