Rate-limiting factors in thin-film evaporative heat transfer processes

In this paper, we present a theoretical study aimed at investigating the rate-limiting factors in thin-film evaporative heat transfer processes, considering the finite-rate evaporation kinetics. The problems of evaporation of a flat thin-film in either pure vapours or vapour-inert-gas mixtures are analysed based on the non-dimensionalised macroscopic transport equations for continuum fluids, coupled with out-of-equilibrium kinetic boundary conditions. Both the full numerical solutions and asymptotic analytical solutions at slow evaporation limit are provided and applied to analyse thin water film evaporation. Existing solutions, assuming negligible heat transfer in the gas domain, or negligible temperature jump across the non-equilibrium kinetic layer, or more boldly a thermodynamically equilibrial interface (i.e. its temperature is at the saturation temperature), can be fully recovered from the more general solutions presented here. Our results show that while these assumptions hold in special cases, they can lead to significant errors in many conditions, especially when the film thickness δ is reduced to a few micrometers or thinner. We show that the conventional views that the rate-limiting factors in thin-film evaporative heat transfer is either the heat diffusion through the liquid film or the mass transfer in the gas domain only apply to thick film (i.e. δ≫λ where λ is the mean free path in the vapour phase). As δ decreases to a few micrometer or smaller (more precisely when the Knudsen number Kn increases beyond O(1) in an pure vapour environment or when the kinetic Peclet number Pe is reduced below O(1) in inert gases), the interfacial thermal resistance due to the evaporation kinetics can be on the same orders of magnitude as the thermal resistance in the liquid film. The analysis also allow us to compare the heat transfer processes during the evaporation of a thin-film in pure vapours to those in inert gases, providing deeper insight into the effectiveness of various strategies for exploring the evaporation process in practical thermal management.