Interfacial Transport of Evaporating Water Confined in Nanopores

Abstract

A semianalytical, continuum analysis of evaporation of water confined in a cylindrical nanopore is presented, wherein the combined effect of electrostatic interaction and van der Waals forces is taken into account. The equations governing fluid flow and heat transfer between liquid and vapor phases are partially integrated analytically, to yield a set of ordinary differential equations, which are solved numerically to determine the flow characteristics and effect on the resulting shape and rate of evaporation from the liquid-vapor interface. The analysis identifies three important parameters that significantly affect the overall performance of the system, namely, the capillary radius, pore-wall temperature, and the degree of saturation of vapor phase. The extension of meniscus is found to be prominent for smaller nanoscale capillaries, in turn yielding a greater net rate of evaporation per unit pore area. The effects of temperature and ambient vapor pressure on net rate of evaporation are shown to be analogous. An increase in pore-wall temperature, which enhances saturation pressure, or a decrease in the ambient vapor pressure result in enhancing the net potential for evaporation and increasing the curvature of the interface.

Effect of nanostructures on heat transfer coefficient of an evaporating meniscus

“…Modeling of heat transfer in an evaporating thin film was pioneered by Wayner et al [23], where the role of disjoining pressure in both liquid delivery and evaporation suppression was identified. A thin film evaporation model was further developed to include the effects of slip boundary [24], thermocapillary [24,25], electrostatic on disjoining pressure [25], heat conduction through thin film [25][26][27], and capillary suppression [27,28]. Wang et al [27] analyzed the evaporation of a meniscus in nanochannels and found that the evaporating thin film region (from the non-evaporating film to the location of film thickness $1 lm) accounts for more than 50% of the total heat transfer.…”

“…Wang et al [27] analyzed the evaporation of a meniscus in nanochannels and found that the evaporating thin film region (from the non-evaporating film to the location of film thickness $1 lm) accounts for more than 50% of the total heat transfer. Narayanan et al [25] showed that the electrostatic disjoining pressure elongates the thin film region and increases the total evaporation rate. Despite their proven success, to the best of authors' knowledge, existing thin film evaporation models have been developed based on planar surfaces where the effects of nanostructures on disjoining pressure, capillary pressure, heat conduction, and thus the overall heat transfer performance are not accounted for.…”

“…It is important to note that the Kapitza resistance at a water-gold interface is $10 À8 m 2 K/W [31,32], equivalent to the conduction resistance of a 10 nm water film. As the non-evaporating water film becomes as thin as a few nanometers [25], the Kapitza resistance, which is significantly affected by nanostructures, becomes nontrivial [32,33]. Molecular dynamic (MD) simulations have become a powerful tool to investigate nanoscale heat transfer, including disjoining pressure [34] and Kapitza resistance [32].…”

Design and Modeling of Membrane-Based Evaporative Cooling Devices for Thermal Management of High Heat Fluxes

“…We denote ξ as the velocity distribution function to yield the mass of molecules dm in a unit volume at a certain velocity u, so that dm = ξ d 3 u. The distribution of molecules emitted out of the nanopore is given by the half Maxwellian [18,29,35]:…”

Scaling regimes of thermocapillarity-driven dynamics of confined long bubbles: Effects of disjoining pressure

“…D espite the w idespread applicability o f the abovem entioned balance criterion, a severe breakdow n o f the notion is inevitable when the thickness o f the liquid region separating the bubble from the channel surface reaches an ultrathin dim ension [9][10][11][12]. U nder such conditions, the length scales in purview dem and an additional accounting o f certain m olecular level interactions, m anifested as the disjoiningpressure contribution in continuum scale [13][14][15][16][17], Interest ingly, for therm ocapillary m igration o f confined long bubbles, prevalence o f such an ultrathin separating region is inevitable for the lim itingly small m agnitude o f the im posed M arangoni stress.…”