Liquid-vapor Interfacial Area Research Articles

Experiment of contact angle hysteresis of a droplet on hydrophobic fibrous membrane

Fibrous membranes are widely used in liquid-gas filtration and separation, porous structures formed by randomly cross-layered fibers have a significant influence on interfacial free energies, showing complex changes in contact angle. The present paper aims to measure the pore structures of a hydrophobic ((C2F4)n, PTFE) fibrous membrane by Confocal Laser Scanning Microscope (CLSM), and analyze the droplet contact angle hysteresis along its circumference. The capillary force of the solid-liquid interface is calculated by the surface integral of Laplace pressure on half droplet surface, and the solid-liquid and liquid-vapor interface area ratios are obtained according to the Cassie-Baxter model. The liquid penetration depth in pore structures is calculated by the quasi-equilibrium of the interface free energy. The experimental result shows that for the PTFE fibrous membrane, the liquid-vapor interface area ratio (f2The experimental result shows that for the PTFE fibrous membrane, the liquid-vapor interface area ratio (f2

Experiment of droplet contact angle hysteresis on PTFE fibrous membrane in pore-scale

The present paper aims to study the influence of pore-scale fiber structure on the Cassie-Baxter contact angle of droplets on PTFE fibrous hydrophobic membranes. The fiber structure is obtained by the Confocal Laser Scanning Microscope (CLSM), and an optical test bench is built to measure the Cassie-Baxter contact angles of a droplet on a PTFE membrane. The free energy of the solid-liquid interface is measured by the surface tension integral on the droplet profile. An iterative algorithm for liquid-vapor interface shrinking is brought forward to analyze the liquid-vapor interface area between the droplet and the membrane, and the interface parameters of the Cassie-Baxter model are recognized. The experiment shows that the Cassie-Baxter contact angles and the contact line radii along the droplet circumference are in a normal distribution due to random fiber structures, and the variance of the normal distribution increases with the membrane pore diameter. The normal distribution of Cassie-Baxter’s contact angle indicates the constraint of the solid-liquid interface to the liquid-vapor interface. On the same normal contact pressure condition, the liquid-vapor area ratio of the droplet and membrane interface changes little, and Cassie-Baxter’s contact angle increases with the solid-liquid interface area ratio.

Phenomenology and kinetics of sessile droplet evaporation on convex contours

In this article we probe experimentally and theoretically the evaporation phenomenology and kinetics of sessile droplets seated over convex hydrophilic and super-hydrophobic (SH) surfaces. To understand the role of convex contours, both cylinders (mono-curvature system) and spheres (two-curvature system) have been explored. The evolution of the droplet shape during evaporation was monitored by optical imaging. The observations reveal improved evaporation rates on convex substrates, and the same tends to increase with increasing curvature. The findings also show that the influence of a two-curvature system (sphere) on the evaporation rate is to a higher extent than that for a mono-curvature system (cylinder). These observations are attributed to the augmented liquid-vapor interfacial area and widened up vapor diffusion domain which renders the liquid-molecules more scope to diffuse in the surrounding environment. The dynamic behavior of the triple line (TL) on convex substrates shows higher receding velocity of the contact line especially on spherical substrates. To visualize the internal flow and understand the effect of substrate convexity on internal advection dynamics, particle image velocimetry (PIV) was carried out. These results show higher strength of circulation velocity inside a droplet evaporating over convex surfaces despite frequent de-pinning of contact line. This behavior can be explicated by the fact than on convex surfaces higher temperature gradient exists along the liquid-vapor interface of the droplet (due to more evaporative cooling, and mapped through infrared thermography), which induces stronger thermal-Marangoni convection, thereby scaling up the circulation velocity. The finding may hold implications towards the design and development of droplet-based thermofluidic devices.

Combined suppression effects on hydrodynamic cavitation performance in Venturi-type reactor for process intensification

Hydrodynamic cavitation is an emerging intensification technology in water treatment or chemical processing, and Venturi-type cavitation reactors exhibit advantages for industrial-scale production. The effects of temperature on hydrodynamic cavitating flows are investigated to find the optimum reaction conditions enhancing cavitating treatment intensity. Results show that the cavitation performance, including the cavitation intensity and cavitation unsteady behavior, is influenced by (1) cavitation number σ (the pressure difference affecting the vaporization process), (2) Reynolds number Re (the inertial/viscous ratio affecting the bubble size and liquid–vapor interface area), and (3) thermodynamic parameter Σ (the thermal effect affecting the temperature drop). With increasing temperature, the cavitation length first increases and then decreases, with a cavitation intensity peak at the transition temperature of 58 °C. With the growth of cavitation extent, the cavity-shedding regimes tend to transition from the attached sheet cavity to the periodic cloud cavity, and the vapor volume fluctuating frequency decreases accordingly. A combined suppression parameter (CSP) is provided to predict that, with increasing CSP value, the cavitation intensity can be decreased. Recommendations are given that working under the low-CSP range (55–60 °C) could enhance the intensification of the cavitation process.

Cassie-Baxter and Wenzel States and the Effect of Interfaces on Transport Properties across Membranes.

Mass transfer across a liquid-repelling gas permeable membrane is influenced by the state(s) of the liquid–vapor interface(s) on the surface of the membrane, the pore geometry, and the solid–fluid interactions inside the membrane. By tuning the different local contributions, it is possible to enhance the temperature difference-driven mass flux across the membrane for a constant driving force. Non-equilibrium molecular dynamics simulations were used to simulate a temperature difference-driven mass flux through a gas permeable membrane with the evaporating liquid on one side and the condensing liquid on the other. Both sides were simulated for Wenzel- and Cassie–Baxter-like states. The interaction between the fluid and the solid inside the gas permeable membrane varied between the wetting angles of θ = 125° and θ = 103°. For a constant driving force, the Cassie–Baxter state led to an increased mass flux of almost 40% in comparison to the Wenzel state (given a small pore resistance). This difference was caused by an insufficient supply of vapor particles at the pore entrance in the Wenzel state. The difference between the Wenzel and Cassie–Baxter states decreased with increasing resistance of the pore. The condensing liquid–vapor interface area contributed in the same manner to the overall transport resistance as the evaporating liquid–vapor interface area. A higher repulsion between the fluid and the solid inside the membrane decreased the overall resistance.

Evaporation of R1234yf, R1234ze(E) and R1234ze(Z) on Cu surface: A molecular dynamics study

Understanding the interface phase transition behavior of the working fluid helps to improve the energy conversion efficiency of a thermodynamic cycle. In this study, the evaporation behaviors of R1234yf, R1234ze(E) and R1234ze(Z) liquid film on the solid surface are performed using molecular dynamics simulation. The results suggest the evaporation rate and heat flux almost remain constant in the steady state. And during this period, the evaporation rate and heat flux of R1234yf is the largest among the studied systems. Meanwhile, the total thermal resistance of R1234ze(Z) system is greater than that of R1234ze(E) and R1234yf. The Kapitza resistance between solid and liquid accounts for only a small part of the total thermal resistance. The main reason for the difference of the total thermal resistance is the large difference of evaporation resistance at the liquid–vapor interface. Furthermore, the largest liquid–vapor interface area gives R1234yf the largest surface area for heat and mass transfer, thus enhancing the performance of evaporation. Besides, R1234yf has the smallest surface tension, followed by R1234ze(E) and R1234ze(Z). And the self-diffusion coefficient of R1234yf is the greatest. R1234yf also has the smallest interaction energy between liquid molecules. Therefore, the R1234yf liquid molecule is easy to escape from the liquid–vapor interface among the studied systems.

Guidelines for Designing Micropillar Structures for Enhanced Evaporative Heat Transfer

Abstract Over the last several decades, cooling technologies have been developed to address the growing thermal challenges associated with high-powered electronics. However, within the next several years, the heat generated by these devices is predicted to exceed 1 kW/cm2, and traditional methods, such as air cooling, are limited in their capacities to dissipate such high heat fluxes. In contrast, two-phase cooling methods, such as microdroplet evaporation, are very promising due to the large latent heat of vaporization associated with the phase change process. Previous studies have shown that nonaxisymmetric droplets have different evaporation characteristics than spherical droplets. The solid–liquid and liquid–vapor interfacial areas, volume, contact angle, and thickness of a droplet confined atop a micropillar are the primary parameters that influence evaporative heat transport. These parameters have a strong influence on both the conduction and diffusion resistance during the evaporation process. For example, a droplet with a higher liquid–vapor interfacial area will favorably increase heat transfer. Increased droplet thickness, on the other hand, has a detrimental influence on the evaporation rate. The dimensions of these droplets will vary in response to changes in each of the aforementioned parameters. Lowering the droplet thickness can be achieved by decreasing the liquid volume while maintaining a constant solid–liquid area. However, if the solid–liquid area and volume vary simultaneously, the average droplet thickness may increase, decrease, or remain constant. Furthermore, changes in the shape of the droplet modify the local equilibrium contact angle of the droplet for different azimuthal angles. As a result, the optimal combination of these parameters must be identified to maximize the heat transfer performance of an evaporating microdroplet. These droplet parameters can be manipulated by selecting different micropillar cross sections. In this work, we develop a shape optimization tool using the particle swarm optimization algorithm to maximize evaporation from a droplet confined atop a micropillar. The tool is used to optimize the shape of a nonaxisymmetric droplet. Compared to droplets atop circular and regular equilateral triangular micropillar structures, we find that droplets confined on pseudo-triangular micropillar structures have 23.7% and 5.7% higher heat transfer coefficients, respectively. The results of this work will advance the design of microstructures that support droplets with maximum heat transfer performance.

Capillary character and evaporation heat transfer in the wicks of high temperature liquid metal heat pipe

The study focuses on the capillary character and evaporation in micro-structures of high temperature liquid metal heat pipe, an important component for the cooling of reusable leading edge of hypersonic vehicle. Based on the free surface shape calculated by Surface Evolver, the rise of liquid and evaporation capacity are investigated theoretically and numerically for the sphere and rectangular grooved wick respectively. The results show that rectangular grooved wick presents better capillary character performance mainly due to its smaller flow resistance than the sphere one. And the evaporation capacity is mainly affected by the thermal conducting path and the liquid-vapor interface area, which combined lead to that the rectangular grooved wick also has more superior evaporating performance, much different from the evaporation of the low temperature liquid such as water or octane and so on. It is also found that decreasing the solid-liquid contact angle is helpful to improve both the capillary and evaporation character.

Boiling Heat Transfer with a Well-Ordered Microporous Architecture.

Boiling heat transfer through a porous medium offers an attractive combination of enormous liquid-vapor interfacial area and high bubble nucleation site density. In this work, we characterize the boiling performances of porous media by employing the well-ordered and highly interconnected architecture of inverse opals (IOs). The boiling characterization identifies hydrodynamic mechanisms through which structural characteristics affect the boiling performance of metallic microporous architecture by validating empirical measurements. The boiling performances can be optimized through the rational design of both the structural thicknesses and pore diameters of IOs, which demonstrate up to 336% enhancement in boiling heat-transfer coefficient (HTC) over smooth surfaces. The optimal HTC and critical heat flux occur at approximately 3-4 μm in porous structure thickness, which is manifested through the balance of liquid-vapor occupation within the spatial confinement of the IO structure. The optimization of boiling performances with varying pore diameters (0.3-1.0 μm) can be attributed to the hydraulic competitions between permeability and viscous resistance to liquid-vapor transport. This study unveils thermophysical understandings to enhance multiphase heat transfer in microporous media for ultrahigh heat flux thermal management.

Numerical Investigation of Shape Effect on Microdroplet Evaporation

Abstract As electronic devices continue to shrink in size and increase in functionality, effective thermal management has become a critical bottleneck that hinders continued advancement. Two-phase cooling technologies are of growing interest for electronics cooling due to their high heat removal capacity and small thermal resistance (<0.1 k cm2/W). One typical example of a two-phase cooling method is droplet evaporation, which can provide a high heat transfer coefficient with low superheat. While droplet evaporation has been studied extensively and used in many practical cooling applications (e.g.,, spray cooling), the relevant work has been confined to spherical droplets with axisymmetric geometries. A rationally designed evaporation platform that yields asymmetric meniscus droplets can potentially achieve larger meniscus curvatures, which gives rise to higher vapor concentration gradients along the contact line region, and therefore, yields higher evaporation rates. In this study, we develop a numerical model to investigate the evaporation behavior of asymmetrical microdroplets suspended on a porous micropillar structure. The equilibrium profiles and mass transport characteristics of droplets with circular, triangular, and square contact shapes are explored using the volume of fluid (VOF) method. The evaporative mass transport at the liquid–vapor interface is modeled using a simplified Schrage model. The results show highly nonuniform mass transport characteristics for asymmetrical microdroplets, where a higher local evaporation rate is observed near the locations where the meniscus has high curvature. This phenomenon is attributed to a higher local vapor concentration gradient that drives faster vapor diffusion at more curved regions, similar to a lightning rod exhibiting a strong electric field along a highly curved surface. By using contact line confinement to artificially tune the droplet into a more curved geometry, we find that the total evaporation rate from a triangular-based droplet is enhanced by 13% compared to a spherical droplet with the same perimeter and liquid–vapor interfacial area. Such a finding can guide the design and optimization of geometric features to improve evaporation in advanced microcooling devices.

Evaporative Wicking Phenomena on Nanotextured Surfaces

AbstractAs modern electronics become miniaturized with high power, thermal management for electronics devices has become significant. This motivates the implementation of new cooling solutions to dissipate high-heat levels from high-performance electronics. Evaporative cooling is one of the most promising approaches for meeting these future thermal demands. Thin-film evaporation promotes heat dissipation through the phase change process with minimal conduction resistance. In this process, it is important to design surface structures and corresponding surface properties that can minimize meniscus thickness, increase liquid–vapor interfacial area, and enhance evaporation performances. In this study, we investigate thin-film evaporation by employing nanotextured copper substrates for varying thermal conditions. The liquid spreading on the nanotextured surfaces is visualized using a high-speed imaging technique to quantify evaporative heat transfer for various surfaces. The permeability is calculated using an enhanced wicking model to estimate the evaporation effect combined with the mass measurements. Then, infrared (IR) thermography is employed to examine two-dimensional temporal temperature profiles of the samples during the evaporative wicking with a given heat flux. The combination of optical time-lapse images, evaporation rate measurements, and temperature profiles will provide a comprehensive understanding of evaporation performances using textured surfaces.

Tricoupled hybrid lattice Boltzmann model for nonisothermal drying of colloidal suspensions in micropore structures

A tricoupled hybrid lattice Boltzmann model (LBM) is developed to simulate colloidal liquid evaporation and colloidal particle deposition during the nonisothermal drying of colloidal suspensions in micropore structures. An entropic multiple-relaxation-time multirange pseudopotential two-phase LBM for isothermal interfacial flow is first coupled to an extended temperature equation for simulating nonisothermal liquid drying. Then the coupled model is further coupled with a modified convection diffusion equation to consider the nonisothermal drying of colloidal suspensions. Two drying examples are considered. First, drying of colloidal suspensions in a two-pillar micropore structure is simulated in two dimensions (2D), and the final configuration of colloidal particles is compared with the experimental one. Good agreement is observed. Second, at the temperature of 343.15 K (70^{∘}C), drying of colloidal suspensions in a complex spiral-shaped micropore structure containing 220 pillars is simulated (also in 2D). The drying pattern follows the designed spiral shape due to capillary pumping, i.e., transport of the liquid from larger pores to smaller ones by capillary pressure difference. Since the colloidal particles are passively carried with liquid, they accumulate at the small menisci as drying proceeds. As liquid evaporates at the small menisci, colloidal particles are deposited, eventually forming solid structures between the pillars (primarily), and at the base of the pillars (secondarily). As a result, the particle deposition conforms to the spiral route. Qualitatively, the simulated liquid and particle configurations agree well with the experimental ones during the entire drying process. Quantitatively, the model demonstrates that the evaporation rate and the particle accumulation rate slowly decrease during drying, similar to what is seen in the experimental results, which is due to the reduction of the liquid-vapor interfacial area. In conclusion, the hybrid model shows the capability and accuracy for simulating nonisothermal drying of colloidal suspensions in a complex micropore structure both qualitatively and quantitatively, as it includes all the required physics and captures all the complex features observed experimentally. Such a tricoupled LBM has a high potential to become an efficient numerical tool for further investigation of real and complex engineering problems incorporating drying of colloidal suspensions in porous media.

LBM Simulation of Self-Assembly of Clogging Structures by Evaporation of Colloidal Suspension in 2D Porous Media

Evaporation of colloidal suspension in two-dimensional (2D) porous media leads to the formation of self-assembled clogging structures (SCS). The self-assembly pattern is studied with a hybrid two-phase lattice Boltzmann method incorporating non-isothermal phase change, particle transport and deposition models. During drying, particles accumulate along the liquid–vapor interface while colloidal suspension is evaporating. Upon reaching a certain local concentration threshold, the particles deposit and form a solid structure. The patterns formed by these structures are analyzed in different 2D porous media. In small porous systems of 4 pillars, the self-assembly of C-shaped and X-shaped structures is observed, which compares well with experimental bridge configurations. SCS in porous media of three different initial particle concentrations and of three different porosities are studied in larger porous systems. Simulated self-assembled clogging configurations show good qualitative matches with experimental configuration results. Particle concentration and porosity are both seen to affect the dynamic drying processes as well as the final self-assembled clogging configuration. The liquid configuration and the clogging structure affect each other mutually during drying. With initial concentration increasing from C0 = 0.00 to C0 = 0.16 at a given porosity $$ \phi_{0} = 0.68 $$ , the average evaporation rate and porosity decrease by 21.9% and 1.9%, respectively, due to blockage of pores. With increasing initial porosity from $$ \phi_{0} = 0.53 $$ to $$ \phi_{0} = 0.81 $$ at a given concentration of C0 = 0.16, the average evaporation rate increases by a factor of 2.9 due to larger liquid–vapor interfacial area. Also with the given concentration of C0 = 0.16, the decrease in the porosity (0.94%, 1.9% and 2.7%) is higher for higher initial porosity ( $$ \phi_{0} = 0.53, \, 0.68,{\text{ and }}0.81 $$ ), since more particles (proportional to $$ \phi_{0} \cdot C_{0} $$ ) are initially present. This work opens the door for numerically assisted design of colloid-deposition-based clogging patterns.

Characterization of the droplet formation phase for the H2O[sbnd]LiBr absorber: An analytical and experimental analysis

The poor heat and mass transfer occurring in the H2OLiBr absorber is one of the main limitations towards reducing the size of absorption chillers. Previous research shows that, as droplets form at the base of the absorber pipes, considerably large mass transfer coefficients can be obtained. However, modeling this phase of droplet formation has not been fully explored, as most of the research focuses on the film flow process preceding the droplet formation. The present study focuses on two aspects. Firstly, the dynamics of the droplet formation is investigated, with a focus on the effect of the solid surface shape on the droplet formation. A model to describe the droplet profile geometry was developed using the Euler-Lagrange equation and validated against experimental tests. Several pin geometries were tested and the results have shown that a 120° rhomboidal geometry is more suitable to increase the liquid-vapor interface area, while lowering the risk of droplet coalescence. Secondly, an analytical heat and mass transfer model based on the Fourier Series method has been developed to study the influence of pin size on the absorption process in an adiabatic absorber. The results show that the optimum width of the 120° rhomboidal pin is found at 6 mm, which maximizes the water absorbed during the droplet formation phase, without excessive use of material. The common assumption that treats the forming droplet as a half sphere fails to capture changes in the pin-droplet interaction which adversely affects the model accuracy. The proposed model shows that for pin widths smaller than 6 mm, the absorption process is impaired by the lower surface area exposed to the water vapor, resulting in up to 67% less mass absorbed obtainable and a decrease in the cooling power obtainable.In more practical terms, a rated 3 kW of cooling power is used as a case study with a 6 mm pin which reduces the absorber volume by 30% with respect to an absorber with 3 mm wide pins. This shows that by treating the droplet formation phase with a more physically-sound geometrical domain can improve the accuracy of the absorption models and can be easily implemented with any programming language to help in the design optimization of the absorber.

Molecular Dynamics Simulation of Water Nanodroplet Bounce Back from Flat and Nanopillared Surface.

Molecular dynamics simulations of impinging nanodroplets were performed to study the bounce-back condition for flat and nanopillared surfaces. We found that the bounce-back condition can be closely related to the degree of droplet deformation upon collision with the solid surface. When the droplets have little or small deformation, the bounce-back condition solely depends on the hydrophobicity of the surface. On the other hand, when the droplet deformation is large, the impinging velocity dependence of the bounce-back condition becomes stronger due to the increase of the liquid-vapor interfacial area of colliding droplet, which is proportional to the liquid-vapor surface energy. The impinging droplet simulations with nanopillared hydrophobic surfaces were also performed. The contribution of droplet deformation in this case is relatively small because the surface hydrophobicity is enhanced due to the existence of pillars. Finally, we find that the maximum spreading diameter of the impinging droplets exhibits a consistent trend, in terms of the Weber number dependence, as the experimental measurements with macrodroplets.

Numerical investigation of condensation on microstructured surface with wettability patterns

A numerical investigation of condensation on microstructured surfaces with wettability patterns is reported in this paper. Detailed droplet dynamics and heat transfer performance of four different wettability patterns are discussed: a hydrophilic case, a superhydrophobic case, a hybrid wettability case, and a dynamic wettability case. Several interesting droplet dynamic phenomena such as droplet coalescence jump, pillar squeezing droplet jump, and droplet dragging up by wettability gradient were observed. Through comparison of droplet distribution on the microstructured surface with the corresponding wall heat flux contour, a previously unknown impact is revealed: the regions where droplets sit have higher heat transfer rate due to the large heat transfer area of the droplet surface. The hybrid wettability case shows the highest heat transfer rate compared to the hydrophilic and superhydrophobic cases, because it not only increases droplet nucleation density but also sustains large liquid–vapor interfacial areas. Dynamic control of wettability is finally suggested to detach large droplets to avoid the flooded state of the hybrid wettability case. The detachment of droplets from the surface decreases the condensation heat transfer rate sharply because of the loss of effective liquid–vapor interfacial area, but it cleans the surface for fast re-nucleation. This paper provides promising insights to improve heat and mass transfer of condensation on microstructured surfaces of heat exchangers.

Effect of Hydrothermal Waves on Evaporation Distribution During Drop Evaporation

The objective of this study is to clarify physical mechanisms involved in the evaporation of small (a few microliters) sessile drops. We aim to understand the relation between local thermal information at the solid–liquid interface and overall evaporation. An infrared (IR) camera and a charge-coupled device (CCD) camera were used to determine the temperature and heat flux distribution at the solid–liquid interface and the profile of the evaporating drop, respectively. The temperature distribution at the solid–liquid interface was determined using a multilayer substrate consisting of a silicon wafer coated with a thin thermal insulator that is partially transparent to IR. The liquids used were water and FC-72. The evaporation rate of water drops was found to occur mostly at the contact line. However, the heat transfer distribution at the liquid–solid interface was relatively uniform, indicating the heat transferred from the wall must be transported within the drop to the contact line. The mechanisms by which this occurs have yet to be determined. In contrast, the evaporation rate of FC-72 drops where hydrothermal waves were present was found to be proportional to the liquid–vapor interface area rather than the circumference of the drop, indicating a more uniform distribution of evaporation.

Closed‐Form Model for Hydraulic Properties Based on Angular Pores with Lognormal Size Distribution

We previously presented a mathematical model for hysteretic soil hydraulic properties based on bundles of angular pores. Upscaling to sample‐scale hydraulic properties was done analytically, assuming a Gamma density distribution of pore sizes. The required parameter constraint for getting the closed‐form solution limited the model's applicability for soils with wide pore‐size distributions. The objective of this study was to improve the model by developing a new analytical solution based on a lognormal density function of the pore‐size distribution. Closed‐form expressions were derived for liquid retention, saturated–unsaturated hydraulic conductivity, liquid–vapor interfacial area, and specific surface area at the sample scale. The new model was applied to retention and conductivity data for three soils with different pore‐size distributions. The results show that the previous model is suitable only for sandy materials, whereas the new one describes the soil hydraulic functions of a wider range of soil types quite well.

Effect of liquid–vapor interface area on the evaporation rate of small sessile droplets

This study is focused on the role of liquid–vapor interface area in the evaporation of small sessile droplets. The evaporation processes of small sessile droplets with different geometric parameters are numerically investigated with the quasi-steady diffusion model. The numerical results show that droplets with the same surface area are approximately equal in the evaporation rate despite the great differences in contact angles and base radii. It is attributed to the fact that the gradient distributions of vapor concentration surrounding droplets with the same surface area tend to be consistent as the distance from droplet surface increases. Based on the numerical results, a new simple expression with no fitting parameter is developed to calculate the evaporation rate of sessile droplets, and it is found that the evaporation rate is proportional to the square root of liquid–vapor interface area. The proposed expression is in good agreement with the expression of Picknett and Bexon and also validated by the experimental data in open literature. Finally, the evaporation cooling effect of small droplets on an isothermal substrate at room temperature is incorporated into the expression using the average temperature of liquid–vapor interface.

Direct molecular diffusion and micro-mixing for rapid dewatering of LiBr solution

A slow molecular diffusion rate often limits the desorption process of an absorbate molecule from a liquid absorbent. To enhance the desorption rate, the absorbent is often boiled to increase the liquid–vapor interfacial area. However, the growth of bubbles generated during the nucleate boiling process still remains mass-diffusion limited. Here, it is shown that a desorption rate higher than that of boiling can be achieved, if the vapor–absorbent interface is continuously replenished with the absorbate-rich solution to limit the concentration boundary layer growth. The study is conducted in a LiBr–water solution, in which the water molecules' diffusion rate is quite slow. The manipulation of the vapor–solution interface concentration distribution is enabled by the mechanical confinement of the solution flow within microchannels, using a hydrophobic vapor-venting membrane and the implementation of microstructures on the flow channel's bottom wall. The microstructures stretch and fold the laminar streamlines within the solution film and produce vortices. The vortices continuously replace the concentrated solution at the vapor–solution interface with the water-rich solution brought from the bottom and middle of the flow channel. The physics of the process is described using a combination of experimental and numerical studies.