Macroscopic limit for an evaporation–condensation problem

Abstract

We investigate the hydrodynamic limit of a vapor–noncondensable gas mixture in a pressure gradient between two walls. Earlier papers based on conventional asymptotic analysis techniques predict the emergence of a boundary layer of noncondensables which completely blocks the vapor flow (Takata and Aoki, 2001; Aoki et al., 2003). This “ghost effect” (Sone, 2007) contradicts physical intuition. In the present paper we reveal the bifurcation structure of the underlying transport operator and combine it with an appropriate macroscopic scaling. As a result, the hydrodynamic limit describes the coexistence of a streaming mode of vapor with the other component at rest thus avoiding the ghost effect.For sake of clarity, the paper restricts to a simplified setting (discrete velocity model, mechanically identical particles). However, the results also apply in more general situations.