Diffusion-controlled evaporation of sodium dodecyl sulfate solution drops placed on a hydrophobic substrate

Water Drop Evaporation on Slippery Liquid-Infused Porous Surfaces (SLIPS): Effect of Lubricant Thickness, Viscosity, Ridge Height, and Pattern Geometry

Sessile drop evaporation and condensation on slippery liquid-infused porous surfaces (SLIPS) is crucial for many applications. However, its modeling is complex since the infused lubricant forms a wetting ridge around the drop close to the contact line, which partially blocks the free surface area and decreases the drop evaporation rate. Although a good model was available after 2015, the effects of initial lubricant heights (h_oil)_i above the pattern, and the corresponding initial ridge heights (h_r)_i, lubricant viscosity, and solid pattern type were not well studied. This work fills this gap where water drop evaporations from SLIPS, which are obtained by infusing silicone oils (20 and 350 cSt) onto hydrophobized Si wafer micropatterns having both cylindrical and square prism pillars, are investigated under constant relative humidity and temperature conditions. With the increase of (h_oil)_i, the corresponding (h_r)_i increased almost linearly on lower parts of the drops for all SLIPS samples, resulting in slower drop evaporation rates. A novel diffusion-limited evaporation equation from SLIPS is derived depending on the available free liquid-air interfacial area, A_LV, which represents the unblocked part of the total drop surface. The calculation of the diffusion constant, D, of water vapor in air from (dA_LV/dt) values obtained by drop evaporation was successful up to a threshold value of (h_oil)_i = 8 μm within ±7%, and large deviations (13-27%) were obtained when (h_oil)_i > 8 μm, possibly due to the formation of thin silicone oil cloaking layers on drop surfaces, which partially blocked evaporation. The increase of infused silicone oil viscosity caused only a slight increase (12-17%) in drop lifetimes. The effects of the geometry and size of the pillars on the drop evaporation rates were minimal. These findings may help optimize the lubricant oil layer thickness and viscosity used for SLIPS to achieve low operational costs in the future.

Evaporation of Sessile Droplets of Polyelectrolyte/Surfactant Mixtures on Silicon Wafers

The wetting and evaporation behavior of droplets of aqueous solutions of mixtures of poly(diallyldimethylammonium chloride) solution, PDADMAC, with two different anionic surfactants, sodium laureth sulfate, SLES, and sodium N-lauroyl N-methyl taurate, SLMT, were studied in terms of the changes of the contact angle θ and contact length L of sessile droplets of the mixtures on silicon wafers at a temperature of 25 °C and different relative humidities in the range of 30–90%. The advancing contact angle θa was found to depend on the surfactant concentration, independent of the relative humidity, with the mixtures containing SLES presenting improved wetting behaviors. Furthermore, a constant droplet contact angle was not observed during evaporation due to pinning of the droplet at the coffee-ring that was formed. The kinetics for the first evaporation stage of the mixture were independent of the relative humidity, with the evaporation behavior being well described in terms of the universal law for evaporation.

Marangoni circulation in evaporating droplets in the presence of soluble surfactants

HYPOTHESIS

Soluble surfactants in evaporating sessile droplets can cause a circulatory Marangoni flow. However, it is not straightforward to predict for what cases this vortical flow arises. It is hypothesized that the occurrence of Marangoni circulation can be predicted from the values of a small number of dimensionless parameters.

SIMULATIONS

A numerical model for the drop evolution is developed using lubrication theory. Surfactant transport is implemented by means of convection-diffusion-adsorption equations. Results are compared to literature.

FINDINGS

It is shown that stronger evaporation, slower adsorption kinetics and lower solubility of the surfactants all tend to increasingly suppress Marangoni circulation. These results are found to be consistent with both experimental and numerical results from literature and can explain qualitative differences in flow behavior of surfactant-laden droplets. Furthermore, diffusion also tends to counteract Marangoni flow, where bulk diffusion has a more significant influence than surface diffusion. Also, the formation of micelles is found to slightly suppress Marangoni circulation. Experimental results from literature, however, show that in some cases circulatory behavior is enhanced by micelles, possibly even resulting in qualitative changes in the flow. Potential explanations for these differences are given and extensions to the model are suggested to improve its consistency with experiments.

Dependency of Contact Angles on Three-Phase Contact Line: A Review

The wetted area of a sessile droplet on a practical substrate is limited by the three-phase contact line and characterized by contact angle, contact radius and drop height. Although, contact angles of droplets have been studied for more than two hundred years, there are still some unanswered questions. In the last two decades, it was experimentally proven that the advancing and receding contact angles, and the contact angle hysteresis of rough and chemically heterogeneous surfaces, are determined by interactions of the liquid and the solid at the three-phase contact line alone, and the interfacial area within the contact perimeter is irrelevant. However, confusion and misunderstanding still exist in this field regarding the relationship between contact angle and surface roughness and chemical heterogeneity. An extensive review was published on the debate for the dependence of apparent contact angles on drop contact area or the three-phase contact line in 2014. Following this old review, several new articles were published on the same subject. This article presents a review of the novel articles (mostly published after 2014 to present) on the dependency of contact angles on the three-phase contact line, after a short summary is given for this long-lasting debate. Recently, some improvements have been made; for example, a relationship of the apparent contact angle with the properties of the three-phase line was obtained by replacing the solid–vapor interfacial tension term, γSV, with a string tension term containing the edge energy, γSLV, and curvature of the triple contact line, km, terms. In addition, a novel Gibbsian thermodynamics composite system was developed for a liquid drop resting on a heterogeneous multiphase and also on a homogeneous rough solid substrate at equilibrium conditions, and this approach led to the same conclusions given above. Moreover, some publications on the line energy concept along the three-phase contact line, and on the “modified” Cassie equations were also examined in this review.

Facilitating the natural semi-drying of oily sludge by changing the form of water

Reducing the water content of oily sludge is essential for the disposal of it. Despite conditioning and solid-liquid separation, the water content of oily sludge generally exceeds 65%. A large amount of this water exists in the form of emulsified and bound water, reducing the efficiency of water removal during the natural semi-drying process of oily sludge. To shorten the time required for natural semi-drying, this study applied an orthogonal test to screen an oily sludge modified material (OSM). The effect and mechanism of OSM on the natural semi-drying of oily sludge were studied using a thermal gravimetric analyzer (TGA), scanning electron microscope (SEM), surface tension measurement, and microscopic observations. The results show that when the ambient temperature exceeded 10°C, the OSM increased in mass by 8-10%, and the time required for the natural semi-drying of oily sludge was shortened from 15 days to less than 5 days. OSM can rupture the emulsion, reduce the surface tension, convert the emulsion and bound water in the oily sludge into free water, and accelerate the rate of water migration, diffusion, and natural evaporation from the inside of the oily sludge to the surface and air. The research results show that changing the form of water can speed up the drying of oily sludge, creating positive economic benefits in the process of oily sludge reduction and recycling.

Practical Applications of Superhydrophobic Materials and Coatings: Problems and Perspectives

Synthetic superhydrophobic (SH) surfaces were developed after 1990s, and the number of publications in this field is around 13 500 at present. However, the industrial production of SH coatings is very unsatisfying after the intensive research activity in the last two decades. The main reason is the loss of the water repellence properties when SH surfaces are exposed to outdoor conditions due to their weak mechanical properties and contamination from the medium which removes the initial SH properties. In this Feature Article, we focus on the scientific and technical reasons which prevent the application of the SH surfaces in our daily lives by highlighting some well-known but mostly overlooked problems in this area. (The synthesis methods of SH surfaces are not the subject of this article since they were reviewed previously in very good articles.) The basic contact angle science and the issue of the cancellation of the Wenzel and Cassie-Baxter equations are reviewed in the first part. The issues of the expensive and small-scale SH surface preparation problems, the difficulties in obtaining a transparent SH surface, the troubles arising from the water vapor condensation on an SH surface, the lack of robustness and abrasion resistance of most of the SH surfaces, the drawbacks of the fabricated self-healing SH surfaces, the short useful service life of self-cleaning SH surfaces due to surface contamination, and the ineffective anti-icing SH coatings are reviewed in the following text. Some important problems affecting the unsuccessful industrial applications of the SH surfaces are discussed critically in the Conclusions and Outlook section. Finally, some proposals are presented for future directions on the synthesis and applications of SH surfaces.

Simple Model for Diffusion-Limited Drop Evaporation of Binary Liquids from Physical Properties of the Components: Ethanol-Water Example

The understanding of the evaporation process of drops consisting of binary mixtures, in particular ethanol-water drops, is important in many industries such as ink-jet printing, cooling of microelectronics, and alcohol-added pesticide spray applications. The theory of the diffusion-limited drop evaporation process for pure liquids has been investigated thoroughly, and linear (dV^(2/3)/dt) slopes were obtained for most of the cases. However, the evaporation of binary liquid drops was found to be much more complicated than that of the pure liquids due to the change of the composition of the drop by time and there is a need for the development of a new model. The experimental results on the diffusion-limited drop evaporation behavior of ethanol-water binary drops initially containing 25 and 50% ethanol by wt and having a volume of 7 μL were reported on a flat hydrophobic Teflon-FEP substrate under the constant relative humidity of 54% and 25 °C temperature conditions, together with pure liquids. The change of contact angles, heights, and contact radius of the drops by time were monitored with a camera. In a parallel study, the concentration changes in the bulk composition of ethanol-water binary drops of 7 μL (25 and 50% ethanol by wt) by time in the same evaporation conditions were monitored using a refractive index-ethanol concentration calibration curve. Then, the parameters affecting the drop evaporation process, such as total vapor pressures, average diffusion coefficient of binary vapors, average molecular weights, and densities of the liquid drops, were calculated using well-known physical chemistry approaches from the previously published data. These parameters were used to estimate the rate of binary ethanol-water drop evaporation, and it was determined that the proposed model fitted the (dV^(2/3)/dt) slopes obtained from experimental data points with lower than 5% error when the surface cooling of the drops was considered.

Evaporation of Dilute Sodium Dodecyl Sulfate Droplets on a Hydrophobic Substrate

Evaporation of surfactant-laden sessile droplets is omnipresent in nature and industrial applications such as inkjet printing. Soluble surfactants start to form micelles in an aqueous solution for surfactant concentrations exceeding the critical micelle concentration (CMC). Here, the evaporation of aqueous sodium dodecyl sulfate (SDS) sessile droplets on hydrophobic surfaces was experimentally investigated for SDS concentrations ranging from 0.025 to 1 CMC. In contrast to the constant contact angle of an evaporating sessile water droplet, we observed that, at the same surface, the contact angle of an SDS laden droplet with concentration below 0.5 CMC first decreases, then increases, and finally decreases, resulting in a local contact angle minimum. Surprisingly, the minimum contact angle was found to be substantially lower than the static receding contact angle and decreased with decreasing initial SDS concentration. Furthermore, the bulk SDS concentration at the local contact angle minimum was found to decrease with decrease in the initial SDS concentration. The location of the observed contact angle minimum relative to the normalized evaporation time and its minimum value proved to be independent of both the relative humidity and droplet volume and thus of the total evaporation time. We discuss the observed contact angle dynamics in terms of the formation of a disordered layer of SDS molecules on the substrate at concentrations below 0.5 CMC. The present work underlines the complexity of the evaporation of sessile liquid-surfactant droplets and the influence of surfactant-substrate interactions on the evaporation process.

Mathematical Modeling of Diffusion of a Hydrophilic Ionic Fertilizer in Plant Cuticles: Surfactant and Hygroscopic Effects

The agricultural industry requires improved efficacy of sprays being applied to crops and weeds to reduce their environmental impact and increase financial returns. One way to improve efficacy is by enhancing foliar penetration. The plant leaf cuticle is the most significant barrier to agrochemical diffusion within the leaf. The importance of a mechanistic mathematical model has been noted previously in the literature, as each penetration experiment is dictated by its specific parameters, namely plant species, environmental conditions such as relative humidity and spray formulation including adjuvant addition. A mechanistic mathematical model has been previously developed by the authors, focusing on plant cuticle diffusion of calcium chloride through tomato fruit cuticles including pore swelling, ion binding and evaporation, along with the ability to vary the active ingredient concentration and type, relative humidity and plant species. Here we further develop this model to include adjuvant effects as well as the hygroscopic nature of deliquescent ionic solutions with evaporation on the cuticle surface. These modifications to a penetration and evaporation model provide a novel addition to the literature and allow the model to be applied to many types of evaporating ionic hygroscopic solutions on many types of substrates, not just plant cuticles. We validate our theoretical model results against appropriate experimental data, discuss key sensitivities and relate theoretical predictions to physical mechanisms. The important governing mechanisms influencing surfactant enhanced penetration of ionic active through plant cuticles were found to be aqueous pore radius, pore density, cuticle thickness and initial contact angle of the applied droplet; ion binding, relative humidity and evaporation including hygroscopic water absorption parameters for point of deliquescence. The sensitivity analysis indicated surfactants increase penetration by changing the point of deliquescence of a solution, which alters the water absorption and the initial contact angle, which alters the number of pores under the droplet. The results of the validation and sensitivity analysis imply that this model accounts for many of the mechanisms governing penetration in plant cuticles.

Liquid Marbles: From Industrial to Medical Applications

Liquid marbles are versatile structures demonstrating a pseudo-Leidenfrost wetting regime formed by encapsulating microscale volumes of liquid in a particle shell. The liquid core is completely separated from the exterior through air pockets. The external phase consists of hydrophobic particles, in most cases, or hydrophilic ones distributed as aggregates. Their interesting features arise from the double solid-fluid character. Thus, these interesting formations, also known as “dry waters”, have gained attention in surface science. This review paper summarizes a series of proposed formulations, fabrication techniques and properties, in correlation with already discovered and emerging applications. A short general review of the surface properties of powders (contact angle, superficial tension) is proposed, followed by a presentation of liquid marbles’ properties (superficial characteristics, elasticity, self-propulsion etc.). Finally, applications of liquid marbles are discussed, mainly as helpful and yet to be exploited structures in the pharmaceutical and medical field. Innovative pharmaceutical forms (Pickering emulsions) are also means of use taken into account as applications which need further investigation.

Evaporation of Nanosuspensions on Substrates with Different Hydrophobicity

Liquid drop evaporation on surfaces is present in many industrial and medical applications, e.g., printed electronics, spraying of pesticides, DNA mapping, etc. Despite this strong interest, a theoretical description of the dynamic of the evaporation of complex liquid mixtures and nanosuspensions is still lacking. Indeed, one of the aspects that have not been included in the current theoretical descriptions is the competition between the kinetics of evaporation and the adsorption of surfactants and/or particles at the liquid/vapor and liquid/solid interfaces. Materials formed by an electrically isolating solid on which a patterned conducting layer was formed by the deposits left after drop evaporation have been considered as very promising for building electrical circuits on flexible plastic substrates. In this work, we have done an exhaustive study of the evaporation of nanosuspensions of latex and hydrophobized silver nanoparticles on four substrates of different hydrophobicity. The advancing and receding contact angles as well as the time dependence of the volume of the droplets have been measured over a broad range of particle concentrations. Also, mixtures of silver particles and a surfactant, commonly used in industrial printing, have been examined. Furthermore, the adsorption kinetics at both the air/liquid and solid/liquid interfaces have been measured. Whereas the latex particles do not adsorb at the solid/liquid and only slightly reduce the surface tension, the silver particles strongly adsorb at both interfaces. The experimental results of the evaporation process were compared with the predictions of the theory of Semenov et al. (Evaporation of Sessile Water Droplets: Universal Behavior in the Presence of Contact Angle Hysteresis. Colloids Surf. Physicochem. Eng. Asp. 2011, 391 (1-3), 135-144) and showed surprisingly good agreement despite that the theory was developed for pure liquids. The morphology of the deposits left by the droplets after total evaporation was studied by scanning electronic microscopy, and the effects of the substrate, the particle nature, and their concentrations on these patterns are discussed.

Recent advances in droplet wetting and evaporation

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

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.

Atypical effects of incorporated surfactants on stability and dissolution properties of amorphous polymeric dispersions

OBJECTIVES

To understand the impact of ionic and non-ionic surfactants on the dissolution and stability properties of amorphous polymeric dispersions using griseofulvin (GF) as a model for poorly soluble drugs.

METHODS

Solid dispersions of the poorly water-soluble drug, griseofulvin (GF) and the polymers, poly(vinylpyrrolidone) (PVP) and poly(2-hydroxypropyl methacrylate) (PHPMA), have been prepared by spray drying and bead milling and the effect of the ionic and non-ionic surfactants, namely sodium dodecyl sulphate (SDS) and Tween-80, on the physico-chemical properties of the solid dispersions studied.

KEY FINDINGS

The X-ray powder diffraction data and hot-stage microscopy showed a fast re-crystallisation of GF. While dynamic vapour sorption (DVS) measurements indicated an increased water uptake, slow dissolution rates were observed for the solid dispersions incorporating surfactants. The order by which surfactants free dispersions were prepared seemed critical as indicated by DVS and thermal analysis. Dispersions prepared by milling with SDS showed significantly better stability than spray-dried dispersions (drug remained amorphous for more than 6 months) as well as improved dissolution profile.

CONCLUSIONS

We suggest that surfactants can hinder the dissolution by promoting aggregation of polymeric chains, however that effect depends mainly on how the particles were prepared.

Transport of Colloids along Corners: Visualization of Evaporation-Induced Flows beyond the Axisymmetric Condition

Nonhomogeneous evaporation fluxes have been shown to promote the formation of internal currents in sessile droplets, explaining the patterns that suspended particles leave after the droplet has dried out. Although most evaporation experiments have been conducted using spherical-cap-shaped drops, which are essentially in an axisymmetric geometry, here we show an example of nonhomogeneous evaporation in asymmetric geometries, which is visualized by following the motion of colloidal particles along liquid fingers forming a meniscus at square corners. It is found that the particle's velocity increases with the diffusive evaporation factor [Formula: see text] for the three tested fluids: water, isopropyl alcohol (IPA), and ethanol (EtOH). Here, [Formula: see text] is the vapor diffusivity in air, RH is the relative amount of vapor in the atmosphere, and cs is the saturated vapor concentration. We observed that in IPA and EtOH the internal currents promote a 3D spiral motion, whereas in water the particle's trajectory is basically unidirectional. By adding 0.25 critical micelle concentration (CMC) of sodium dodecyl sulfate (SDS) surfactant in water, a velocity blast was observed in the whole circulation flow pattern, going from [Formula: see text] to nearly [Formula: see text] in the longitudinal velocity component. To assess the effect of breaking the axisymmetric condition on the evaporation flux profile, we numerically solved the diffusive equation in model geometries that preserve the value of the contact angle θ but introduce an additional angle ϕ that characterizes the solid substrate. By testing different combinations of θ and ϕ, we corroborated that the evaporation flux increases when the substrate and the gas-liquid curves meet at corners with increasing sharpness.

Inkjet Printing of Colloidal Nanospheres: Engineering the Evaporation-Driven Self-Assembly Process to Form Defined Layer Morphologies

We report on inkjet printing of aqueous colloidal suspensions containing monodisperse silica and/or polystyrene nanosphere particles and a systematic study of the morphology of the deposits as a function of different parameters during inkjet printing and solvent evaporation. The colloidal suspensions act as a model ink for an understanding of layer formation processes and resulting morphologies in inkjet printing in general. We investigated the influence of the surface energy and the temperature of the substrate, the formulation of the suspensions, and the multi-pass printing aiming for layer stacks on the morphology of the deposits. We explain our findings with models of evaporation-driven self-assembly of the nanosphere particles in a liquid droplet and derive methods to direct the self-assembly processes into distinct one- and two-dimensional deposit morphologies.

Control of stain geometry by drop evaporation of surfactant containing dispersions

Control of stain geometry by drop evaporation of surfactant containing dispersions is an important topic of interest because it plays a crucial role in many applications such as forming templates on solid surfaces, in ink-jet printing, spraying of pesticides, micro/nano material fabrication, thin film coatings, biochemical assays, deposition of DNA/RNA micro-arrays, and manufacture of novel optical and electronic materials. This paper presents a review of the published articles on the diffusive drop evaporation of pure liquids (water), the surfactant stains obtained from evaporating drops that do not contain dispersed particles and deposits obtained from drops containing polymer colloids and carbon based particles such as carbon nanotubes, graphite and fullerenes. Experimental results of specific systems and modeling attempts are discussed. This review also has some special subtopics such as suppression of coffee-rings by surfactant addition and "stick-slip" behavior of evaporating nanosuspension drops. In general, the drop evaporation process of a surfactant/particle/substrate system is very complex since dissolved surfactants adsorb on both the insoluble organic/inorganic micro/nanoparticles in the drop, on the air/solution interface and on the substrate surface in different extends. Meanwhile, surfactant adsorbed particles interact with the substrate giving a specific contact angle, and free surfactants create a solutal Marangoni flow in the drop which controls the location of the particle deposition together with the rate of evaporation. In some cases, the presence of a surfactant monolayer at the air/solution interface alters the rate of evaporation. At present, the magnitude of each effect cannot be predicted adequately in advance and consequently they should be carefully studied for any system in order to control the shape and size of the final deposit.

Evaporation of droplets on strongly hydrophobic substrates

The manner in which the extreme modes of droplet evaporation (namely, the constant contact radius and the constant contact angle modes) become indistinguishable on strongly hydrophobic substrates is described. Simple asymptotic expressions are obtained which provide good approximations to the evolutions of the contact radius, the contact angle, and the volume of droplets evaporating in the extreme modes for a wide range of hydrophobic substrates. As a consequence, on strongly hydrophobic substrates it is appropriate to use the so-called "2/3 power law" to extrapolate the lifetimes of droplets evaporating in the constant contact radius mode as well as in the constant contact angle mode.

Transient volume of evaporating sessile droplets: 2/3, 1/1, or another power law?

The transient shape and volume of evaporating sessile droplets are critical to our understanding and prediction of deposits left over on the solid surface after droplet evaporation. The 2/3 power law of scaling, (V/Vo)(β) = 1 - t/tf with β = 2/3, has been widely used. The 1/1 power law of scaling with β = 1 was also obtained for vanishingly small contact angles. Here we show that β significantly deviates from 2/3 and 1 when the droplet base is pinned: β depends on both initial and transient contact angles. The 1/1 power law presents the upper limit of β = 1, while β = 2/3 is the lower limit if contact angles are smaller than 148°. Unexpectedly, β can be smaller than 2/3 if contact angles are larger than 148°. We also present a semianalytical approximation for β as a function of the initial contact angle.

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.

Evaporation of droplets of surfactant solutions

The simultaneous spreading and evaporation of droplets of aqueous trisiloxane (superspreader) solutions onto a hydrophobic substrate has been studied both experimentally, using a video-microscopy technique, and theoretically. The experiments have been carried out over a wide range of surfactant concentration, temperature, and relative humidity. Similar to pure liquids, four different stages have been observed: the initial one corresponds to spreading until the contact angle, θ, reaches the value of the static advancing contact angle, θad. Duration of this stage is rather short, and the evaporation during this stage can be neglected. The evaporation is essential during the next three stages. The next stage after the spreading, which is referred to herein as the first stage, takes place at constant perimeter and ends when θ reaches the static receding contact angle, θr. During the next, second stage, the perimeter decreases at constant contact angle θ = θr for surfactant concentration above the critical wetting concentration (CWC). The static receding contact angle decreases during the second stage for concentrations below CWC because the concentration increases due to the evaporation. During the final stage both the perimeter and the contact angle decrease. In what follows, we consider only the longest stages I and II. The developed theory predicts universal curves for the contact angle dependency on time during the first stage, and for the droplet perimeter on time during the second stage. A very good agreement between theory and experimental data has been found for the first stage of evaporation, and for the second stage for concentrations above CWC; however, some deviations were found for concentrations below CWC.

Bulk, surface, and gas-phase limited water transport in aerosol

The influence of solute species on mass transfer to and from aqueous aerosol droplets is investigated using an electrodynamic balance coupled with light scattering techniques. In particular, we explore the limitations imposed on water evaporation by slow bulk phase diffusion and by the formation of surface organic films. Measurements of evaporation from ionic salt solutions, specifically sodium chloride and ammonium sulfate, are compared with predictions from an analytical model framework, highlighting the uncertainties associated with quantifying gas diffusional transport. The influence of low solubility organic acids on mass transfer is reported and compared to both model predictions and previous work. The limiting value of the evaporation coefficient that can be resolved by this approach, when uncertainties in key thermophysical quantities are accounted for, is estimated. The limitation of slow bulk phase diffusion on the evaporation rate is investigated for gel and glass states formed during the evaporation of magnesium sulfate and sucrose droplets, respectively. Finally, the effect of surfactants on evaporation has been probed, with soluble surfactants (such as sodium dodecyl sulfate) leading to little or no retardation of evaporation through slowing of surface layer kinetics.

Evaporation of pure liquid sessile and spherical suspended drops: a review

A sessile drop is an isolated drop which has been deposited on a solid substrate where the wetted area is limited by a contact line and characterized by contact angle, contact radius and drop height. Diffusion-controlled evaporation of a sessile drop in an ambient gas is an important topic of interest because it plays a crucial role in many scientific applications such as controlling the deposition of particles on solid surfaces, in ink-jet printing, spraying of pesticides, micro/nano material fabrication, thin film coatings, biochemical assays, drop wise cooling, deposition of DNA/RNA micro-arrays, and manufacture of novel optical and electronic materials in the last decades. This paper presents a review of the published articles for a period of approximately 120 years related to the evaporation of both sessile drops and nearly spherical droplets suspended from thin fibers. After presenting a brief history of the subject, we discuss the basic theory comprising evaporation of micrometer and millimeter sized spherical drops, self cooling on the drop surface and evaporation rate of sessile drops on solids. The effects of drop cooling, resultant lateral evaporative flux and Marangoni flows on evaporation rate are also discussed. This review also has some special topics such as drop evaporation on superhydrophobic surfaces, determination of the receding contact angle from drop evaporation, substrate thermal conductivity effect on drop evaporation and the rate evaporation of water in liquid marbles.