Coupled Kinetic-Continuum Analysis of Temperature Jump Reversal During Evaporation

A.Raheem1, A.Sadaghiani1, Y.Akkus2, O.Akdag3
1University of Birmingham, Birmingham, West Midlands, UK
2Ericsson, Stockholm, Sweden
3Aselsan, Turkey
Published in 2026

Evaporation is a fundamental transport process that plays a critical role in a wide range of natural and engineering systems[1], including thermal management technologies, additive manufacturing, energy conversion devices, atmospheric processes, coating applications, particles deposition, inkjet printing, bio-medical applications, and phase-change heat transfer equipment. Despite its apparent simplicity, evaporation involves complex interactions between fluid flow, heat transfer, mass transport, and molecular-scale processes occurring at the liquid-vapour interface. The transport phenomena within the immediate vicinity of an evaporating interface deviate from local thermodynamic equilibrium, giving rise to interfacial discontinuities in temperature and vapour density. Classical kinetic theory predicts that a temperature jump should exist across the liquid-vapour interface because of the finite rate of molecular exchange between the two phases. This interfacial temperature discontinuity directly influences the evaporation mass flux and therefore plays a key role in determining evaporation and condensation coefficients. Although the existence of an interfacial temperature jump is generally accepted, its sign and magnitude remain subjects of ongoing debate. Classical kinetic models typically predict that the vapour adjacent to an evaporating interface is cooler than the liquid, resulting in a negative temperature jump. However, recent experimental, theoretical, and numerical studies have reported both positive and negative temperature jumps under different operating conditions. In particular, Chen proposed a coupled kinetic-continuum framework demonstrating that interfacial heating, cooling, and even temperature inversion can occur depending on the local transport processes within the Knudsen layer and surrounding continuum region [2-3]. The physical mechanisms responsible for these apparently contradictory observations remain incompletely understood. To understand this complex phenomenon, droplet evaporation, involving a single droplet placed on a solid surface, serves as a fundamental and well-defined platform for studying the interfacial phase-change processes. A two-dimensional axisymmetric sessile droplet evaporating in its own vapour was simulated using COMSOL Multiphysics 6.3 using multiphase flow, The droplet radius was maintained at 5 mm, which is greater than the capillary length of water (2.7 mm). Therefore, the droplet profile was governed by the Young-Laplace equation. The droplet was positioned on a thermally heated substrate under vacuum conditions. To maintain a steady-state droplet volume, the mass leaving the interface during evaporation was replenished through a narrow opening at the bottom of the substrate. Transient simulations were performed using a weakly compressible, laminar multiphase phase-change model, solving the continuity, Navier-Stokes, and energy equations, coupled with mass-flux and heat-flux boundary conditions on both the liquid and vapour sides of the interface, as proposed by Chen[2-3]. The substrate temperature was varied from 0°C to 35°C. The vapour side was maintained at a constant temperature of 26°C with a pressure ratio of 0.9. At higher substrate temperatures, the vapour side became hotter than the liquid side, whereas the opposite behaviour was observed at lower substrate temperatures due to reverse heat transfer within the vapour phase. Moreover, slight condensation was observed at higher temperatures because of density variations at the interface. Owing to the enhanced evaporation near the triple-phase contact line, the temperature discontinuity in this region was significantly greater than that observed at the droplet apex. These results improve the fundamental understanding of non-equilibrium thermal discontinuities during droplet evaporation under varying thermal conditions, and provide valuable insights for accurately predicting interfacial phase-change phenomena.

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