Evaporation of droplets of surfactant solutions

Competition between thermal and surfactant-induced Marangoni flow in evaporating sessile droplets

HYPOTHESIS

Thermal Marangoni flow in evaporating sessile water droplets is much weaker in experiments than predicted theoretically. Often this is attributed to surfactant contamination, but there have not been any in-depth analyses that consider the full fluid and surfactant dynamics. It is expected that more insight into this problem can be gained by using numerical models to analyze the interplay between thermal Marangoni flow and surfactant dynamics in terms of dimensionless parameters.

SIMULATIONS

Two numerical models are implemented: one dynamic model based on lubrication theory and one quasi-stationary model, that allows for arbitrary contact angles.

FINDINGS

It is found that insoluble surfactants can suppress the thermal Marangoni flow if their concentration is sufficiently large and evaporation and diffusion are sufficiently slow. Soluble surfactants, however, either reduce or increase the interfacial velocity, depending on their sorption kinetics. Furthermore, insoluble surfactant concentrations that cause an order 0.1% surface tension reduction are sufficient to reduce the spatially averaged tangential flow velocity at the interface by a factor 100. For larger contact angles and smaller droplets this required concentration is larger (typically <1% surface tension reduction). The numerical models are mutually validated by comparing their results in cases where both are valid.

Effect of Corrosion and Wall Textures on Wettability and Heat Flux at Non-Isothermal Conditions

The corrosion behavior, evaporation and heat transfer of aluminum alloy during droplet evaporation of an aggressive solution of NaCl and hydrogen peroxide in water have been studied experimentally. To date, the effect of corrosion on the evaporation and heat transfer of droplet salt solutions on textured surfaces remains insufficiently explored. The corrosion resistance of the material and the contact angle increase with an increase in the number of laser penetrations after laser texturing. Studies conducted using an electron microscope and Energy-Dispersive X-ray Spectroscopy (EDS) mapping show that the maximum amount of adsorbed hydrocarbon impurities falls on areas with a large number of pits. In the process of metal corrosion, wettability and heat transfer change. In spite of the fact that laser exposure significantly increases the corrosion resistance, the wettability of the wall changes significantly due to corrosion. The wetted diameter of a droplet changes over time, which leads to an increase in the evaporation rate and heat flux. The heat flux during evaporation of a droplet on a heated wall depends on the water droplet diameter, the texture of the wall and the corrosion resistance.

Absorption of surfactant-laden droplets into porous media: A numerical study

HYPOTHESIS

Droplets can absorb into permeable substrates due to capillarity. It is hypothesized that the contact line dynamics influence this process and that an unpinned contact line results in slower absorption than a pinned contact line, since the contact area between the droplet and the substrate will decrease over time for the former. Furthermore, it is expected that surfactants can be used to accelerate the absorption.

SIMULATIONS

Lubrication theory is employed to model the droplet and Darcy's law is combined with the conservation law of mass to describe the absorption dynamics. For the surfactant transport, several convection-diffusion-adsorption equations are solved.

FINDINGS

It is found that moving contact lines result in a parabola-shaped wetted area and a slower absorption and a deeper penetration depth than pinned contact lines. The evolution of the penetration depth was quantitatively validated by comparison with two experimental studies from literature. Surfactants were shown to accelerate the absorption process, but only if their adsorption kinetics are slow compared to the absorption. Otherwise, all surfactant adsorbs onto the pore walls before reaching the wetting front, resulting in the same absorption rate as without surfactants. This behavior agrees with both experimental and analytical literature.

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.

Evaporating droplets on inclined plant leaves and synthetic surfaces: Experiments and mathematical models

HYPOTHESIS

Evaporation of surfactant droplets on leaves is complicated due to the complex physical and chemical properties of the leaf surfaces. However, for certain leaf surfaces for which the evaporation process appears to follow the standard constant-contact-radius or constant-contact-angle modes, it should be possible to mimic the droplet evaporation with both a well-chosen synthetic surface and a relatively simple mathematical model.

EXPERIMENTS

Surfactant droplet evaporation experiments were performed on two commercial crop species, wheat and capsicum, along with two synthetic surfaces, up to a 90° incline. The time-dependence of the droplets' contact angles, height, volume and contact radius was measured throughout the evaporation experiments. Mathematical models were developed to simulate the experiments.

FINDINGS

With one clear exception, for all combinations of surfaces, surfactant concentrations and angles, the experiments appear to follow the standard evaporation modes and are well described by the mathematical models (modified Popov and Young-Laplace-Popov). The exception is wheat with a high surfactant concentration, for which droplet evaporation appears nonstandard and deviates from the diffusion limited models, perhaps due to additional mechanisms such as the adsorption of surfactant, stomatal density or an elongated shape in the direction of the grooves in the wheat surface.

Ring patterns generated by an expanding colloidal meniscus

The drop-and-dry is a common technique allowing for creation of periodic nanoparticle (NP) structures for sensing, photonics, catalysis, etc. However, the reproducibility and scalability of this approach for fabrication of NP-based structures faces serious challenges due to the complexity of the simple, at first glance, evaporation process. In this work we study the effect of the spatial confinement on the NP self-assembly under slow solvent evaporation, when the air-liquid-substrate contact line (CL) expands from the center towards the walls of a cylindrical cell, forming a toroid. Using in situ video monitoring of the stick-slip CL motion, we find regular hydrodynamic perturbations in the meniscus, and reveal fine details of the formation of quasiperiodic rings of close packed NP layers. We report that drying of the toroidal NP droplet has a number of important differences from drying of the classical hemispherical colloidal drops. In toroidal drops we observe linear-in-time average meniscus motion, in contrast to the hemispherical drops where the meniscus moves as a square root of time. While both droplet geometries produce NP ring patterns, the ring width for the toroidal drop decreases with increasing ring radius, while it decreases with decreasing the radius of the hemispherical drop. We suggest that free ligands are the main cause of the Marangoni instabilities driving the periodic vorticity in the meniscus. In addition, we show that the usually ignored contact line tension may yield a considerable contribution to the CL pinning causing the CL slip-stick motion and the ring formation.

The evaporation of surfactant-laden droplets: A comparison between contact line models

HYPOTHESIS

There are two different sharp-interface models for moving contact lines: slip models and precursor film models. While both models predict a mostly constant contact angle during the evaporation of pure droplets, it is expected that they behave differently when surfactants are present, because of the inherent dissimilarities in their respective interface definitions.

SIMULATIONS

Both contact line models are numerically implemented using lubrication theory to analyze evaporating droplets. A convection-diffusion equation is implemented for insoluble surfactants. For pure droplets the models are compared with experiments performed by Nguyen et al. (2012).

FINDINGS

The two contact line models show results comparable to the experiments with pure droplets. If insoluble surfactants are present, the slip model increasingly shows pinning-like behavior as the initial surfactant concentration is increased. This 'quasi-pinning' is found to be consistent with experimental results in literature. The precursor film model, in contrast, shows no significant change when surfactants are added. This lack of change is a result of surfactant flowing from the droplet into the precursor film and vice versa. While suggesting potential solutions to this unphysical behavior, it is concluded that in the context of surfactants, slip models are preferable over precursor film models given the current state of the art.

Competitive Electrohydrodynamic and Electrosolutal Advection Arrests Evaporation Kinetics of Droplets

This article reports the hitherto unreported phenomenon of arrested evaporation dynamics in pendant droplets because of electric field stimulus. The evaporation kinetics of pendant droplets of electrically conducting saline solutions in the presence of a transverse, alternating electric field is investigated experimentally. While the increase of field strength reduces the evaporation rate, increment in field frequency has the opposite effect. The same has been explained on the solvation kinetics of ions in polar water. Theoretical analysis reveals that change in surface tension and the diffusion-driven evaporation model cannot predict the decelerated evaporation. With the aid of particle image velocimetry, suppression of internal circulation velocity within the droplet is observed under electric field stimulus, which directly affects the evaporation rate. A mathematical scaling model is proposed to quantify the effects of electrohydrodynamic circulation and electrothermal and electrosolutal advection on the evaporation kinetics. The analysis encompasses major governing parameters, namely, the thermal and solutal Marangoni numbers, the electrohydrodynamic number, the electro-Prandtl and electro-Schmidt numbers, and their respective contributions. It has been shown that the electrothermal Marangoni effect is suppressed by the electric field, leading to deteriorated evaporation rates. Additionally, the electrosolutal Marangoni effect further suppresses the internal advection, further reducing the evaporation rate by a larger proportion. Stability analysis reveals that the electric body force retards the stable internal advection. The stability mapping also illustrates that if the field strength is high enough for the electrosolutal advection to overshadow the solutal Marangoni effect completely, it can lead to improvement in evaporation rates.

In honor to Ramón G. Rubio on the occasion of his 65th birthday

This Honorary Note is dedicated to the 65th birthday of Ramón G. Rubio and summarizes some of his contributions to the current knowledge in the science and technology of colloids and interfaces. Since 1995, Ramón González Rubio is Full Professor at the Complutense University of Madrid (Spain) where he has developed an extensive research activity in different scientific and technological aspects related to colloidal systems and interfacial phenomena: from particle-laden interfaces to polyelectrolyte multilayers, including the kinetics of simultaneous spreading and evaporation of solutions (and dispersions) and interfacial rheology. This broad research activity has contributed to some of the most recent advances in colloid and interface science, which is reflected in more than 200 papers in peer-reviewed journals and more than 4000 citations according to the Web of Science.

The crystallization behavior of the aqueous solution of CaCl2 salt in a drop and a layer

Non-isothermal evaporation during crystallization of CaCl₂ salt in a droplet and a thin layer on a hot wall has been investigated experimentally. The growth of salt crystal hydrates (CaCl₂·2H₂O) on the interface has been studied. It has been found that the change in the initial salt concentration leads to different crystallization rates. The crystallization rate on the droplet interface is many times lower than for a thin layer. The description of crystallization in the salt solution droplet should take into account the crystallization anisotropy, which is associated with the direction of crystallization. The crystallization rate along the contact line of the droplet is many times higher than in the direction of the droplet radius. For a long time of crystallization, the area of the crystal film (outside the drop) increases several times. Four characteristic modes of crystallization to a drop of salt solution have been distinguished. When modeling crystallization, it is necessary to take into account multiple changes in the growth rate of salt crystallohydrates over time, as well as the anisotropic nature of crystallization.

Molecular Dynamics Simulation of the Superspreading of Surfactant-Laden Droplets. A Review

Superspreading is the rapid and complete spreading of surfactant-laden droplets on hydrophobic substrates. This phenomenon has been studied for many decades by experiment, theory, and simulation, but it has been only recently that molecular-level simulation has provided significant insights into the underlying mechanisms of superspreading thanks to the development of accurate force-fields and the increase of computational capabilities. Here, we review the main advances in this area that have surfaced from Molecular Dynamics simulation of all-atom and coarse-grained models highlighting and contrasting the main results and discussing various elements of the proposed mechanisms for superspreading. We anticipate that this review will stimulate further research on the interpretation of experimental results and the design of surfactants for applications requiring efficient spreading, such as coating technology.

Mathematical Modelling of Hydrophilic Ionic Fertiliser Diffusion in Plant Cuticles: Lipophilic Surfactant Effects

The global agricultural industry requires improved efficacy of sprays being applied to weeds and crops to increase financial returns and reduce environmental impact. Enhancing foliar penetration is one way to improve efficacy. Within the plant leaf, the cuticle is the most significant barrier to agrochemical diffusion. It has been noted that a comprehensive set of mechanisms for ionic active ingredient (AI) penetration through plant leaves with surfactants is not well defined, and oils that enhance penetration have been given little attention. The importance of a mechanistic mathematical model has been noted previously in the literature. Two mechanistic mathematical models have been previously developed by the authors, focusing on plant cuticle penetration of calcium chloride through tomato fruit cuticles. The models included ion binding and evaporation with hygroscopic water absorption, along with the ability to vary the AI concentration and type, relative humidity, and plant species. Here, we further develop these models to include lipophilic adjuvant effects, as well as the adsorption and desorption, of compounds on the cuticle surface with a novel Adaptive Competitive Langmuir model. These modifications to a penetration model provide a novel addition to the literature. We validate our theoretical model results against appropriate experimental data, discuss key sensitivities, and relate theoretical predictions to physical mechanisms. The results indicate the addition of the desorption mechanism may be one way to predict increased penetration at late times, and the sensitivity of model parameters compares well to those present in the literature.

Interplay of electro-thermo-solutal advection and internal electrohydrodynamics governed enhanced evaporation of droplets

The article experimentally examines and theoretically establishes the influence of electric field on the evaporation kinetics of pendant droplets. It is observed that the evaporation of saline-pendant droplets can be augmented by the application of an external alternating electric field. The evaporation behaviour is modulated by an increase in the field strength and frequency. The classical diffusion driven evaporation model is found insufficient in predicting the improved evaporation rates. The change in surface tension due to field constraint is also unable to explain the observed physics. Consequently, the internal hydrodynamics of the droplet is investigated through particle image velocimetry. The electric field is found to induce enhanced internal advection, which improves the evaporation rates. A scaled analytical model is proposed to quantify the role of internal electrohydrodynamics, electro-thermal and electro-solutal effects. Stability maps reveal that the advection is caused nearly equally by the electro-solutal and electro-thermal effects within the droplet. The model is able to illustrate the influence played by the governing thermal and solutal Marangoni number, the electro-Prandtl and electro-Schmidt number, and the associated electrohydrodynamic number. The magnitude of the internal circulation can be predicted by the proposed model, which validates the proposed mechanism.

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.

A numerical model of superspreading surfactants on hydrophobic surface

Many contributions significantly on experimental and mathematical studies are made to understand the mechanism of superspreading. Only few numerical methods have been proposed which solve the system of equations with soluble and insoluble surfactants. Among them, we propose a computational fluid dynamics model, based on the volume of fluid technique, with the piecewise linear interface calculation method. Interface reconstruction is applied to simulate the time evolution of the dynamics of drop spreading of surfactants on a thin water layer. We have allowed the occurrence of both the regimes relating to a series of trisiloxane (M(D′EnOH)M), sodium dodecyl sulphate, and Tergitol NP10 surfactants drop on a thin water layer with the influence of Marangoni stress. The numerical data seem consistent with those experimental for both regimes. It validates predictions for the spreading exponent in which the law of the radius of the circular area covered by the surfactant grows as tα, where 0 &lt; α &lt; 1. The comparison of the numerical and experimental predictions by Lee et al. [“Spreading of trisiloxanes over thin aqueous layers,” Colloid J. 71, 365–369 (2009)] is well represented in both regimes. The numerical study confirms that the spreading rates during the first stage increase as the solubility increases. This finding suggests that the model is adequate for describing the spreading of surfactants on thin fluid layers.

Magnetohydrodynamics- and magnetosolutal-transport-mediated evaporation dynamics in paramagnetic pendant droplets under field stimulus

Evaporation kinetics of pendant droplets is an area of immense importance in several applications, in addition to possessing rich fluid dynamics and thermal transport physics. This article experimentally and analytically sheds insight into the augmented evaporation dynamics of paramagnetic pendant droplets in the presence of a magnetic field stimulus. The literature provides information that solutal advection and the solutal Marangoni effect lead to enhanced evaporation in droplets with solvated ions. The main focus of this article is to modulate the thermosolutal advection with the aid of an external magnetic field and comprehend the dynamics of the evaporation process under such complex multiphysics interactions. Experimental observations reveal that the evaporation rate enhances as a direct function of the magnetic moment of the solvated magnetic element ions, thereby pointing at the magnetophoretic and magnetosolutal advection. Additionally, flow visualization by particle image velocimetry illustrates that the internal advection currents within the droplet increase in magnitude and are distorted in orientation by the magnetic field. A mathematical formalism based on magnetothermal and magnetosolutal advection has been proposed via scaling analysis of the species and energy conservation equations. The formalism takes into account all major governing factors, viz., the magnetothermal and magnetosolutal Marangoni numbers, magneto-Prandtl and magneto-Schmidt numbers, and the Hartmann number. The modeling establishes the magnetosolutal advection to be the dominant factor behind the augmented evaporation dynamics. Accurate validation of the experimental internal circulation velocity is obtained from the proposed model. This study reveals rich insight into the magnetothermosolutal hydrodynamics in paramagnetic droplets.

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.

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: θ_app ∼ (RH_eq - 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.

Nonlinear Porous Diffusion Modeling of Hydrophilic Ionic Agrochemicals in Astomatous Plant Cuticle Aqueous Pores: A Mechanistic Approach

The agricultural industry requires improved efficacy of sprays being applied to crops and weeds in order to reduce their environmental impact and deliver improved financial returns. Enhanced foliar uptake is one means of improving efficacy. The plant leaf cuticle is known to be the main barrier to diffusion of agrochemicals within the leaf. The usefulness of a mathematical model to simulate uptake of agrochemicals in plant cuticles has been noted previously in the literature, as the results of each uptake experiment are specific to each formulation of active ingredient, plant species and environmental conditions. In this work we develop a mathematical model and numerical simulation for the uptake of hydrophilic ionic agrochemicals through aqueous pores in plant cuticles. We propose a novel, nonlinear, porous diffusion model for ionic agrochemicals in isolated cuticles, which extends simple diffusion through the incorporation of parameters capable of simulating: plant species variations, evaporation of surface droplet solutions, ion binding effects on the cuticle surface and swelling of the aqueous pores with water. We validate our theoretical results against appropriate experimental data, discuss the key sensitivities in the model and relate theoretical predictions to appropriate physical mechanisms. Major influencing factors have been found to be cuticle structure, including tortuosity and density of the aqueous pores, and to a lesser extent humidity and cuticle surface ion binding effects.

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.

Self-wrapping of an ouzo drop induced by evaporation on a superamphiphobic surface

Evaporation of multi-component drops is crucial to various technologies and has numerous potential applications because of its ubiquity in nature. Superamphiphobic surfaces, which are both superhydrophobic and superoleophobic, can give a low wettability not only for water drops but also for oil drops. In this paper, we experimentally, numerically and theoretically investigate the evaporation process of millimetric sessile ouzo drops (a transparent mixture of water, ethanol, and trans-anethole) with low wettability on a superamphiphobic surface. The evaporation-triggered ouzo effect, i.e. the spontaneous emulsification of oil microdroplets below a specific ethanol concentration, preferentially occurs at the apex of the drop due to the evaporation flux distribution and volatility difference between water and ethanol. This observation is also reproduced by numerical simulations. The volume decrease of the ouzo drop is characterized by two distinct slopes. The initial steep slope is dominantly caused by the evaporation of ethanol, followed by the slower evaporation of water. At later stages, thanks to Marangoni forces the oil wraps around the drop and an oil shell forms. We propose an approximate diffusion model for the drying characteristics, which predicts the evaporation of the drops in agreement with experiment and numerical simulation results. This work provides an advanced understanding of the evaporation process of ouzo (multi-component) drops.

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.

Dewetting transition induced by surfactants in sessile droplets at the early evaporation stage

As surfactants are employed to control the wettability of solutions, we observe that the sessile droplet dewetting induced by autophobing exhibits a unique relation with the surfactant concentration. Below the critical micelle concentration (cmc) of the surfactant, the autophobic effect makes the droplet go through a rapid depinning at first (Phase 1) and then a relatively slower shrinkage (Phase 2). Unexpectedly, the rapid velocity of the three-phase contact line in Phase 1 shows a transition as the surfactant concentration increases above 0.043 cmc, while such a transition is absent for the velocity in Phase 2. The spreading of the sessile droplets as they form before retraction, the maximum contact angle led by dewetting, and the droplet lifetime are regularly sensitive to the surfactant concentration as well. These phenomena are correlated with the assembling structure and the adsorbed amount at different interfaces with the loading of surfactant inventory.

The evaporation behavior of sessile droplets from aqueous saline solutions

Quantitative experiments on the evaporation from sessile droplets of aqueous saline (NaCl) solutions show a strong dependence on salt concentration and droplet shape. The experiments were performed with seven decades of initial NaCl concentrations, with various droplet sizes and with different contact angles. The evaporation rate is significantly lower for high salt concentrations and small contact angles than what is expected from the well-accepted diffusion-controlled evaporation scenario for sessile droplets, even if the change of the vapor pressure due to the salt is taken into account. Particle tracking velocimetry reveals that this modification of the evaporation behavior is caused by marangoni flows that are induced by surface tension gradients originating from the local evaporative peripheral salt enrichment. In addition it is found that already very low salt concentrations lead to a pinning of the three phase contact line. Whereas droplets with concentration ≥10(-6) M NaCl are pinned as soon as evaporation starts, droplets with lower salt concentration do evaporate in a constant contact angle mode. Aside from new, fundamental insights the findings are also relevant for a better understanding of the widespread phenomenon of corrosion initiated by sessile droplets.

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.

Surfactant-adsorption-induced initial depinning behavior in evaporating water and nanofluid sessile droplets

A surfactant-induced autophobic effect has been observed to initiate an intense depinning behavior at the initial stage of evaporation in both pure water and nanofluid sessile droplets. The cationic surfactant adsorbing to the negatively charged silicon wafer makes the solid surface more hydrophobic. The autophobing-induced depinning behavior, leading to an enlarged contact angle and a shortened base diameter, takes place only when the surfactant concentration is below its critical micelle concentration (cmc). The initial spreading degree right before the droplet retraction, the retracting velocity of the contact line, and the duration of the initial droplet retraction are shown to depend negatively on the surfactant concentration below the cmc. An unexpected enhancement in the initial depinning has been found in the nanofluid droplets, possibly resulting from the hydrophilic interplay between the graphite nanoparticle deposition and the surfactant molecules. Such promotion of the initial depinning due to the nanoparticle deposition makes the droplet retract even at a surfactant concentration higher than the cmc (1.5 cmc). The resulting deposition formed in the presence of the depinning behavior has great enhancement for coffee-ring formation as compared to the one free of surfactant, implying that the formation of a coffee ring does not require the pinning of the contact line during the entire drying process.

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.

Superspreading: mechanisms and molecular design

The intriguing ability of certain surfactant molecules to drive the superspreading of liquids to complete wetting on hydrophobic substrates is central to numerous applications that range from coating flow technology to enhanced oil recovery. Despite significant experimental efforts, the precise mechanisms underlying superspreading remain unknown to date. Here, we isolate these mechanisms by analyzing coarse-grained molecular dynamics simulations of surfactant molecules of varying molecular architecture and substrate affinity. We observe that for superspreading to occur, two key conditions must be simultaneously satisfied: the adsorption of surfactants from the liquid-vapor surface onto the three-phase contact line augmented by local bilayer formation. Crucially, this must be coordinated with the rapid replenishment of liquid-vapor and solid-liquid interfaces with surfactants from the interior of the droplet. This article also highlights and explores the differences between superspreading and conventional surfactants, paving the way for the design of molecular architectures tailored specifically for applications that rely on the control of wetting.

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.