Influence of substrate heating on the evaporation dynamics of pinned water droplets

Mathematical Modeling of the Evaporation of a Water Drop from a Heated Surface

This paper presents the results of mathematical modeling of the evaporation of a single water drop from the surface of a copper substrate using a new model, which does not require special experiments to close the system of equations and the corresponding boundary conditions with empirical constants. On the basis of the results of mathematical modeling, it was found that convective currents that occur in a small water drop (≤1 mm in diameter) do not significantly affect the characteristics or conditions of heat and mass transfer processes occurring in a liquid drop heated on a copper substrate. The results of numerical simulation showed that during the initial period of droplet heating, the latter undergoes a rapid transformation of the flow field. Five seconds after the beginning of the thermal action, a quasi-stationary regime of flows in the drop sets in. The model is tested on known experimental data. The theoretical analysis of temperatures at the characteristic points of a water drop and the surface on which the drop is located is carried out in ranges of thermal loads quite typical for practice, conditions for transferring heat and water vapor to the environment. According to the results of mathematical modeling, the possibility of using the developed model in the analysis of the state of cooling of surfaces heated to high temperatures, in cases typically used, is substantiated.

Multiscale Self-Assembly of Distinctive Weblike Structures from Evaporated Drops of Dilute American Whiskeys

When a sessile droplet of a complex mixture evaporates, its nonvolatile components may deposit into various patterns. One such phenomena, the coffee ring effect, has been a topic of interest for several decades. Here, we identify what we believe to be a fascinating phenomenon of droplet pattern deposition for another well-known beverage-what we have termed a "whiskey web". Nanoscale agglomerates were generated in diluted American whiskeys (20-25% alcohol by volume), which later stratified as microwebs on the liquid-air interface during evaporation. The web's strandlike features result from monolayer collapse, and the resulting pattern is a function of the intrinsic molecular constituents of the whiskey. Data suggest that, for our conditions (diluted 1.0 μL drops evaporated on cleaned glass substrates), whiskey webs were unique to diluted American whiskey; however, similar structures were generated with other whiskeys under different conditions. Further, each product forms their own distinct pattern, demonstrating that this phenomenon could be used for sample analysis and counterfeit identification.

Effect of Substrate Conductivity on the Transient Thermal Transport of Hygroscopic Droplets during Vapor Absorption

In all kinds of liquid desiccant dehumidification systems, the temperature increase of the desiccant solution due to the effect of absorptive heating is one of the main reasons of performance deterioration. In this study, we look into the thermal effects during vapor absorption into single hygroscopic liquid desiccant droplets. Specifically, the effect of substrate conductivity on the transient heat and mass transfer process is analyzed in detail. The relative strength of the thermal effect and the solutal effect on the rate of vapor absorption is investigated and compared to the thermal effect by evaporative cooling taking place in pure water droplets. In the case of liquid desiccants, results indicate that the high thermal conductivity of copper substrates ensures more efficient heat removal, and the temperature at the droplet surface decreases more rapidly than that on Polytetrafluoroethylene (PTFE) substrates. As a result, the initial rate of vapor absorption on copper substrates slightly outweighs that on PTFE substrates. Further analysis by decomposing the vapor pressure difference indicates that the variation of vapor pressure caused by the temperature change during vapor absorption is much weaker than that induced by the concentration change. The conclusions demonstrate that a simplified isothermal model can be applied to capture the main mechanisms during vapor absorption into hygroscopic droplets even though it is evidenced to be unreliable for droplet evaporation.

Recent advances in droplet wetting and evaporation

Wetting and evaporation of a simple sessile droplet is a very complex problem involving strongly coupled physics.

Experimental investigation of interfacial energy transport in an evaporating sessile droplet for evaporative cooling applications

In this paper we experimentally examine evaporation flux distributions and modes of interfacial energy transport for continuously fed evaporating spherical sessile water droplets in a regime that is relevant for applications, particularly for evaporative cooling systems. The contribution of the thermal conduction through the vapor phase was found to be insignificant compared to the thermal conduction through the liquid phase for the conditions we investigated. The local evaporation flux distributions associated with thermal conduction were found to vary along the surface of the droplet. Thermal conduction provided a majority of the energy required for evaporation but did not account for all of the energy transport, contributing 64±3%, 77±3%, and 77±4% of the energy required for the three cases we examined. Based on the temperature profiles measured along the interface we found that thermocapillary flow was predicted to occur in our experiments, and two convection cells were consistent with the temperature distributions for higher substrate temperatures while a single convection cell was consistent with the temperature distributions for a lower substrate temperature.

Insight into the Evaporation Dynamics of a Pair of Sessile Droplets on a Hydrophobic Substrate

In this work, we have demonstrated three unique regimes in the evaporation lifecycle of a pair of sessile droplets placed in variable proximity on a hydrophobic substrate. For small separation distance, the droplets undergo asymmetric spatiotemporal evaporation leading to contact angle hysteresis and suppressed vaporization. The reduced evaporation has been attributed quantitatively to the existence of a constrained vapor-rich dome between the two droplets. However, a dynamic decrease in the droplet radius due to solvent removal marks a return to symmetry in terms of evaporation and contact angle. We have described the variation in evaporation flux using a universal correction factor. We have also demonstrated the existence of a critical separation distance beyond which the droplets in the droplet pair do not affect each other. The results are crucial to a plethora of applications ranging from surface patterning to lab-on-a-chip devices.

A numerical investigation on the drainage of a surfactant-modified water droplet in paraffin oil

A volume of fluid approach is used in numerical simulations of the settling motion of a surfactant modified water droplet in a continuous paraffin oil phase. The droplet is millimeter-sized and confined in a square two dimensional domain. The surfactant interfacial and bulk concentration-equations are solved together with the incompressible Navier-Stokes equation. The role of boundary walls in the overall settling dynamics is described. As the droplet moves downwards the interfacial shear creates non-homogeneous interfacial surfactant concentrations and Marangoni driven phenomena come into play. A decrease of the drainage velocity is then evidenced indicating that buoyancy forces are counter balanced by Marangoni induced lift-forces. The lateral migration of the droplet due to boundary wall proximity is discussed. It is shown to increase with wall proximity and to decrease when increasing the interfacial concentration. Finally, a simplified model is used to investigate the evolution of the bulk concentration assuming the surfactant is insoluble in paraffin oil and poorly soluble in water.

Combined effects of underlying substrate and evaporative cooling on the evaporation of sessile liquid droplets

The evaporation of pinned, sessile droplets resting on finite thickness substrates was investigated numerically by extending the combined field approach to include the thermal properties of the substrate. By this approach, the combined effects of the underlying substrate and the evaporative cooling were characterized. The results show that the influence of the substrate on the droplet evaporation depends largely on the strength of the evaporative cooling. When the evaporative cooling is weak, the influence of substrate is also weak. As the strength of evaporative cooling increases, the influence of the substrate becomes more and more pronounced. Further analyses indicated that it is the cooling at the droplet surface and the temperature dependence of the saturation vapor concentration that relate the droplet evaporation to the underlying substrate. This indicates that the evaporative cooling number, Ec, can be used to identify the influence of the substrate on the droplet evaporation. The theoretical predictions by the present model are compared and found to be in good agreement with the experimental measurements. The present work may contribute to the body of knowledge concerning droplet evaporation and may have applications in a wide range of industrial and scientific processes.

Simultaneous spreading and evaporation: recent developments

The recent progress in theoretical and experimental studies of simultaneous spreading and evaporation of liquid droplets on solid substrates is discussed for pure liquids including nanodroplets, nanosuspensions of inorganic particles (nanofluids) and surfactant solutions. Evaporation of both complete wetting and partial wetting liquids into a nonsaturated vapour atmosphere are considered. However, the main attention is paid to the case of partial wetting when the hysteresis of static contact angle takes place. In the case of complete wetting the spreading/evaporation process proceeds in two stages. A theory was suggested for this case and a good agreement with available experimental data was achieved. In the case of partial wetting the spreading/evaporation of a sessile droplet of pure liquid goes through four subsequent stages: (i) the initial stage, spreading, is relatively short (1-2 min) and therefore evaporation can be neglected during this stage; during the initial stage the contact angle reaches the value of advancing contact angle and the radius of the droplet base reaches its maximum value, (ii) the first stage of evaporation is characterised by the constant value of the radius of the droplet base; the value of the contact angle during the first stage decreases from static advancing to static receding contact angle; (iii) during the second stage of evaporation the contact angle remains constant and equal to its receding value, while the radius of the droplet base decreases; and (iv) at the third stage of evaporation both the contact angle and the radius of the droplet base decrease until the drop completely disappears. It has been shown theoretically and confirmed experimentally that during the first and second stages of evaporation the volume of droplet to power 2/3 decreases linearly with time. The universal dependence of the contact angle during the first stage and of the radius of the droplet base during the second stage on the reduced time has been derived theoretically and confirmed experimentally. The theory developed for pure liquids is applicable also to nanofluids, where a good agreement with the available experimental data has been found. However, in the case of evaporation of surfactant solutions the process deviates from the theoretical predictions for pure liquids at concentration below critical wetting concentration and is in agreement with the theoretical predictions at concentrations above it.

Temperature distribution along the surface of evaporating droplets

The surface temperature can significantly affect the flow field of drying droplets. Most previous studies assumed a monotonic temperature variation along the droplet surface. However, the present analyses indicate that a nonmonotonic spatial distribution of the surface temperature should occur. Three different patterns of the surface temperature distribution may appear during the evaporation process of liquid droplets: (i) the surface temperature increases monotonically from the center to the edge of the droplet; (ii) the surface temperature exhibits a nonmonotonic spatial distribution along the droplet surface; (iii) the surface temperature decreases monotonically from the center to the edge of the droplet. These surface temperature distributions can be explained by combining the evaporative cooling at the droplet surface and the heat conduction across the substrate and the liquid. Furthermore, a "phase diagram" for the distribution of the surface temperature is introduced and the effect of the spatial temperature distribution along the droplet surface on the flow structure of the droplet is discussed. The results may provide a better understanding of the Marangoni effect of drying droplets and provide a potential way to control evaporation-driven deposition as well as the assembly of colloids and other materials.

Thermal patterns and hydrothermal waves (HTWs) in volatile drops

Experimental measurements of temperature and heat flux at the liquid-wall interface during the evaporation of sessile FC-72 droplets have been reported for the first time using infrared (IR) thermography. Simultaneous high-speed imaging of the evaporating drop was carried out to monitor the drop profile. The study demonstrates that recently evidenced hydrothermal waves are actually bulk waves that extend across the entire droplet volume. More importantly, thermal patterns occurring in the bulk of the drop affect the temperature and heat-flux distributions on the solid substrate and ultimately influence the droplet evaporation rate. These effects were found to be increasingly pronounced as the substrate temperature was raised. The implications for heat-transfer mechanisms and energy transport are discussed.

Characteristic size for onset of coffee-ring effect in evaporating lysozyme-water solution droplets

Liquid droplets containing suspended particles deposited on a solid surface often form a ring-like structure due to the redistribution of solute during evaporation, a phenomenon known as the "coffee ring effect". The complex patterns left on the substrate after evaporation are characteristic of the nature of the solute and the particle transport mechanisms. In this study, the morphological evolution and conditions for coffee ring formation for simplified model biological solutions of DI water and lysozyme are examined by AFM and optical microscopy. Lysozyme is a globular protein found in high concentration, for example, in human tears and saliva. The drop diameters studied are very small, ranging from 1 to 50 μm. In this size range, protein motion and the resulting dried residue morphology are highly influenced by the decreased evaporation time of the drop. In this work, we consider the effect of droplet size and concentration on the morphology of the deposited drop as well as the minimal conditions for coffee ring formation in this system. Two distinct deposit types are observed: a simple cap-shaped deposit for drops with small diameters and a ring-like deposit at larger diameters. Ring formation occurs at a critical diameter, which depends systematically on initial lysozyme concentration.

Use of IR thermography to investigate heated droplet evaporation and contact line dynamics

In this paper we present the results of an experimental study investigating interfacial properties during the evaporation of sessile water droplets on a heated substrate. This study uses infrared thermography to map the droplet interfacial temperature. The measurements evidence nonuniform temperature and gradients that evolve in time during the evaporation process. A general scaling law for the interfacial temperature is deduced from the experimental observations. A theoretical analysis is performed to predict the local evaporation rates and their evolution in time. The use of energy conservation laws enabled us to deduce a general expression for the interfacial temperature. The comparison between the theory and experiments shows good agreement and allows us to rationalize the experimental observations. The thermography analysis also enabled the detection of the three-phase contact line location and its dynamics. To our knowledge, such measurements are performed for the first time using thermography.

Criterion for reversal of thermal Marangoni flow in drying drops

The thermal Marangoni flow induced by nonuniform surface temperature has been widely invoked to interpret the deposition pattern from drying drops. The surface temperature distribution of a drying droplet, although being crucial to the Marangoni flow, is still controversial. In this paper, the surface temperature in the drop central region is analyzed theoretically based on an asymptotic analysis on the heat transfer in such region, and a quantitative criterion is established for the direction of the surface temperature gradient and the direction of the induced Marangoni flow of drying drops. The asymptotic analysis indicates that these two directions will reverse at a critical contact angle, which depends not only on the relative thermal conductivities of the substrate and liquid, but also on the ratio of the substrate thickness to the contact-line radius of the droplet. The theory is corroborated experimentally and numerically, and may provide a potential means to control deposition patterns from drying droplets.