PHASE-FIELD DESCRIPTIONS OF TWO-PHASE COMPRESSIBLE FLUID FLOW: INTERSTITIAL WORKING AND A REDUCTION TO KORTEWEG THEORY

摘要

The Navier-Stokes-Allen-Cahn (NSAC), the Navier-Stokes-Cahn-Hilliard (NSCH), and the Navier-Stokes-Korteweg (NSK) equations have been used in the literature to model the dynamics of two-phase fluids. In their previous article Phase-field and Korteweg-type models for the time-dependent flow of compressible two-phase fluids, Arch. Rational Mech. Anal. 224 (2017), 1-20, the authors showed that both NSAC and NSCH reduce to versions of NSK, when one makes the (unphysical) assumption that microforces are absent. The present paper shows that the same reduction property holds without that assumption.