Evaporation from arbitrary nanoporous membrane configurations: An effective evaporation coefficient approach

Abstract

Thin-film evaporation from nanoporous membranes is a promising cooling technology employed for the thermal management of modern electronic devices. We propose an effective one-dimensional analytical approach that can accurately predict the temperature and density jump relations, and evaporation rates, for arbitrary nanoporous membrane configurations. This is accomplished through the specification of an effective evaporation coefficient that encompasses the influence of different system parameters, such as porosity, meniscus shape, evaporation coefficient, and receding height. Our proposed approach can accurately predict all the typical output evaporation parameters of interest like mass flux, and temperature and density jumps, without the need to carry out computationally demanding numerical simulations. Several exemplar cases comprising of nanoporous configurations with a wide range of parameters have been considered to demonstrate the feasibility and accuracy of this analytic approach. This work thus enables a quick, efficient, and accurate means of aiding the design and engineering analysis of nanoporous membrane-based cooling devices.

Theoretical and numerical study of nanoporous evaporation with receded liquid surface: effect of Knudsen number

“…Under such conditions, the boundary slip effects (Karniadakis et al 2005a) or the inner friction force between molecules may add to the two-dimensional feature. John et al (2021) reported the existence of Moffatt eddies near the top pore wall at a lower porosity (0.25) and Kn (0.05). They concluded that the one-dimensionality of vapour flow tends to break down with small porosity and low Kn.…”

“…Boundary 4 is simply a specular surface which does not affect the evaporation process. The boundary 5 is set in such a way that vapour near 5 has a macroscopic speed u ∞ (John et al 2021;Wu et al 2001). Since the evaporation problem has only one independent variable, we control the evaporation rate through u ∞ and the results of ρ ∞ and T ∞ will be outputs of the DSMC simulation.…”

“…Their findings are consistent with our results, which indicate the difficulty in modelling nanoporous evaporation with small porosity and high vapour densities. We also note that John et al (2021) employed a plane two-dimensional geometry for simulation, while the present work utilizes an axisymmetric domain which better reflects the shape of nanopores.…”

“…Particularly, they calculated the pore transmissivity using Berman's correlation (Berman 1965) to account for the vapour flow resistance in pores. John et al (2019John et al ( , 2021 investigated the nanoporous evaporation by direct simulation Monte Carlo (DSMC) and provided an effective evaporation coefficient approach to handling the nanoporous evaporation using the solution of half-space evaporation problems. Li, Wang & Xia (2021b) introduced the transitional gas flow formulation into the calculation of vapour flow resistance and extended the nanoporous evaporation model to a wider range of Knudsen numbers.…”

“…The significance of studying evaporation from a receded liquid meniscus could be multifaceted. In electronics cooling, the receded meniscus is undesirable because it aggravates the risk of dry out (John et al 2021). Studying the evaporation kinetics of a receded meniscus thus assists in understanding the mechanism of performance degradation when the capillary force fails to balance the viscous pressure drop.…”