Knudsen-Layer Non-Equilibrium in One-Dimensional Pure-Argon Evaporation and Condensation Across the Rarefaction Range: A Unified Gas-Kinetic Scheme Study

Evaporation and condensation at liquid–vapour interfaces are governed by Knudsen layers, where the molecular velocity distribution departs from equilibrium. In these layers, unequal normal and transverse kinetic energies create kinetic temperature anisotropy that local-equilibrium models cannot capture. This non-equilibrium structure causes temperature-gradient inversion and evaporative refrigeration, in which vapour temperature can fall below the cold wall temperature. Using an asymptotic-preserving Unified Gas Kinetic Scheme with phase-change boundary conditions, this study examines phase-change transport in a standard 1D pure-argon benchmark across the free-molecular to near-continuum regimes. Under strong driving, the Schrage relation and linearised Navier–Stokes over-predict evaporation rates by more than 17%, whereas the Moment Method remains within 15%. Based on this 1D pure-argon setup, the results show that kinetic temperature anisotropy is the common microscopic origin of inversion, refrigeration, and reduced-model failure, and that these effects strengthen as rarefaction increases.