Derivation of the macroscopic continuum equations for multiphase flow

Macroscopic continuum equations for multiphase flow are derived from a modi fied Boltzmann equation using the Chapman-Enskog expansion technique. Phase separation and interface formation are naturally driven by an intermolecul ar interaction. At the equilibrium state, these equations reduce to previou s results of thermodynamical studies. This work provides a solid physical f oundation for the continuum descriptions of surface. tension and will be us eful for studying multiphase flow. [S1063-651X(99)03601-6].