An asymptotic analysis of two-phase fluid mixing

We study the motion of the slightly compressible multi-phase flow model proposed by Chen, Glimm, Sharp and Zhang. The interface velocity and constitutive law are analyzed by derivation of the exact quantity. Using singular perturbation theory, a formal asymptotic expansion is derived for the solution of the compressible equations. An asymptotic analysis in the incompressible limit, for slightly compressible flows supplies important new information to resolve nonuniqueness of the pressure difference between the two fluid species of the incompressible flow equations.Supported in part by the U.S. Department of Energy DE-FG02-90ER25084, DE-FG02-989ER2536, DE-FG03-98DP00206, the National Science Foundation DMS-0102480, the Army Research Office grant DAAD19-01-0642 and Los Alamos National Laboratory.Supported in part by the Clay Mathematics Institute.