Expressions for the Evaporation and Condensation Coefficients in the Hertz-Knudsen Relation

Exploring Anomalous Fluid Behavior at the Nanoscale: Direct Visualization and Quantification via Nanofluidic Devices

Nanofluidics is the study of fluids under nanoscale confinement, where small-scale effects dictate fluid physics and continuum assumptions are no longer fully valid. At this scale, because of large surface-area-to-volume ratios, the fluid interaction with boundaries becomes more pronounced, and both short-range steric/hydration forces and long-range van der Waals forces and electrostatic forces dictate fluid behavior. These forces lead to a spectrum of anomalous transport and thermodynamic phenomena such as ultrafast water flow, enhanced ion transport, extreme phase transition temperatures, and slow biomolecule diffusion, which have been the subject of extensive computational studies. Experimental quantification of these phenomena was also enabled by the advent of nanofluidic technology, which has transformed challenging nanoscale fluid measurements into facile optical and electrical recordings. Our groups' focus is to investigate nanoscale (2 to 10³ nm) fluid behaviors in the context of fluid mechanics and thermodynamics through the development of novel nanofluidic tools, to examine the applicability of classical equations at the nanoscale, to identify the source of deviations, and to explore new physics emerging at this scale. In this Account, we summarize our recent findings regarding liquid transport, vaporization, and condensation of nanoscale-confined liquids. Our study of nanoscale water transport identified an additional resistance in hydrophilic nanochannels, attributed to the reduced cross-sectional area caused by the formation of an immobile hydration layer on the surfaces. In contrast, a reduction in flow resistance was discovered in graphene-coated hydrophobic nanochannels, due to water slippage on the graphene surface. In the context of vaporization, the kinetic-limited evaporation flux was measured and found to exceed the classical theoretical prediction by an order of magnitude in hydrophilic nanochannels/nanopores as a result of the thin film evaporation outside of the apertures. This factor was eliminated by modifying the hydrophobicity of the aperture's exterior surface, enabling the identification of the true kinetic limits inside nanoconfinements and a crucial confinement-dependent evaporation coefficient. The transport-limited evaporation dynamics was also quantified, where experimental results confirmed the parallel diffusion-convection resistance model in both single nanoconduits and nanoporous systems at high accuracy. Furthermore, we have extended our studies to different aspects of condensation in nanoscale-confined spaces. The initiation of condensation for a single-component hydrocarbon was observed to follow the Kelvin equation, whereas for hydrocarbon mixtures it deviated from classical theory because of surface-selective adsorption, which has been corroborated by simulations. Moreover, the condensation dynamics deviates from the bulk and is governed by either vapor transport or liquid transport depending on the confinement scale. Overall, by using novel nanofluidic devices and measurement strategies, our work explores and further verifies the applicability of classical fluid mechanics and thermodynamic equations such as the Navier-Stokes, Kelvin, and Hertz-Knudsen equations at the nanoscale. The results not only deepen our understanding of the fundamental physical phenomena of nanoscale fluids but also have important implications for various industrial applications such as water desalination, oil extraction/recovery, and thermal management. Looking forward, we see tremendous opportunities for nanofluidic devices in probing and quantifying nanoscale fluid thermophysical properties and more broadly enabling nanoscale chemistry and materials science.

Unveiling Heterogeneity of Interfacial Water through the Water Bending Mode

The water bending mode provides a powerful probe of the microscopic structure of bulk aqueous systems because its frequency and spectral line shape are responsive to the intermolecular interactions. Furthermore, interpreting the bending mode response is straightforward, as the intramolecular vibrational coupling is absent. Nevertheless, bending mode has not been used for probing the interfacial water structure, as it has been yet argued that the signal is dominated by bulk effects. Here, through the sum-frequency generation measurement of the water bending mode at the water/air and water/charged lipid interfaces, we demonstrate that the bending mode signal is dominated not by the bulk but by the interface. Subsequently, we disentangle the hydrogen-bonding of water at the water/air interface using the bending mode frequency distribution and find distinct interfacial hydrogen-bonded structures, which can be directly related to the interfacial organization of water. The bending mode thus provides an excellent probe of aqueous interfacial structure.

Transport phenomena in the Knudsen layer near an evaporating surface

Using the combination of the kinetic theory of gases (KTG), Boltzmann transport equation (BTE), and molecular dynamics (MD) simulations, we study the transport phenomena in the Knudsen layer near a planar evaporating surface. The MD simulation is first used to validate the assumption regarding the anisotropic velocity distribution of vapor molecules in the Knudsen layer. Based on this assumption, we use the KTG to formulate the temperature and density of vapor at the evaporating surface as a function of the evaporation rate and the mass accommodation coefficient (MAC), and we use these vapor properties as the boundary conditions to find the solution to the BTE for the anisotropic vapor flow in the Knudsen layer. From the study of the evaporation into a vacuum, we show the ratio of the macroscopic speed of vapor to the most probable thermal speed of vapor molecules in the flow direction will always reach the maximum value of sqrt[1.5] at the vacuum boundary. The BTE solutions predict that the maximum evaporation flux from a liquid surface at a given temperature depends on both the MAC and the distance between the evaporating surface and the vacuum boundary. From the study of the evaporation and condensation between two parallel plates, we show the BTE solutions give good predictions of transport phenomena in both the anisotropic vapor flow within the Knudsen layer and the isotropic flow out of the Knudsen layer. All the predictions from the BTE are verified by the MD simulation results.

A unified relationship for evaporation kinetics at low Mach numbers

We experimentally realized and elucidated kinetically limited evaporation where the molecular gas dynamics close to the liquid–vapour interface dominates the overall transport. This process fundamentally dictates the performance of various evaporative systems and has received significant theoretical interest. However, experimental studies have been limited due to the difficulty of isolating the interfacial thermal resistance. Here, we overcome this challenge using an ultrathin nanoporous membrane in a pure vapour ambient. We demonstrate a fundamental relationship between the evaporation flux and driving potential in a dimensionless form, which unifies kinetically limited evaporation under different working conditions. We model the nonequilibrium gas kinetics and show good agreement between experiments and theory. Our work provides a general figure of merit for evaporative heat transfer as well as design guidelines for achieving efficient evaporation in applications such as water purification, steam generation, and thermal management.

Evaporation plays a key role in applications such as cooling and desalination. Here, the authors experimentally demonstrated a unifying relationship between dimensionless flux and driving potential for evaporation kinetics under different working conditions.

Edges facilitate water evaporation through nanoporous graphene

Understanding molecular processes of evaporation at the liquid-vapor interfaces is of critical importance for development of phase-change-related applications. The interfacial behaviors are defined by liquid-vapor equilibrium following thermodynamic rules, while the process through nanopores can be modulated by spatial confinement and intermolecular interaction with the pore. Based on molecular dynamics simulations, we explore water evaporation across nanoporous graphene membranes, which have been recently fabricated by, for example, ion or beam irradiation. The simulation results suggest that the molecular outflow can be facilitated by the graphene edges, boosting the overall evaporative flux by more than 100%. Free-energy analysis shows that the affinity of the graphene edge for water molecules provides a 'hub'-like function in the path of molecular effusion, reducing the free energy barrier for evaporation across the liquid-vapor interface. This prominent edge effect can be further engineered by modifying the atomic charges. Our findings demonstrate the feasibility of nanoengineering for the liquid-vapor phase-change processes using nanoporous graphene as a model system, which can find applications in heat transfer and energy conversion with high efficiency.

Atomic Scale Interfacial Transport at an Extended Evaporating Meniscus

Recent developments in fabrication techniques have enabled the production of nano- and Ångström-scale conduits. While scientists are able to conduct experimental studies to demonstrate extreme evaporation rates from these capillaries, theoretical modeling of evaporation from a few nanometers or sub-nanometer meniscus interfaces, where the adsorbed film, the transition film, and the intrinsic region are intertwined, is absent in the literature. Using the computational setup constructed, we first identified the detailed profile of a nanoscale evaporating interface and then discovered the existence of lateral momentum transport within and associated net evaporation from adsorbed liquid layers, which are long believed to be at the equilibrium established between equal rates of evaporation and condensation. Contribution of evaporation from the adsorbed layer increases the effective evaporation area, reducing the excessively estimated evaporation flux values. This work takes the first step toward a comprehensive understanding of atomic/molecular scale interfacial transport at extended evaporating menisci. The modeling strategy used in this study opens an opportunity for computational experimentation of steady-state evaporation and condensation at liquid-vapor interfaces located in capillary nanoconduits.

Ultrafast Diameter-Dependent Water Evaporation from Nanopores

Evaporation from nanopores plays an important role in various natural and industrial processes that require efficient heat and mass transfer. The ultimate performance of nanopore-evaporation-based processes is dictated by evaporation kinetics at the liquid-vapor interface, which has yet to be experimentally studied down to the single nanopore level. Here we report unambiguous measurements of kinetically limited intense evaporation from individual hydrophilic nanopores with both hydrophilic and hydrophobic top outer surfaces at 22 °C using nanochannel-connected nanopore devices. Our results show that the evaporation fluxes of nanopores with hydrophilic outer surfaces show a strong diameter dependence with an exponent of nearly -1.5, reaching up to 11-fold of the maximum theoretical predication provided by the classical Hertz-Knudsen relation at a pore diameter of 27 nm. Differently, the evaporation fluxes of nanopores with hydrophobic outer surfaces show a different diameter dependence with an exponent of -0.66, achieving 66% of the maximum theoretical predication at a pore diameter of 28 nm. We discover that the ultrafast diameter-dependent evaporation from nanopores with hydrophilic outer surfaces mainly stems from evaporating water thin films outside of the nanopores. In contrast, the diameter-dependent evaporation from nanopores with hydrophobic outer surfaces is governed by evaporation kinetics inside the nanopores, which indicates that the evaporation coefficient varies in different nanoscale confinements, possibly due to surface-charge-induced concentration changes of hydronium ions. This study enhances our understanding of evaporation at the nanoscale and demonstrates great potential of evaporation from nanopores.

The microstructural evolution of water ice in the solar system through sintering

Ice sintering is a form of metamorphism that drives the microstructural evolution of an aggregate of grains through surface and volume diffusion. This leads to an increase in the grain-to-grain contact area ("neck") and density of the aggregate over time, resulting in the evolution of its strength, porosity, thermal conductivity, and other properties. This process plays an important role in the evolution of icy planetary surfaces, though its rate and nature are not well constrained. In this study, we explore the model of Swinkels and Ashby (1981), and assess the extent to which it can be used to quantify sintering timescales for water ice. We compare predicted neck growth rates to new and historical observations of ice sintering, and find agreement to some studies at the order of magnitude level. First-order estimates of neck growth timescales on planetary surfaces show that ice may undergo significant modification over geologic timescales, even in the outer solar system. Densification occurs over much longer timescales, suggesting some surfaces may develop cohesive, but porous, crusts. Sintering rates are extremely sensitive to temperature and grain size, occurring faster in warmer aggregates of smaller grains. This suggests that the microstructural evolution of ices may vary not only throughout the solar system, but also spatially across the surface and in the near-surface of a given body. Our experimental observations of complex grain growth and mass redistribution in ice aggregates point to components of the model that may benefit from improvement, and areas where additional laboratory studies are needed.

Evaporation Mass Flux: A Predictive Model and Experiments

Evaporation is a fundamental and core phenomenon in a broad range of disciplines including power generation and refrigeration systems, desalination, electronic/photonic cooling, aviation systems, and even biosciences. Despite its importance, the current theories on evaporation suffer from fitting coefficients with reported values varying in a few orders of magnitude. Lack of a sound model impedes simulation and prediction of characteristics of many systems in these disciplines. Here, we studied evaporation at a planar liquid-vapor interface through a custom-designed, controlled, and automated experimental setup. This experimental setup provides the ability to accurately probe thermodynamic properties in vapor, liquid, and close to the liquid-vapor interface. Through analysis of these thermodynamic properties in a wide range of evaporation mass fluxes, we cast a predictive model of evaporation based on nonequilibrium thermodynamics with no fitting parameters. In this model, only the interfacial temperatures of liquid and vapor phases along with the vapor pressure are needed to predict evaporation mass flux. The model was validated by the reported study of an independent research group. The developed model provides a foundation for all liquid-vapor phase change studies including energy, water, and biological systems.

The evaporation kinetics of pure water droplets at varying drying rates and the use of evaporation rates to infer the gas phase relative humidity

Numerous analytical models have been applied to describe the evaporation/condensation kinetics of volatile components from aerosol particles for use in many applications. However, the applicability of these models for treating cases that lead to substantial and rapid changes in particle temperature due to, for example, evaporative cooling remain to be compared with measurements. We consider three typical treatments, comparing predictions of the evaporation rates of pure water droplets over a wide range in gas phase relative humidity (RH) and exploring the sensitivity of the predictions to uncertainties in the thermophysical gas and condensed-phase parameters. We also compare predictions from the three treatments to measurements of the evaporation rates of pure water droplets with varying RH using an electrodynamic balance (EDB), concluding that only two of the model treatments are sufficiently able to account for the level of evaporative cooling (typically as high as 12 K). Finally, we show that the RH can be inferred accurately from the evaporation rate of pure water droplets over the full range in accessible RH and comparison with the model predictions (within absolute uncertainties of 2.5% RH over the range 20% to 95% RH), considering the level of agreement with independent measurements made through determining the equilibrated size of aqueous sodium chloride and sodium nitrate droplets.

Simulation and Optimization of Film Thickness Uniformity in Physical Vapor Deposition

Optimization of thin film uniformity is an important aspect for large-area coatings, particularly for optical coatings where error tolerances can be of the order of nanometers. Physical vapor deposition is a widely used technique for producing thin films. Applications include anti-reflection coatings, photovoltaics etc. This paper reviews the methods and simulations used for improving thin film uniformity in physical vapor deposition (both evaporation and sputtering), covering characteristic aspects of emission from material sources, projection/mask effects on film thickness distribution, as well as geometric and rotational influences from apparatus configurations. Following the review, a new program for modelling and simulating thin film uniformity for physical vapor deposition was developed using MathCAD. Results from the program were then compared with both known theoretical analytical equations of thickness distribution and experimental data, and found to be in good agreement. A mask for optimizing thin film thickness distribution designed using the program was shown to improve thickness uniformity from ±4% to ±0.56%.

Thermodynamics of ionic liquid evaporation under vacuum

The low volatility of ionic liquids (ILs) is one of their most interesting physico-chemical properties; however, the general understanding of their evaporation dynamics under vacuum is still lagging. Here, we studied the thermodynamics of IL evaporation by employing thermogravimetry (TG) measurements under vacuum. The thermodynamic parameters of ILs, such as the evaporation onset temperatures, enthalpies, entropies, saturation vapor pressures, and boiling points were quantified by analyzing the TG data. The obtained evaporation enthalpies (110-140 kJ mol-1) were higher than those of typical molecular liquids, and the entropies (>88 J mol-1 K-1) suggested that they are exceptions of the Trouton's rule. The obtained Clausius-Clapeyron equations demonstrated that the saturation vapor pressures of ILs only depend on temperature. Further, we derived the empirical equation for estimating the upper limit temperature of the liquid phase of IL under given external pressures. Using the evaporation behaviors of referential normal alkanes and charge-transfer complex and the evaporation entropies of the ILs, the vaporized IL structure was thermodynamically modelled. The ILs were found to evaporate as ion pairs, instead of as individual ions or higher-ordered cluster structures. By comparing a series of ILs with various cations and a fixed anion, it was found that the IL evaporation dynamics under vacuum is strongly and systematically affected by their chemical structures, charge balances between the cations and the anions, molecular weights, and the higher-ordered structures including polar and non-polar regions. Our concept, measurement method, and equation can be extended to other ILs and low-volatile liquids under vacuum, and help with the design of ILs with higher thermal stabilities.

Stratification in Drying Films Containing Bidisperse Mixtures of Nanoparticles

Large scale molecular dynamics simulations for bidisperse nanoparticle suspensions with an explicit solvent are used to investigate the effects of evaporation rates and volume fractions on the nanoparticle distribution during drying. Our results show that "small-on-top" stratification can occur when Pe _sϕ _s ≳ c with c ∼ 1, where Pe _s is the Péclet number and ϕ _s is the volume fraction of the smaller particles. This threshold of Pe _sϕ _s for "small-on-top" is larger by a factor of ∼α² than the prediction of the model treating solvent as an implicit viscous background, where α is the size ratio between the large and small particles. Our simulations further show that when the evaporation rate of the solvent is reduced, the "small-on-top" stratification can be enhanced, which is not predicted by existing theories. This unexpected behavior is explained with thermophoresis associated with a positive gradient of solvent density caused by evaporative cooling at the liquid/vapor interface. For ultrafast evaporation the gradient is large and drives the nanoparticles toward the liquid/vapor interface. This phoretic effect is stronger for larger nanoparticles, and consequently the "small-on-top" stratification becomes more distinct when the evaporation rate is slower (but not too slow such that a uniform distribution of nanoparticles in the drying film is produced), as thermophoresis that favors larger particles on the top is mitigated. A similar effect can lead to "large-on-top" stratification for Pe _sϕ _s above the threshold when Pe _s is large but ϕ _s is small. Our results reveal the importance of including the solvent explicitly when modeling evaporation-induced particle separation and organization and point to the important role of density gradients brought about by ultrafast evaporation.

Modeling solvent evaporation during thin film formation in phase separating polymer mixtures

Preparation of thin films by dissolving polymers in a common solvent followed by evaporation of the solvent has become a routine processing procedure. However, modeling of thin film formation in an evaporating solvent has been challenging due to a need to simulate processes at multiple length and time scales. In this work, we present a methodology based on the principles of linear non-equilibrium thermodynamics, which allows systematic study of various effects such as the changes in the solvent properties due to phase transformation from liquid to vapor and polymer thermodynamics resulting from such solvent transformations. The methodology allows for the derivation of evaporative flux and boundary conditions near each surface for simulations of systems close to the equilibrium. We apply it to study thin film microstructural evolution in phase segregating polymer blends dissolved in a common volatile solvent and deposited on a planar substrate. Effects of the evaporation rates, interactions of the polymers with the underlying substrate and concentration dependent mobilities on the kinetics of thin film formation are studied.

Capillary Condensation in 8 nm Deep Channels

Condensation on the nanoscale is essential to understand many natural and synthetic systems relevant to water, air, and energy. Despite its importance, the underlying physics of condensation initiation and propagation remain largely unknown at sub-10 nm, mainly due to the challenges of controlling and probing such small systems. Here we study the condensation of n-propane down to 8 nm confinement in a nanofluidic system, distinct from previous studies at ∼100 nm. The condensation initiates significantly earlier in the 8 nm channels, and it initiates from the entrance, in contrast to channels just 10 times larger. The condensate propagation is observed to be governed by two liquid-vapor interfaces with an interplay between film and bridging effects. We model the experimental results using classical theories and find good agreement, demonstrating that this 8 nm nonpolar fluid system can be treated as a continuum from a thermodynamic perspective, despite having only 10-20 molecular layers.

Simple scaling laws for the evaporation of droplets pinned on pillars: Transfer-rate- and diffusion-limited regimes

The evaporation of droplets can give rise to a wide range of interesting phenomena in which the dynamics of the evaporation are crucial. In this work, we find simple scaling laws for the evaporation dynamics of axisymmetric droplets pinned on millimeter-sized pillars. Different laws are found depending on whether evaporation is limited by the diffusion of vapor molecules or by the transfer rate across the liquid-vapor interface. For the diffusion-limited regime, we find that a mass-loss rate equal to 3/7 of that of a free-standing evaporating droplet brings a good balance between simplicity and physical correctness. We also find a scaling law for the evaporation of multicomponent solutions. The scaling laws found are validated against experiments of the evaporation of droplets of (1) water, (2) blood plasma, and (3) a mixture of water and polyethylene glycol, pinned on acrylic pillars of different diameters. These results shed light on the macroscopic dynamics of evaporation on pillars as a first step towards the understanding of other complex phenomena that may be taking place during the evaporation process, such as particle transport and chemical reactions.

The Effect of Menisci on Kinetic Analysis of Evaporation for Molten Alkali Metal Salts (CsNO3, CsCl, LiCl, and NaCl) in Small Cylindrical Containers

Using isothermal thermogravimetric data of alkali metal salts (CsNO3, CsCl, LiCl, and NaCl), we conducted kinetic analysis on atmospheric evaporation to investigate the effect of meniscus on determining the condensation coefficient. In the process of evaporation into an atmospheric gas, molten salt decomposed at the interface between molten salt and an atmospheric gas reacts with chemical compositions of the atmospheric gas to be an equilibrium state. In this atmospheric evaporation, the interface shape of molten salts is affected by the container diameter and the contact angle at the container wall. In the analysis results, the formed concave/convex meniscus led to underestimating the condensation coefficient of molten salts. However, whether the values of the condensation coefficient of molten salts were affected by menisci, the range of the predicted values was still low from 10−3 to 10−5. This result means that the presence of the foreign gas (air and Ar) is a dominant parameter in determining the condensation coefficient of atmospheric evaporation.

Ultra-fast vapor generation by a graphene nano-ratchet: a theoretical and simulation study

Vapor generation is of prime importance for a broad range of applications: domestic water heating, desalination and wastewater treatment, etc. However, slow and inefficient evaporation limits its development. In this study, a nano-ratchet, a multilayer graphene with cone-shaped nanopores (MGCN), to accelerate vapor generation has been proposed. By performing molecular dynamics simulation, we found that air molecules were spontaneously transported across MGCN and resulted in a remarkable pressure difference, 21 kPa, between the two sides of MGCN. We studied the dependence of the pressure difference on the ambient temperature and geometry of MGCN in detail. Through further analysis of the diffusive transport, we found that pressure difference depended on the competition between ratchet transport and Knudsen diffusion and it was further found that ratchet transport is dominant. The significant pressure difference could lead to a 15-fold or greater enhancement of vapor generation, which shows the wide applications of this nano-ratchet.

Double Contact During Drop Impact on a Solid Under Reduced Air Pressure

Drops impacting on solid surfaces entrap small bubbles under their centers, owing to the lubrication pressure which builds up in the thin intervening air layer. We use ultrahigh-speed interference imaging, at 5 Mfps, to investigate how this air layer changes when the ambient air pressure is reduced below atmospheric. Both the radius and the thickness of the air disc become smaller with reduced air pressure. Furthermore, we find the radial extent of the air disc bifurcates, when the compressibility parameter exceeds ∼25. This bifurcation is also imprinted onto some of the impacts, as a double contact. In addition to the central air disc inside the first ring contact, this is immediately followed by a second ring contact, which entraps an outer toroidal strip of air, which contracts into a ring of bubbles. We find this occurs in a regime where Navier slip, due to rarefied gas effects, enhances the rate gas can escape from the path of the droplet.

Evaporation of liquid droplets of nano- and micro-meter size as a function of molecular mass and intermolecular interactions: experiments and molecular dynamics simulations

Transport of heat to the surface of a liquid is a limiting step in the evaporation of liquids into an inert gas. Molecular dynamics (MD) simulations of a two component Lennard-Jones (LJ) fluid revealed two modes of energy transport from a vapour to an interface of an evaporating droplet of liquid. Heat is transported according to the equation of temperature diffusion, far from the droplet of radius R. The heat flux, in this region, is proportional to temperature gradient and heat conductivity in the vapour. However at some distance from the interface, Aλ, (where λ is the mean free path in the gas), the temperature has a discontinuity and heat is transported ballistically i.e. by direct individual collisions of gas molecules with the interface. This ballistic transport reduces the heat flux (and consequently the mass flux) by the factor R/(R + Aλ) in comparison to the flux obtained from temperature diffusion. Thus it slows down the evaporation of droplets of sizes R ∼ Aλ and smaller (practically for sizes from 10³ nm down to 1 nm). We analyzed parameter A as a function of interactions between molecules and their masses. The rescaled parameter, A(k_BT_b/ε₁₁)^1/2, is a linear function of the ratio of the molecular mass of the liquid molecules to the molecular mass of the gas molecules, m₁/m₂ (for a series of chemically similar compounds). Here ε₁₁ is the interaction parameter between molecules in the liquid (proportional to the enthalpy of evaporation) and T_b is the temperature of the gas in the bulk. We tested the predictions of MD simulations in experiments performed on droplets of ethylene glycol, diethylene glycol, triethylene glycol and tetraethylene glycol. They were suspended in an electrodynamic trap and evaporated into dry nitrogen gas. A changes from ∼1 (for ethylene glycol) to approximately 10 (for tetraethylene glycol) and has the same dependence on molecular parameters as obtained for the LJ fluid in MD simulations. The value of x = A(k_BT_b/ε₁₁)^1/2 is of the order of 1 (for water x = 1.8, glycerol x = 1, ethylene glycol x = 0.4, tetraethylene glycol x = 2.1 evaporating into dry nitrogen at room temperature and for Lennard-Jones fluids x = 2 for m₁/m₂ = 1 and low temperature).

Exploring Ultimate Water Capillary Evaporation in Nanoscale Conduits

Capillary evaporation in nanoscale conduits is an efficient heat/mass transfer strategy that has been widely utilized by both nature and mankind. Despite its broad impact, the ultimate transport limits of capillary evaporation in nanoscale conduits, governed by the evaporation/condensation kinetics at the liquid-vapor interface, have remained poorly understood. Here we report experimental study of the kinetic limits of water capillary evaporation in two dimensional nanochannels using a novel hybrid channel design. Our results show that the kinetic-limited evaporation fluxes break down the limits predicated by the classical Hertz-Knudsen equation by an order of magnitude, reaching values up to 37.5 mm/s with corresponding heat fluxes up to 8500 W/cm². The measured evaporation flux increases with decreasing channel height and relative humidity but decreases as the channel temperature decreases. Our findings have implications for further understanding evaporation at the nanoscale and developing capillary evaporation-based technologies for both energy- and bio-related applications.

Specificity Switching Pathways in Thermal and Mass Evaporation of Multicomponent Hydrocarbon Droplets: A Mesoscopic Observation

For well over one century, the Hertz-Knudsen equation has established the relationship between thermal - mass transfer coefficients through a liquid - vapour interface and evaporation rate. These coefficients, however, have been often separately estimated for one-component equilibrium systems and their simultaneous influences on evaporation rate of fuel droplets in multicomponent systems have yet to be investigated at the atomic level. Here we first apply atomistic simulation techniques and quantum/statistical mechanics methods to understand how thermal and mass evaporation effects are controlled kinetically/thermodynamically. We then present a new development of a hybrid method of quantum transition state theory/improved kinetic gas theory, for multicomponent hydrocarbon systems to investigate how concerted-distinct conformational changes of hydrocarbons at the interface affect the evaporation rate. The results of this work provide an important physical concept in fundamental understanding of atomistic pathways in topological interface transitions of chain molecules, resolving an open problem in kinetics of fuel droplets evaporation.

Experimental and Numerical Study of the Evaporation of Water at Low Pressures

Although evaporation is considered to be a surface phenomenon, the rate of molecular transport across a liquid-vapor boundary is strongly dependent on the coupled fluid dynamics and heat transfer in the bulk fluids. Recent experimental thermocouple measurements of the temperature field near the interface of evaporating water into its vapor have begun to show the role of heat transfer in evaporation. However, the role of fluid dynamics has not been explored sufficiently. Here, we have developed a mathematical model to describe the coupling of the heat, mass, and momentum transfer in the fluids with the transport phenomena at the interface. The model was used to understand the experimentally obtained velocity field in the liquid and temperature profiles in the liquid and vapor, in evaporation from a concave meniscus for various vacuum pressures. By using the model, we have shown that an opposing buoyancy flow suppressed the thermocapillary flow in the liquid during evaporation at low pressures in our experiments. As such, in the absence of thermocapillary convection, the evaporation is controlled by heat transfer to the interface, and the predicted behavior of the system is independent of choosing between the existing theoretical expressions for evaporation flux. Furthermore, we investigated the temperature discontinuity at the interface and confirmed that the discontinuity strongly depends on the heat flux from the vapor side, which depends on the geometrical shape of the interface.

Condensation in One-Dimensional Dead-End Nanochannels

Phase change at the nanoscale is at the heart of many biological and geological phenomena. The recent emergence and global implications of unconventional oil and gas production from nanoporous shale further necessitate a higher understanding of phase behavior at these scales. Here, we directly observe condensation and condensate growth of a light hydrocarbon (propane) in discrete sub-100 nm (∼70 nm) channels. Two different condensation mechanisms at this nanoscale are distinguished, continuous growth and discontinuous growth due to liquid bridging ahead of the meniscus, both leading to similar net growth rates. The growth rates agree well with those predicted by a suitably defined thermofluid resistance model. In contrast to phase change at larger scales (∼220 and ∼1000 nm cases), the rate of liquid condensate growth in channels of sub-100 nm size is found to be limited mainly by vapor flow resistance (∼70% of the total resistance here), with interface resistance making up the difference. The condensation-induced vapor flow is in the transitional flow regime (Knudsen flow accounting for up to 13% of total resistance here). Collectively, these results demonstrate that with confinement at sub-100 nm scales, such as is commonly found in porous shale and other applications, condensation conditions deviate from the microscale and larger bulk conditions chiefly due to vapor flow and interface resistances.

Vapour adsorption kinetics: statistical rate theory and zeta adsorption isotherm approach

The zeta adsorption isotherm may be combined with statistical rate theory to formulate an expression for vapour adsorption kinetics that is in terms of a rate constant. For heptane adsorbing on silica, the rate constant is experimentally shown to depend only on temperature.