Evaporation Of Sessile Droplets Research Articles

Analysis and feasibility of an evaporative cooling system with diffusion-based sessile droplet evaporation for cooling microprocessors

In this study, a feasibility analysis is undertaken to assess the capability of an evaporative cooling system using diffusion-based evaporation of sessile water droplets to provide sufficient cooling of microprocessors within the space requirements of the current heat sinks. The study investigates the cooling requirements for the Intel Xenon Processor and the Intel Core i7-900 Processor. An analytical model is developed to determine the capacity of a single layer of water droplets to provide sufficient cooling and calculates the size of the droplets required to meet the cooling needs. It is found that a single layer can provide sufficient cooling for the Xenon Processor with 21,316 droplets having a radius of 0.25mm and the Core i7-900 Processor with 27,556 droplets having a radius of 0.25mm. A numerical model is developed to analyze a tiered system that fits within the space restrictions corresponding to the current heat sinks, but can provide the required cooling needs with larger droplets and fewer of them. To decrease the complexity of manufacturing the evaporative cooling system, the numerical model simulated cases to find both (i) the minimum number of posts required to connect each of the tiers and (ii) the minimum number of tiers required to provide sufficient cooling for the microprocessors. The results of the numerical modelling work found that a minimum of 60 posts connecting each of the tiers were required to cool the Xenon Processor and 52 posts for the Core i7-900 Processor. It was also found that a minimum of 3 tiers was required for the Xenon Processor, with a total of 867 droplets having a radius of 2mm, and 5 tiers required for the Core i7-900 Processor, with a total of 1620 droplets having a radius of 2mm. The results of the work demonstrate that evaporative cooling systems with diffusion-based evaporation of sessile droplets can provide sufficient cooling for the selected microprocessors, with a number of feasible configurations.

Thermal effects of substrate on Marangoni flow in droplet evaporation: Response surface and sensitivity analysis

In this paper, the evaporation of sessile droplets resting on a substrate with different thermal properties is numerically investigated. Computations are based on a transient axisymmetric numerical model. Special attention is paid to evaluate thermal effects of substrate on the structure of bulk fluid flow in the course of evaporation. Numerical results reveal that Marangoni convection induced by non-uniform distribution of temperature along the interface exhibits three distinctly different behaviours: inward flow, multicellular flow and outward flow, consequently resulting in different particle depositions. It is highlighted that three factors (i.e. relative thermal conductivity, relative substrate thickness and relative substrate temperature) strongly affect the flow pattern. In order to further investigate the coupling effects of different influential factors, a Kriging-based response surface method is introduced. We model the flow behaviour as a function of continuous influential factors using a limited number of computations corresponding to discrete values of the inputs. The sensitivities of the Marangoni flow are also analysed using Sobol’ index to study the coupling mechanisms of influential factors. The proposed method can be used to forecast the flow patterns for any input parameter without additional sophisticated computer simulation, and allows to confidently estimate an unknown environmental parameter.

Evaporation kinetics of surfactant solution droplets on rice (Oryza sativa) leaves.

The dynamics of evaporating sessile droplets on hydrophilic or hydrophobic surfaces is widely studied, and many models for these processes have been developed based on experimental evidence. However, few research has been explored on the evaporation of sessile droplets of surfactant or pesticide solutions on target crop leaves. Thus, in this paper the impact of surfactant concentrations on contact angle, contact diameter, droplet height, and evolution of the droplets’ evaporative volume on rice leaf surfaces have been investigated. The results indicate that the evaporation kinetics of surfactant droplets on rice leaves were influenced by both the surfactant concentrations and the hydrophobicity of rice leaf surfaces. When the surfactant concentration is lower than the surfactant CMC (critical micelle concentration), the droplet evaporation time is much longer than that of the high surfactant concentration. This is due to the longer existence time of a narrow wedge region under the lower surfactant concentration, and such narrow wedge region further restricts the droplet evaporation. Besides, our experimental data are shown to roughly collapse onto theoretical curves based on the model presented by Popov. This study could supply theoretical data on the evaporation of the adjuvant or pesticide droplets for practical applications in agriculture.

Marangoni Contraction of Evaporating Sessile Droplets of Binary Mixtures.

The Marangoni contraction of sessile drops of a binary mixture of a volatile and a nonvolatile liquid has been investigated experimentally and theoretically. The origin of the contraction is the locally inhomogeneous evaporation rate of sessile drops. This leads to surface tension gradients and thus to a Marangoni flow. Simulations show that the interplay of Marangoni flow, capillary flow, diffusive transport, and evaporative losses can establish a quasistationary drop profile with an apparent nonzero contact angle even if both liquid components individually wet the substrate completely. Experiments with different solvents, initial mass fractions, and gaseous environments reveal a previously unknown universal power-law relation between the apparent contact angle and the relative undersaturation of the ambient atmosphere: θapp ∼ (RHeq – RH)1/3. This experimentally observed power law is in quantitative agreement with simulation results. The exponent can also be inferred from a scaling analysis of the hydrodynamic-evaporative evolution equations of a binary mixture of liquids with different volatilities.

Octagon to Square Wetting Area Transition of Water-Ethanol Droplets on a Micropyramid Substrate by Increasing Ethanol Concentration.

The wettability and evaporation of water-ethanol binary droplets on the substrate with micropyramid cavities are studied by controlling the initial ethanol concentrations. The droplets form octagonal initial wetting areas on the substrate. As the ethanol concentration increases, the side ratio of the initial wetting octagon increases from 1.5 at 0% ethanol concentration to 3.5 at 30% ethanol concentration. The increasing side ratio indicates that the wetting area transforms from an octagon to a square if we consider the octagon to be a square with its four corners cut. The droplets experience a pinning-depinning transition during evaporation. The pure water sessile droplet evaporation demonstrates three stages from the constant contact line (CCL) stage, and then the constant contact angle (CCA) stage, to the mixed stage. An additional mixed stage is found between the CCL and CCA stages in the evaporation of water-ethanol binary droplets due to the anisotropic depinning along the two different axes of symmetry of the octagonal wetting area. Droplet depinning occurs earlier on the patterned surface as the ethanol concentration increases.

Transient effects and mass convection in sessile droplet evaporation: The role of liquid and substrate thermophysical properties

In this paper, a transient droplet evaporation model based on Arbitrary Lagrangian–Eulerian (ALE) frame, which tracks the liquid-gas interface evolution and fully couples heat and mass transfer in solid, liquid and gas domains, was used to study the spontaneous evaporation of water, methanol and 3MP droplet (with low to high volatility) on PTFE substrates with small thermal conductivities and Al substrates with large thermal conductivities. It was found that because of the fully coupled transportation processes in droplet evaporation, the duration of transient periods determined according to the judgment criterion based on whether droplet or substrate are very close to each other. The larger the droplet volatility and the smaller the substrate thermal diffusivity, the longer the period of transient stage (normalized) of droplet evaporation, with 33.3% of the droplet lifetime for 3MP on a PTFE substrate. The larger the volatility and the substrate thermal conductivity, the larger the contribution of convective mass transfer for total evaporation, with the under-predictions of diffusive model of 41% for 3MP droplet on Al substrates. The percentage of contribution of natural convection is 29–64% of total contribution of convective mass transport, which points out the necessity of considering natural convection in the modelling of convective mass transfer. The main characteristics of flow field with and without buoyancy flow under the different combination of substrate and liquid material and their roles on mass transfer are discussed.

Spatiotemporal infrared measurement of interface temperatures during water droplet evaporation on a nonwetting substrate

High-fidelity experimental characterization of sessile droplet evaporation is required to understand the interdependent physical mechanisms that drive the evaporation. In particular, cooling of the interface due to release of the latent heat of evaporation, which is not accounted for in simplified vapor-diffusion-based models of droplet evaporation, may significantly suppress the evaporation rate on nonwetting substrates, which support tall droplet shapes. This suppression is counteracted by convective mass transfer from the droplet to the air. While prior numerical modeling studies have identified the importance of these mechanisms, there is no direct experimental evidence of their influence on the interfacial temperature distribution. Infrared thermography is used here to simultaneously measure the droplet volume, contact angle, and spatially resolved interface temperatures for water droplets on a nonwetting substrate. The technique is calibrated and validated to quantify the temperature measurement accuracy; a correction is employed to account for reflections from the surroundings when imaging the evaporating droplets. Spatiotemporally resolved interface temperature data, obtained via infrared thermography measurements, allow for an improved prediction of the evaporation rate and can be utilized to monitor temperature-controlled processes in droplets for various lab-on-a-chip applications.

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.

Confinement-induced alterations in the evaporation dynamics of sessile droplets.

Evaporation of sessile droplets has been a topic of extensive research. However, the effect of confinement on the underlying dynamics has not been well explored. Here, we report the evaporation dynamics of a sessile droplet in a confined fluidic environment. Our findings reveal that an increase in the channel length delays the completion of the evaporation process and leads to unique spatio-temporal evaporation flux and internal flow. The evaporation modes (constant contact angle and constant contact radius) during the droplet lifetime however exhibit global similarity when normalized by appropriate length and timescales. These results are explained in light of an increase in vapor concentration inside the channel due to greater accumulation of water vapor on account of increased channel length. We have formulated a theoretical framework which introduces two key parameters namely an enhanced concentration of the vapor field in the vicinity of the confined droplet and a corresponding accumulation lengthscale over which the accumulated vapor relaxes to the ambient concentration. Using these two parameters and modified diffusion based evaporation we are able to show that confined droplets exhibit a universal behavior in terms of the temporal evolution of each evaporation mode irrespective of the channel length. These results may turn out to be of profound importance in a wide variety of applications, ranging from surface patterning to microfluidic technology.

Experimental study of water evaporation of sessile droplets on a solid substrate with different thermal conductivities

The results of experimental studies of water evaporation of sessile droplet on solid substrates with different thermal conductivities are presented. In experiments during droplet evaporation the temperature of its surface was determined using the infrared thermography method. The obtained results showed that interfacial temperature was higher than the adiabatic evaporation temperature for all substrates. As thermal conductivity of the substrate decreased, the droplet temperature decreased and the evaporation lifetime increased significantly. As a result it was established that the thermal conductivity of the material has a significant effect on the evaporation of droplets.

Evaporation of a nanodroplet on a rough substrate

The wettability and roughness of a substrate are crucial to the evolution of the contact angle and three-phase contact line in the evaporation of sessile droplets. In this paper, by performing molecular dynamics simulations for droplet evaporation at the nanoscale, we show that the wettability is more important than the roughness. For a smooth substrate, the evaporation behavior of a nanodroplet is similar to that at the macroscopic scale. This similarity is also observed in the case of a rough hydrophilic substrate. However, for a rough hydrophobic substrate, both the constant contact angle and contact line pinning appear in turn during evaporation. This suggests that the roughness of the hydrophobic substrate is useful for the evaporation technique in self-assembly at the nanoscale.

Effect of substrate conductivity on the evaporation of small sessile droplets.

Here we show the effect of the thermal conductivity of the substrate on the evaporation process of small droplets. We deposited small droplets on the order of 100-500μm in diameter on four different substrates with different thermal conductivities and surface properties, and we measured the evaporation time. Also, a numerical model that describes this process was developed to include thermal effects inside the droplet and heat transfer from the substrate. Our model considers the entire time of evaporation including the pinned and depinned stages. This model uses a new approach for the contact line behavior. It uses experimental results to define the movement of the contact line as a function of the contact angle.

Local Heat Transfer to an Evaporating Sessile Droplet in an Electric Field

Local heat transfer of an evaporating sessile droplet under a static electric field is an underdeveloped topic. In this research an 80 μl water droplet is placed in the centre of a 25 μm thick stainless steel substrate. A static electric field is applied by an electrode positioned 10 mm above the substrate. A high speed thermal imaging camera is placed below the substrate to capture the thermal footprint of the evaporating droplet. Four electric fields were characterised; 0, 5, 10 and 11 kV/cm. As the electric field is increased the contact angle was observed to decrease. The local heat flux profile, peak and radial location of this peek were observed to be independent of the applied electric field for all test points for this working fluid and surface combination.

Deposition patterns from evaporating sessile droplets with suspended mixtures of multi-sized and multi-species hydrophilic and non-adsorbing nanoparticles

Effects of multi-sized and multi-species nanoparticles on the deposition profiles from evaporating sessile droplets are investigated experimentally. With specific combinations of the small and the large size alumina nanoparticles, the heterogeneities of the two single-sized nanoparticle patterns are eliminated, and a homogeneous mixture pattern is produced. The small particles prevent the droplet from shrinking which occurs in the droplet of the large alumina nanoparticles, and the interactions between the small and the large particles suppress the center-oriented accumulation of the small nanoparticles taking place in the droplet of the small nanoparticles. The mixture pattern assembled by two different species of nanoparticles either exhibits both the features of the single-species patterns or is analogous to solely one of them. An energy dispersive X-ray spectroscope analysis confirms that each nanoparticle species tends to behave similarly for its mixture pattern and its single species pattern. Nanoparticles with a greater pinning effect prohibit the inward transport of the other species, while two nanoparticle species behaving similarly in their single patterns repeat their respective features in the mixture pattern. Particle-particle interactions coupling with the particle-dependent droplet dynamics controls the deposit morphology from the nanofluid droplets.

Evaporation of Sessile Droplets Laden with Particles and Insoluble Surfactants.

We consider the flow dynamics of a thin evaporating droplet in the presence of an insoluble surfactant and noninteracting particles in the bulk. On the basis of lubrication theory, we derive a set of evolution equations for the film height, the interfacial surfactant, and bulk particle concentrations, taking into account the dependence of liquid viscosity on the local particle concentration. An important ingredient of our model is that it takes into account the fact that the surfactant adsorbed at the interface hinders evaporation. We perform a parametric study to investigate how the presence of surfactants affects the evaporation process as well as the flow dynamics with and without the presence of particles in the bulk. Our numerical calculations show that the droplet lifetime is affected significantly by the balance between the ability of the surfactant to enhance spreading, suppressing the effect of thermal Marangoni stresses-induced motion, and to hinder the evaporation flux through the reduction of the effective interfacial area of evaporation, which tend to accelerate and decelerate the evaporation process, respectively. For particle-laden droplets and in the case of dilute solutions, the droplet lifetime is found to be weakly dependent on the initial particle concentration. We also show that the particle deposition patterns are influenced strongly by the direct effect of the surfactant on the evaporative flux; in certain cases, the "coffee-stain" effect is enhanced significantly. A discussion of the delicate interplay between the effects of capillary pressure and solutal and thermal Marangoni stresses, which drive the liquid flow inside of the evaporating droplet giving rise to the observed results, is provided herein.

Evaporation dynamics and sedimentation pattern of a sessile particle laden water droplet

The dynamics of the flow inside an evaporating sessile droplet of water with polystyrene micro-spheres of 1.0 μm in diameter in suspension is described. The initial volume of the droplets is in the range from 0.6 to 1.0 μl, and observations were made in the last stages before total evaporation. The flow was recorded in a sequence of images that were analyzed with a micro-PIV system to extract quantitative information. Also, using image analysis techniques we determined the dynamics of the retreating liquid film once unpinned from the original contact line. Additionally, we have explored its correlation to the formation of the sediment pattern which is organized in elongated mounds roughly deposited in azimuthal and radial orientations. It is found that the aggregation dynamics of micro-spheres in the segments of the two orientations is different. This might have a substantial influence on the final arrangement of micro-spheres in the sediments.

Velocity field measurements in an evaporating sessile droplet by means of micro-PIV technique

Velocity fields are measured in evaporating sessile droplets on two substrates with different contact angles and contact angle hysteresis using micro resolution particle image velocimetry technique. Different flow patterns are observed in different stages of droplet evaporation: a flow with vortices and a radial flow. Flow structure is found to be similar for droplets on different substrates.

Towards universal buckling dynamics in nanocolloidal sessile droplets: the effect of hydrophilic to superhydrophobic substrates and evaporation modes.

The evaporation of a nanocolloidal sessile droplet exhibits preferential particle assembly, nanoporous shell formation and buckling to form cavities with unique morphological features. Here, we have established many universal trends that explain the buckling dynamics under one umbrella irrespective of hydrophobicity, evaporation mode and particle loading. We provide a regime map explaining the droplet morphology and buckling characteristics for droplet evaporation on various substrates. Specifically, we find that the final droplet volume and the radius of curvature at the buckling onset are universal functions of particle concentration. Furthermore, we establish that post-buckling cavity growth is evaporation driven regardless of the substrate.

Effect of Marangoni Flows on the Shape of Thin Sessile Droplets Evaporating into Air.

Freely receding evaporating sessile droplets of perfectly wetting liquids, for which the observed finite contact angles are attributed to evaporation, are studied with a Mach-Zehnder interferometer. The experimentally obtained droplet shapes are found to depart, under some conditions, from the classical macroscopic static profile of a sessile droplet. The observed deviations (or the absence thereof) are explained in terms of a Marangoni flow due to evaporation-induced thermal gradients along the liquid-air interface. When such a Marangoni effect is strong, the experimental profiles exhibit a maximum of the slope at a certain distance from the contact line. In this case, the axisymmetric flow is directed from the contact line to the apex (along the liquid-air interface), hence delivering more liquid to the center of the droplet and making it appear inflated. These findings are quantitatively confirmed by predictions of a lubrication model accounting for the impact of the Marangoni effect on the droplet shape.

Contribution of convective transport to evaporation of sessile droplets: Empirical model

Despite the fact that sessile droplets evaporation dynamics has been studied for more than half a century, the scientific community struggles with the creation of an accurate quantitative description of the rate of evaporation. The classically used description considers evaporation as a quasi-steady process controlled by the diffusion of vapour into the air and the whole system is assumed to be isothermal at the ambient temperature. However, when two types of fluids (alcohols and alkanes) are let to evaporate on heated substrates, their evaporation rates tend to be underestimated by this model, mostly due to convection. This experimental study aims to understand how atmospheric convective transport in the vapour phase influences evaporation in order to develop an empirical model that accurately describes the evaporation rate. The Rayleigh number is used to analyse the contribution of natural convection and an empirical model is developed combining diffusive and convective transport for each type of fluid. The influence of the molecular chain length (and the increasing number of carbon atoms) is also being discussed.