A unified relationship for evaporation kinetics at low Mach numbers

Evaluation of Evaporation Fluxes for Pesticides and Low Volatile Hazardous Materials Based on Evaporation Kinetics of Net Liquids

Evaporation is the phase transition process that plays a significant role in many spheres of life and science. Volatilization of hazardous materials, pesticides, petroleum spills, etc., impacts the environment and biosphere. Predicting evaporation fluxes under specific environmental conditions is challenging from theoretical and empirical points of view. A new practical method for estimating fluxes is proposed based on our experimental results and previously published data. It is demonstrated that some parameters in theoretical equations for near-equilibrium evaporation can be estimated from experiments, and these formulas can be exploited to predict steady-state evaporation fluxes in the air in a range of 8 orders of magnitude based on a single experiment carried out for nontoxic volatile compounds.

Intrinsic Water Transport in Moisture-Capturing Hydrogels

Moisture-capturing hydrogels have emerged as attractive sorbent materials capable of converting ambient humidity into liquid water. Recent works have demonstrated exceptional water capture capabilities of hydrogels while simultaneously exploring different strategies to accelerate water capture and release. However, on the material level, an understanding of the intrinsic transport properties of moisture-capturing hydrogels is currently missing, which hinders their rational design. In this work, we combine absorption and desorption experiments of macroscopic hydrogel samples in pure vapor with models of water diffusion in the hydrogels to demonstrate the first measurements of the intrinsic water diffusion coefficient in hydrogel-salt composites. Based on these insights, we pattern hydrogels with micropores to significantly decrease the required absorption and desorption times by 19% and 72%, respectively, while reducing the total water capacity of the hydrogel by only 4%. Thereby, we provide an effective strategy toward hydrogel material optimization, with a particular significance in pure-vapor environments.

Effects of Organic Surface Contamination on the Mass Accommodation Coefficient of Water: A Molecular Dynamics Study

The mass accommodation coefficient (MAC), a parameter that quantifies the possibility of a phase change to occur at a liquid-vapor interface, can strongly affect the evaporation and condensation rates at a liquid surface. Due to the various challenges in experimental determination of the MAC, molecular dynamics (MD) simulations have been widely used to study the MAC on liquid surfaces with no impurities or contaminations. However, experimental studies show that airborne hydrocarbons from various sources can adsorb on liquid surfaces and alter the liquid surface properties. In this work, therefore, we study the effects of organic surface contamination, which is immiscible with water, on the MAC of water by equilibrium and nonequilibrium MD simulations. The equilibrium MD simulation results show that the MAC decreases almost linearly with increasing surface coverage of the organic contaminants. With the MAC determined from EMD simulations, the nonequilibrium MD simulation results show that the Schrage equation, which has been proven to be accurate in predicting the evaporation/condensation rates on clean liquid surfaces, is also accurate in predicting the condensation rate at contaminated water surfaces. The key assumption about the molecular velocity distribution in the Schrage analysis is still valid for condensing vapor molecules near contaminated water surfaces. We also find that under nonequilibrium conditions the adsorption of the water vapor molecules on the organic surface results in an adsorption vapor flux near the contaminated water surface. When the water surface is almost fully covered by the model organic contaminants, the adsorption flux dominates over the water condensation flux and leads to a false prediction of the MAC from the Schrage equation.

Pickering Emulsion Templated 3D Cylindrical Open Porous Aerogel for Highly Efficient Solar Steam Generation

Porous-structured evaporators have been fabricated for achieving a high clean water throughput due to their maximized surface area. However, most of the evaporation surfaces in the porous structure are not active because of the trapped vapor in pores. Herein, a three-dimensional (3D) cylindrical aerogel-based photothermal evaporator with a disordered interconnected hierarchical porous structure is developed via a Pickering emulsion-involved polymerization method. The obtained cotton cellulose/aramid nanofibers/polypyrrole (CAP) aerogel-based evaporator achieved all-cold evaporation under 1.0 sun irradiation, which not only completely eliminated energy loss via radiation, convection, and conduction, but also harvested massive extra energy from the surrounding environment and bulk water, thus significantly increasing the total energy input for vapor generation to deliver an extremely high evaporation rate of 5.368 kg m-2 h-1 . In addition, with the external convective flow, solar steam generation over the evaporator can be dramatically enhanced due to fast vapor diffusion out of its unique opened porous structure, realizing an ultrahigh evaporation rate of 18.539 kg m-2 h-1 under 1.0 sun and 4.0 m s-1 . Moreover, this evaporator can continuously operate with concentrated salt solution (20 wt.% NaCl). This work advances rational design and construction of solar evaporator to promote the application of solar evaporation technology in freshwater production.

Achieving efficient power generation by designing bioinspired and multi-layered interfacial evaporator

Water evaporation is a natural phase change phenomenon occurring any time and everywhere. Enormous efforts have been made to harvest energy from this ubiquitous process by leveraging on the interaction between water and materials with tailored structural, chemical and thermal properties. Here, we develop a multi-layered interfacial evaporation-driven nanogenerator (IENG) that further amplifies the interaction by introducing additional bionic light-trapping structure for efficient light to heat and electric generation on the top and middle of the device. Notable, we also rationally design the bottom layer for sufficient water transport and storage. We demonstrate the IENG performs a spectacular continuous power output as high as 11.8 μW cm⁻² under optimal conditions, more than 6.8 times higher than the currently reported average value. We hope this work can provide a new bionic strategy using multiple natural energy sources for effective power generation.

The energy harvesting from ubiquitous natural water evaporation offers a great green energy source. Here, the authors report a bioinspired and multi-layered interfacial evaporation-driven nanogeneration strategy for efficient light-to-heat and electricity generation with continuous power output.

Electro-osmosis Aided Thin-Film Evaporation from a Micropillar Wick Structure

The heat-dissipating capacity of a surface having micropillar wick structures, which resembles the evaporator section of a vapor chamber, is mainly limited by the liquid flow rate through the porous structure (permeability) and the capillary pressure gradient. The efficacy of a regular vapor chamber is determined from two parameters, namely, the dry-out heat flux and temperature of the evaporator surface. These two parameters possess a counter relation to each other. The work described herein introduces and evaluates the performance of a novel idea of electro-osmosis-aided thin-film evaporation from a micropillar array structure. This study is conducted using a discretized approach that is validated against the thin-film evaporation model and additionally the electro-osmotic flow model with pre-existing pressure gradient conditions. The unique feature of this approach is that it results in an increment in the magnitude of dry-out heat flux without significantly changing the surface temperature, wherein the increase in permeability is due to the addition of electro-osmotic flow. This comprehensive model considers various geometries, zeta potentials, and extremal electric fields and establishes the beneficial effects of the application of an external electric field. The results are used to predict the sensitivity and the dependence of the dry-out heat flux and the evaporator surface temperature on these parameters. For a host of electro-osmotic parameters considered herein, a maximum increment of up to 320% in the dry-out heat flux is observed for an external electric field of 10⁵ V/m. The study, therefore, conclusively demonstrates the beneficial impact of electro-osmosis in enhancing the dry-out heat flux without any significant Joule heating.

Numerical and Theoretical Analysis of Sessile Droplet Evaporation in a Pure Vapor Environment

The evaporation of sessile droplets is not only a common occurrence in daily life, but it also plays a vital role in many scientific and industrial fields. However, most of the current research is focused on the evaporation of droplets in the air environment, where vapor transport is controlled by the diffusion model, but when the droplet evaporation is in its own pure vapor environment, the above model will no longer apply, and the evaporation will be dominated by kinetic theory. Thus the Hertz–Knudsen model can be applied to describe the evaporation kinetics. However, in most of the studies, it is assumed that the temperature distribution is uniform along the vapor-liquid interface of the droplet, but due to the evaporative cooling effect, this assumption is not correct in actual evaporation. In this paper, theoretical analysis and numerical simulation were combined to study the characteristics of droplet evaporation with multiphysics coupling. In the theoretical model, heat conduction in the droplet and substrate was coupled with vapor transport at the droplet surface. In the numerical simulation, internal thermocapillary flow and heat transfer of the droplet were coupled with vapor transport at the droplet surface. The effects of contact angle, thermocapillary convection, ambient pressure ratio, and substrate superheat on the droplet evaporation characteristics were quantitatively analyzed. It was found that the high substrate superheat or low ambient pressure ratio will enhance the droplet thermocapillary convection as well as evaporation rate. Furthermore, a critical contact angle was found; below this value, the droplet evaporation rate was inversely proportional to the contact angle, but upon this value, the trend was reversed. These findings have important implications for revealing the physical mechanism of kinetics-controlled droplet evaporation in a pure vapor environment.

Neural network-based cooling design for high-performance processors

Ultra-high chip power densities that are expected to surpass 1-2kW/cm² in future high-performance systems cannot be easily handled by conventional cooling methods. Various emerging cooling methods, such as liquid cooling via microchannels, thermoelectric coolers (TECs), two-phase vapor chambers, and hybrid cooling options have been designed to efficiently remove heat from high-performance processors. However, selecting the optimal cooling solution for a given chip and determining the optimal cooling parameters for that solution to achieve high efficiency are open problems. These problems are, in fact, computationally expensive because of the massive space of possible solutions. To address this design challenge, this article introduces a deep learning-based cooling design optimization flow that rapidly and accurately converges to the optimal cooling solution as well as the optimal cooling parameters for a given chip floorplan and its power profile.

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The paper introduces a Deep Learning-based chip cooling design optimization flow

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The proposed flow is built using multi-output convolutional neural networks

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The proposed flow is fast and accurate for selecting the optimal cooling design

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The proposed flow is modular for various chip architectures and cooling designs

Interfacial Water Structure of Binary Liquid Mixtures Reflects Nonideal Behavior

The evaporation of molecules from water-organic solute binary mixtures is key for both atmospheric and industrial processes such as aerosol formation and distillation. Deviations from ideal evaporation energetics can be assigned to intermolecular interactions in solution, yet evaporation occurs from the interface, and the poorly understood interfacial, rather than the bulk, structure of binary mixtures affects evaporation kinetics. Here we determine the interfacial structure of nonideal binary mixtures of water with methanol, ethanol, and formic acid, by combining surface-specific vibrational spectroscopy with molecular dynamics simulations. We find that the free, dangling OH groups at the interfaces of these differently behaving nonideal mixtures are essentially indistinguishable. In contrast, the ordering of hydrogen-bonded interfacial water molecules differs substantially at these three interfaces. Specifically, the interfacial water molecules become more disordered (ordered) in mixtures with methanol and ethanol (formic acid), showing higher (lower) vapor pressure than that predicted by Raoult's law.

Energy-Based Interface Detection for Phase Change Processes of Monatomic Fluids in Nanoconfinements

An energy-based liquid-vapor interface detection method is presented using molecular dynamics simulations of liquid menisci confined between two parallel plates under equilibrium and evaporation/condensation conditions. This method defines the liquid-vapor interface at the location where the average kinetic energy of atoms first exceeds the average potential energy imposed by all neighboring molecules. This definition naturally adapts to the location of the menisci relative to the walls and can properly model the behavior of the liquid adsorbed layers. Unlike the density cutoff methods frequently used in the literature that suffer from density layering effects, this new method gives smooth and continuous liquid-vapor interfaces in nanoconfinements. Surface tension values calculated from the equilibrium MD simulations match the Young-Laplace equation better when using the radius of curvatures calculated from this method. Overall, this energy-based liquid-vapor interface detection method can be used in studies of nanoscale phase change processes and other relevant applications.

Enhanced Evaporation of Ultrathin Water Films on Silicon-Terminated Si3N4 Nanopore Membranes

Water evaporation confined in nanoscale is a ubiquitous phenomenon in nature and has crucial importance in a broad range of technical applications. With the nonequilibrium molecular dynamics simulation, we elucidate nanothin water film evaporation characteristics on a silicon nitride nanopore membrane considering the effects of pore size and pore chemistry. Pore chemistry plays the main role in regulating the evaporation flux. The terminated Si atoms on the pore surface lead to a higher evaporation intensity than the N ones. We attribute this enhancement to the transition of the structural properties of fluid, where liquid molecules are packed loosely and disorderedly under the inducement of terminated silicon atoms. The findings in the present work can contribute to the fundamental understanding of the nanopore-enhanced evaporation process and provide new guidance to the design of advanced nanopore membrane materials.

Evaporation in nano/molecular materials

Evaporation is a physical phenomenon with fundamental significance to both nature and technology ranging from plant transpiration to DNA engineering. Various analytical and empirical relationships have been proposed to characterize evaporation kinetics at macroscopic scales. However, theoretical models to describe the kinetics of evaporation from nano and sub-nanometer (molecular) confinements are absent. On the other hand, the fast advancements in technology concentrated on development of nano/molecular-scale devices demand appropriate models that can accurately predict physics of phase-change in these systems. A thorough understanding of the physics of evaporation in nano/molecular materials is, thus, of critical importance to develop the required models. This understanding is also crucial to explain the intriguing evaporation-related phenomena that only take place when the characteristic length of the system drops to several nanometers. Here, we comprehensively review the underlying physics of evaporation phenomenon and discuss the effects of nano/molecular confinement on evaporation. The role of liquid-wall interface-related phenomena including the effects of disjoining pressure and flow slippage on evaporation from nano/molecular confinements are discussed. Different driving forces that can induce evaporation in small confinements, such as heat transfer, pressure drop, cavitation and density fluctuations are elaborated. Hydrophobic confinement induced evaporation and its potential application for synthetic ion channels are discussed in detail. Evaporation of water as molecular clusters rather than isolated molecules is discussed. Despite the lack of experimental investigations on evaporation at nanoscale, there exist an extensive body of literature that have applied different simulation techniques to predict the phase change behavior of liquids in nanoconfinements. We infer that exploring the effect of electrostatic interactions and flow slippage to enhance evaporation from nanoconduits is an interesting topic for future endeavors. Further future studies could be devoted to developing nano/molecular channels with evaporation-based gating mechanism and utilization of 2D materials to tune energy barrier for evaporation leading to enhanced evaporation.

Molecular dynamics study on characteristics of reflection and condensation molecules at vapor-liquid equilibrium state

The kinetic boundary condition (KBC) represents the evaporation or condensation of molecules at the vapor–liquid interface for molecular gas dynamics (MGD). When constructing the KBC, it is necessary to classify molecular motions into evaporation, condensation, and reflection in molecular-scale simulation methods. Recently, a method that involves setting the vapor boundary and liquid boundary has been used for classifying molecules. The position of the vapor boundary is related to the position where the KBC is applied in MGD analyses, whereas that of the liquid boundary has not been uniquely determined. Therefore, in this study, we conducted molecular dynamics simulations to discuss the position of the liquid boundary for the construction of KBCs. We obtained some variables that characterize molecular motions such as the positions that the molecules reached and the time they stayed in the vicinity of the interface. Based on the characteristics of the molecules found from these variables, we investigated the valid position of the liquid boundary. We also conducted an investigation on the relationship between the condensation coefficient and the molecular incident velocity from the vapor phase to the liquid phase. The dependence of the condensation coefficient on the incident velocity of molecules was confirmed, and the value of the condensation coefficient becomes small in the low-incident-velocity range. Furthermore, we found that the condensation coefficient in the non-equilibrium state shows almost the same value as that in the equilibrium state, although the corresponding velocity distribution functions of the incident velocity significantly differ from each other.

New Model for Liquid Evaporation and Vapor Transport in Nanopores Covering the Entire Knudsen Regime and Arbitrary Pore Length

Liquid evaporation and the associated vapor transport in micro/nanopores are ubiquitous in nature and play an important role in industrial applications. Accurate modeling of the liquid evaporation process in nanopores is critical to achieving a better design of devices for enhanced evaporation. Although having high impact on evaporation rate, vapor transport resistance in micro/nanopores remains incompletely understood. In this study, we proposed a new model which, for the first time, considered vapor transport in finite-length pores under various Knudsen regimes and then coupled the transport resistance to liquid evaporation. Direct Simulation Monte Carlo and laboratory experiments were conducted to provide validation for our model. The model successfully predicts the variation of pore transmissivity with Knudsen number and nanopore size, which cannot be revealed by prior theories. The relative error of model-predicted evaporation rate was within 1% in L/r = 0 cases and within 3.5% in L/r > 0 cases. Our model is featured by its applicability under the entire range of Knudsen numbers. The evaporation of various types of liquids in arbitrarily sized pores can be modeled using a universal relation.

Nano Heat Pump Based on Reverse Thermo-osmosis Effect

Heat pumps are widely used in domestic applications, agriculture, and industry. Here, we report a novel heat pump based on the reverse thermo-osmosis (RTO) effect in a nanoporous graphene (NPG) membrane. Through classical molecular dynamics (MD) simulation, we prove that the heat pump can transport mass and heat efficiently. The heat and mass fluxes are increased linearly with the hydraulic pressure provided. Ultrahigh heat fluxes of 6.2 ± 1.0 kW/cm² and coefficient of performance (COP) of 20.2 are obtained with a temperature increment of 5 K and a working pressure of 80 MPa. It is interesting that water molecules on the NPG membrane can evaporate in a cluster state, and the cluster evaporations reduce the vaporization enthalpy of the processes.

Probing the temperature profile across a liquid-vapor interface upon phase change

Understanding the temperature profile across a liquid-vapor interface in the presence of phase change is essential for the accurate prediction of evaporation, boiling, and condensation. It has been shown experimentally, from non-equilibrium thermodynamics and using molecular dynamics simulations, the existence of an inverted temperature profile across an evaporating liquid-vapor interface, where the vapor-side interface temperature observes the lowest value and the vapor temperature increases away from the interface, opposite to the direction of heat flow. It is worth noting, however, that an inverted temperature profile is not always the case from other experiments and simulations. In this study, we apply non-equilibrium molecular dynamics simulations to systematically study the temperature profile across a liquid-vapor interface during phase change under various heat fluxes in a two-interface setting consisting of both an evaporating and a condensing interface. The calculated vapor temperature shows different characteristics inside the Knudsen layer and in the bulk vapor. In addition, both the direction and magnitude of the vapor temperature gradient, as well as the temperature jump at the liquid-vapor interface, are functions of the applied heat flux. The interfacial entropy generation rate calculated from the vibrational density of state of the interfacial liquid and vapor molecules shows a positive production during evaporation, and the results qualitatively agree with the predictions from non-equilibrium thermodynamics.

Nanoconfined Fluids: What Can We Expect from Them?

Nanoconfined fluids (NCFs), which are confined in nanospaces, exhibit distinctive nanoscale effects, including surface effects, small-size effects, quantum effects, and others. The continuous medium hypothesis in fluid mechanics is not valid in this context because of the comparable characteristic length of spaces and molecular mean free path, and accordingly, the classical continuum theories developed for the bulk fluids usually cannot describe the mass and energy transport of NCFs. In this Perspective, we summarize the nanoscale effects on the thermodynamics, mass transport, flow dynamics, heat transfer, phase change, and energy transport of NCFs and highlight the related representative works. The applications of NCFs in the fields of membrane separation, oil and gas production, energy harvesting and storage, and biological engineering are especially indicated. Currently, the theoretical description framework of NCFs is still missing, and it is expected that this framework can be established by adopting the classical continuum theories with the consideration of nanoscale effects.

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.

High Heat Flux Evaporation of Low Surface Tension Liquids from Nanoporous Membranes

Water is often considered as the highest performance working fluid for liquid-vapor phase change due to its high thermal conductivity and large enthalpy of vaporization. However, a wide range of industrial systems require using low surface tension liquids where heat transfer enhancement has proved challenging for boiling and evaporation. Here, we enable a new paradigm of phase change heat transfer, which favors high volatility, low surface tension liquids rather than water. We utilized a nanoporous membrane of ≈600 nm thickness and <140 nm pore diameters supported on efficient liquid supply architectures, decoupling capillary pumping from viscous loss. Proof-of-concept devices were microfabricated and tested in a custom-built environmental chamber. We used R245fa, pentane, methanol, isopropyl alcohol, and water as working fluids with devices of total membrane area varying from 0.017 to 0.424 cm². We realized a device-level pure evaporation heat flux of 144 ± 6 W/cm² for water, and the highest evaporation heat flux was obtained with pentane at 550 ± 90 W/cm². We developed a three-level model to understand vapor dynamics near the interface and thermal conduction within the device, which showed good agreement with experiments. We then compared pore-level heat transfer of different fluids, where R245fa showed approximately 10 times the performance of water under the same working conditions. Finally, we illustrate the usefulness of a figure of merit extracted from the kinetic theory for evaporation. The current work provides fundamental insights into the evaporation of low surface tension liquids, which can impact various applications such as refrigeration and air conditioning, petroleum and solvent distillation, and on-chip electronics cooling.

Identification of Parameters of Evaporation Equations Using an Optimization Technique Based on Pan Evaporation

Countries in arid regions are presently facing challenges in managing their limited water resources. Assessing the evaporation losses from various sources of water is a daunting task that is inevitable for the sustainability of water resource management schemes in these regions. Although several techniques are available for simulating evaporation rates, identifying the parameters of various evaporation equations still needs to be further investigated. The main goal of this research was to develop a framework for determining the parameters influencing the evaporation rate of evaporation pans. Four different equations, including those of Hamon, Penman, Jensen–Haise, and Makkink, were chosen to estimate evaporation from the evaporation pans installed in the Qassim Region of Saudi Arabia. The parameters of these four equations were identified by a state-of-the-art optimization technique, known as the general reduced gradient (GRG). Three types of objective functions used for optimization were tested. Forty-year monitoring records for pan evaporation, temperature, relative humidity, and sunshine hours were collected from the Municipality of Buraydah Al Qassim, for the period of 1976 to 2016. These data were mainly manually recorded at a weather station situated in the Buraydah city. Preliminary data analysis was performed using the Mann–Kendall and Sen’s slope tests to study the trends. The first 20-year (1976–1995) data were used for calibrating the equations by employing an optimization technique and the remaining data were used for validation purposes. Four new equations were finally developed and their performance, along with the performance of the four original equations, was evaluated using the Nash and Sutcliffe Efficiency (NSE) and the Mean Biased Error (MBE). The study revealed that among the original equations, the Penman equation performed better than the other three equations. Additionally, among the new equations, the Hamon method performed better than the remaining three equations.

Unified Modeling Framework for Thin-Film Evaporation from Micropillar Arrays Capturing Local Interfacial Effects

Thin-film evaporation from micropillar array porous media has gained attention in a number of fields including energy conversion and thermal management of electronics. Performance in these applications is enhanced by leveraging the geometries of the micropillar arrays to both optimize flow through these arrays via capillary pumping and increase the curved liquid-vapor interface (meniscus) area for active phase-change heat transfer. In this work, we present a unified semianalytical modeling framework to predict the dry-out heat flux accurately for thin-film evaporation from micropillar arrays with the precise prediction of (i) the pressure profile along the wick achieved by discretizing the porous media domain and (ii) the local permeability that depends on the local meniscus shape. We validate the permeability model with 3D numerical simulations and verify the accuracy of the thin-film evaporation modeling framework with available experimental data from the literature. We emphasize the importance of predicting an accurate liquid-vapor interface shape for the prediction accuracy of both the permeability and the associated governing equations for liquid propagation and phase-change heat transfer through porous materials. This modeling framework is an accurate non-CFD-based methodology for predicting the dry-out heat flux during thin-film evaporation from micropillar arrays and will serve as a general framework for modeling steady liquid-vapor phase-change processes (evaporation and condensation) in porous media.