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(a) Schematic illustration of a high-resolution dual X-ray imaging by combination of transmission (TI) and reflection imaging (RI). (b) An example of an evaporating nanoliter water droplet (429 nL). This method allows precise measurements of droplet geometry (from TI) and complete evaporation time tf (from RI). For instance, tf = 208.2 s when the trace of the water film, as marked by an arrow in 120 s, completely disappears. (c) Initial conditions of nanoliter (2 to 700 nL) water droplets on silicon wafer: R0 = 100–1000 μm and contact angle θ0 = 20–50 deg.
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Water vapor is lighter than air; this can enhance water evaporation by triggering vapor convection but there is little evidence. We directly visualize evaporation of nanoliter (2 to 700 nL) water droplets resting on silicon wafer in calm air using a high-resolution dual X-ray imaging method. Temporal evolutions of contact radius and contact angle r...
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Citations
... suppression or enhancement) counterbalanced each other. Higher evaporation rate in the presence of convection in the gas domain was also reported in [316]. ...
Evaporation of liquid is important in a diverse range of engineering applications, such as ink-jet printing, pesticide spraying, micro- and nanofabrication, thin-film coatings, biochemical assays, deposition of DNA/RNA microarrays, the manufacture of novel optical and electronic materials, and cooling microelectronics and power electronic devices. In particular, evaporation at the microscale has attracted increasing interest as an effective cooling strategy for overcoming the thermal challenges in high heat flux microelectronics devices. A large number of studies have demonstrated the prospect of evaporative heat transfer methods to tackle die-level hotspots reaching 1 kW/cm2 on each high-power tier in a 3D microelectronics device. Furthermore, evaporation at the microscale (thin-film evaporation) can achieve higher heat removal than evaporation at macroscale. However, evaporation is a complicated process involving several physical transport phenomena, and their dominance can vary with variations in device dimensions and other system parameters. This article reviews the literature on the factors affecting microscale evaporation, which include the properties and temperature of the solid substrate, vapor transport in the gas domain, microconvection, and engineered surface features. Techniques to enhance evaporative heat transfer are highlighted. Extending the contact line region effectively enhances evaporative heat transfer, and this technique is employed in surface coatings or micro- and nanostructures, wicking structures, and micro- and nanoporous membranes. The evaporation rate can also be enhanced by manipulating the meniscus shape to provide an energy barrier at sharp edges of micro- and nanostructures. This review also summarizes the theoretical models for estimating evaporation rates, then discusses the physical transport processes associated with evaporation and their corresponding thermal resistances. Because non-invasive, high resolution temperature measurement and visualization are critical for implementing evaporative cooling in high heat flux applications, state-of-art techniques are also discussed. Laser-induced fluorescence techniques are judged the most advanced for temperature measurement, and particle image velocimetry (PIV) is the most advanced means of flow field visualization. This review identifies the most promising evaporative cooling techniques for next generation of ultra-high heat flux microelectronics applications. It also compares the performance of these cooling technologies in a regime plot, providing useful information for designing effective cooling solutions. We end by summarizing the current challenges and discussing the outlook for evaporative cooling technologies, then consider future research needs.
... For example, the classic diffusion-limited evaporation model assumes that the distribution of vapor is spherically symmetric for a single droplet [7,8]. However for actual evaporation process, the distribution of vapor could be asymmetric due to the natural convection [9][10][11][12][13][14]. This is the reason why many researchers have been paying attention to the effect of natural convection on droplet evaporation. ...
The direct visualization of vapor distribution and quantitative measurement of vapor concentration plays an important role in studying droplet evaporation. In this study, we propose a method to measure the vapor concentration field based on the modified background oriented Schlieren, inverse Radon transform, high-speed imaging, and image processing. The method is demonstrated for the measurement of the transient concentration field during the impact of volatile droplets on solid surfaces. The results show that the vapor distribution is remarkably different from the diffusion-limited model because of the strong convection. The complex structure of the vapor cloud is the result of the interplay among fluid inertia, fluid evaporation, vapor diffusion, vapor convection, and droplet shape evolution.
... According to formulas (2.7), (2.8), (2.9), (2.10), the Nusselt number Nu of different boundary heat transfer can be calculated. The Nusselt number of the horizontal plate outside the air is in accordance with formula (2.7) [18,22,37]: ...
... The picture is extracted from Ref. [2]. [11,12,13,14,15,16,17,18,19]. ...
... This Grashof number will be derived from the equations of hydrodynamics in Section 3.2. This number predicts the dynamics of evaporation [11,12,13,14,15,16,17,19]. For small Grashof numbers, the evaporation is diffusive such that the ambient air can be considered as quiescent. ...
Motivated by the evaporation of soap films, which has a significant effect on their lifetime, we performed an experimental study on the evaporation of vertical surfaces with model systems based on hydrogels. From the analogy between heat and mass transfer, we adopt a model describing the natural convection in the gas phase due to a density contrast of dry and saturated air. Our measurements show a good agreement with this model, both in terms of scaling law with the Grashof number and in terms of order of magnitude. We discuss the corrections to take into account, notably the contribution of edge effects, which have a small but visible contribution when sides and bottom surface areas are not negligible compared to the main evaporating surface area.
... For small Grashof numbers, evaporation is limited by diffusion while for large Grashof numbers, buoyancy creates a convective flow. Additional experimental questioning [11] and evidences [12,13,14,15,16,17] of the importance of convective effects have been reported more recently in the literature. Direct visualizations of evaporating drops have been achieved by X-ray imaging method [12], IR absorption [14], Schlieren technique [18] or by interferometric measurements [19] and they also concluded that evaporation can be enhanced by convection. ...
... Additional experimental questioning [11] and evidences [12,13,14,15,16,17] of the importance of convective effects have been reported more recently in the literature. Direct visualizations of evaporating drops have been achieved by X-ray imaging method [12], IR absorption [14], Schlieren technique [18] or by interferometric measurements [19] and they also concluded that evaporation can be enhanced by convection. The transition between diffusive and convective evaporation regimes has been reported and the convective evaporation rate can be captured as Gr β with β ≈ 0.20 [13,14,15]. ...
... Therefore, we analyze in the next paragraphs the set of equations (7) to derive this concentration gradient. : Dimensionless vapor concentration map above an evaporating disk in the dimensionless space (r,z) obtained from equation (12). White and cyan lines are the oblate spheroidal coordinates (κ, σ), for respectively constant κ and σ values. ...
We investigate theoretically and experimentally the evaporation of liquid disks in the presence of natural convection due to a density difference between the vapor and the surrounding gas. From the analogy between thermal convection above a heated disk and our system, we derive scaling laws to describe the evaporation rate. The local evaporation rate depends on the presence of a boundary layer in the gas phase such that the total evaporation rate is given by a combination of different scaling contributions, which reflect the structure of the boundary layer. We compare our theoretical predictions to experiments performed with water in an environment controlled in humidity, which validate our approach.
... Therefore, thermo-capillary convection may enhance substantially the global evaporation rate in the case of heated substrate, but with negligible effect in the case of nonheated substrate. Moreover, the dependence of fluid density on temperature induces buoyancy convection in the liquid and surrounding gas [35][36][37][38][39], but its importance is still questionable. Some authors demonstrated that buoyancy effect in liquid phase can be neglected in the case where the substrate is at room temperature [40], whereas numerical results of Ait Saada et al. [38] revealed that neglecting buoyancy effect in the gas phase underestimates the evaporation rate especially for heated cases. ...
... The combined evaporation mode appears for the evaporation dynamics of the inclined droplet at φ = 0 and π and the mixed evaporation mode at φ = π/4, π/2, and 3π/4. Considering the possible onset of convection in the atmosphere which would enhance the evaporation 8,30,31 , one may expect the onset of convection on the vertical substrate and the shorter lifetime than on the horizontal substrate. However, our experimental results clearly show that the lifetime of an evaporating droplet on a tilted substrate is controlled by the depinning dynamics of the contact line and not by the onset of convection. ...
When a drop is placed on a flat substrate tilted at an inclined angle, it can be deformed by gravity and its initial contact angle divides into front and rear contact angles by inclination. Here we study on evaporation dynamics of a pure water droplet on a flat solid substrate by controlling substrate inclination and measuring mass and volume changes of an evaporating droplet with time. We find that complete evaporation time of an inclined droplet becomes longer as gravitational influence by inclination becomes stronger. The gravity itself does not change the evaporation dynamics directly, whereas the gravity-induced droplet deformation increases the difference between front and rear angles, which quickens the onset of depinning and consequently reduces the contact radius. This result makes the evaporation rate of an inclined droplet to be slow. This finding would be important to improve understanding on evaporation dynamics of inclined droplets.
... In this section, we briefly analyze the effect of convection on evaporation. Recent studies have addressed the importance of convection on the evaporation of drops [38][39][40][41][42][43]. In the case of water, humid air is less dense than dry air, which leads to natural convection in the surrounding air. ...
The drying of a drop containing particles often results in the accumulation of the particles at the contact line. In this work, we investigate the drying of an aqueous colloidal drop surrounded by a hydrogel that is also evaporating. We combine theoretical and experimental studies to understand how the surrounding vapor concentration affects the particle deposit during the constant radius evaporation mode. In addition to the common case of evaporation on an otherwise dry surface, we show that in a configuration where liquid is evaporating from a flat surface around the drop, the singularity of the evaporative flux at the contact line is suppressed and the drop evaporation is homogeneous. For both conditions, we derive the velocity field and we establish the temporal evolution of the number of particles accumulated at the contact line. We predict the growth dynamics of the stain and the drying timescales. Thus, dry and wet conditions are compared with experimental results and we highlight that only the dynamics is modified by the evaporation conditions, not the final accumulation at the contact line.
... D'unemanì ere plus générale, un modèle empirique pour l'´ evaporation de l'eau a ´ etéetéélaboré par Weon et al. [32]. Il regroupe les cas o` u l'´ evaporation est limitée par la diffusion ou la convection. ...
... Pour cela, nous traçons la figure 3.9, obtenuè a partir de l'´ equation 1.20, et les données expérimentales (carrés bleus) sont ajustées par une droite (en rouge). L'exposant β de l'´ equation 1.20 est doncégaìdoncégaì a 1, validant l'hypothèse d'un régime ancré [32]. Comme nous l'avons mentionné dans la section 2.2.4.3, la décroissance de l'angle de contact est accélérée par la croissance du dépôt périphérique, ce dernier masquant la ligne triple de la goutte. ...
... Pour uné evaporation limitée par la diffusion, l'exposant n de l'´ equation 1.21 estégaìestégaì a 1, tandis Figure 3.13 -´ Evolution du volume de la goutte en fonction du temps t pour différentes valeurs de R, pour T s = 60°C, RH = 18% et θ = 45°. que si l'´ evaporation est limitée par la convection, il estégaìestégaì a 2 [32]. Pour déterminer dans quel cas lesévaporationslesévaporations de gouttes sur substrat solubles se situent, nous traçons l'´ evolution du volume de gouttes d'eau pure de rayons différents s'´ evaporant sur un monocristal de NaCì a une température T s = 60°C, ` a une humidité RH = 18% ( figure 3.13). ...
La compréhension des mécanismes pilotant la cinétique d'évaporation d'une gouttelette sessile sur un substrat inerte a notablement progressé ces dernières années. Ainsi, l'influence de l'angle de contact de la goutte, de la conductivité thermique du solide, de sa rugosité, de la convection thermocapillaire à l'intérieur de la goutte, ou de la convection dans la vapeur environnante, sont maintenant bien compris. Parallèlement, la façon dont des dépôts de type ‘tâche de café' se forment pendant l'évaporation de fluides complexes (suspension colloïdale, sang …) a été étudiée en détail.Toutes ces études ont été réalisées avec des solides non-réactifs. Nous proposons ici d'étudier le comportement d'une goutte d'eau s'évaporant sur un substrat soluble. Dans cette configuration, trois phénomènes sont en interaction complexe : la dissolution/précipitation du substrat à l'interface solide-liquide, la diffusion/convection des espèces dissoutes dans la gouttelette, l'évaporation de l'eau à l'interface liquide-air. Nous avons travaillé avec des solides à dissolution rapide, des monocristaux de NaCl et KCl, à température et humidité contrôlées. Pour tester l'influence des instabilités thermo- et soluto-gravitationnelles, nous avons réalisé des expériences au sol et en micropesanteur, lors de plusieurs campagnes de vols paraboliques CNES.Nous avons observé que la dissolution induisait un ancrage de la ligne triple au tout début de l'évaporation, conduisant à une décroissance linéaire de l'angle de contact avec le temps. A la fin de l'évaporation, un dépôt périphérique apparaît. Cette configuration permet ainsi de faire apparaître des dépôts de type ‘tâche de café' à partir d'une goutte d'eau pure. Ces dépôts sont la preuve d'un écoulement radial de l'intérieur vers l'extérieur au sein de la goutte. L'observation de gouttes ensemencées de particules fluorescentes s'évaporant sur un monocristal de sel a permis de mettre en évidence des écoulements capillaires complexes au sein de celle-ci. La morphologie des dépôts périphériques est très variée, passant continument de la forme de parois inclinées à celle de demi-tore creux, lorsque le volume initial de la goutte ou la température varient
... (24) It means the water molecules diffuse through the liquid-air interface during evaporation. Practically, the convective evaporation effect was observed in a nano-scale droplet (25) and volatile liquid droplets. (26) To investigate contact line movements, we extract the contact line contours from the reconstructed tomographic images. ...
We investigate an internal flow pattern of an evaporating droplet where the contact line non-uniformly recedes. By using tomographic Particle Image Velocimetry, we observe a three-dimensional azimuthal vortex pair that is maintained until the droplet is completely dried. The non-uniformly receding contact line motion breaks the flow symmetry. Finally, a simplified scaling model presents that the mechanical stress along the contact line is proportional to the vorticity magnitude, which is validated by the experimental results.
