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

Droplet evaporation on soft solid substrates

Droplet evaporation on soft solid substrates is relevant to applications such as fabrication of microlenses and controlled particle deposition. Here, we develop a lubrication-theory-based model to advance fundamental understanding of the important limiting case of a planar droplet evaporating on a linear viscoelastic solid. A set of partial differential equations describing the time evolution of the liquid-air and liquid-solid interfaces is derived and solved with a finite-difference method. A disjoining-pressure/precursor-film approach is used to describe contact-line motion, and the one sided model is used to describe solvent evaporation. Parametric studies are conducted to investigate the effect of solid properties (thickness, viscosity, shear modulus, wettability) and evaporation rate on droplet dynamics. Our results indicate that softer substrates speed up droplet evaporation due to prolonged pinning of the contact line. Results from our model are able to qualitatively reproduce some key trends observed in experiments. Due to its systematic formulation, our model can readily be extended to more complex situations of interest such as evaporation of particle-laden droplets on soft solid substrates.

Chirality Affecting Reaction Dynamics of HgS Nanostructures Simultaneously Visualized in Real and Reciprocal Space

Chirality involved reactions enable to probe features in the fields of asymmetric synthesis and catalysis, which allow to gain insight into the fundamental mechanisms of topochemically controlled reactions. However, in situ observation of the chirality-associated reaction dynamics with simultaneous structural determination of microscopic features has been lacking. Here, we report the direct visualization of the electron-beam-stimulated reaction dynamics of HgS nanostructures with chiral and achiral morphologies simultaneously in both real and reciprocal space. Under the electron-beam excitation of HgS nanostructures, the formation and evaporation dynamics of Hg nanodroplets were vividly pictured, while the reciprocal space imaging revealed the structural transformation from monocrystalline to polycrystalline. Interestingly, such induced changes were size dependent, which were slowed when involving the chirality in the nanostructures. The finding offers a fundamental understanding of topochemically controlled reaction mechanisms and holds promise of tuning asymmetric synthesis for catalysis-related applications.

Manipulating Nano-suspension Droplet Evaporation by Particle Surface Modification

The evaporation of a nano-suspension droplet on a substrate has gained extensive attention recently due to its potential application in the rising industry of functional coating. In this paper, we reported that the droplet evaporation behavior can be controlled by the nanoparticles' concentration and the functional group on the surface of nanoparticles. Experimental results indicated that the suspension of nanoparticles notably enhanced the evaporation rate of droplets and decreased the duration time of the continuous-contact-radius (CCR) stage. This effect was more obvious when the nanoparticles were modified by the perfluorodecyltrimethoxysilane (PDTS), which made the particles more hydrophobic. Besides, the modified nanoparticles can effectively inhibit the formation of coffee rings during evaporation. These results may have important applications for the energy-efficient enhancement of the water evaporation rate.

Quantifying Contact-Electrification Induced Charge Transfer on a Liquid Droplet after Contacting with a Liquid or Solid

Contact electrification (CE) is a common physical phenomenon, and its mechanisms for solid-solid and liquid-solid cases have been widely discussed. However, the studies about liquid-liquid CE are hindered by the lack of proper techniques. Here, a contactless method is proposed for quantifying the charges on a liquid droplet based on the combination of electric field and acoustic field. The liquid droplet is suspended in an acoustic field, and an electric field force is created on the droplet to balance the acoustic trap force. The amount of charges on the droplet is thus calculated based on the equilibrium of forces. Further, the liquid-solid and liquid-liquid CE are both studied by using the method, and the latter is focused. The behavior of negatively precharged liquid droplet in the liquid-liquid CE is found to be different from that of the positively precharged one. The results show that the silicone oil droplet prefers to receive negative charges from a negatively charged aqueous droplet rather than positive charges from a positively charged aqueous droplet, which provides a strong evidence about the dominant role played by electron transfer in the liquid-liquid CE.

Surface Acoustic Waves to Control Droplet Impact onto Superhydrophobic and Slippery Liquid-Infused Porous Surfaces

Superhydrophobic coatings and slippery liquid-infused porous surfaces (SLIPS) have shown their potentials in self-cleaning, anti-icing, anti-erosion, and antibiofouling applications. Various studies have been done on controlling the droplet impact on such surfaces using passive methods such as modifying the lubricant layer thickness in SLIPS. Despite their effectiveness, passive methods lack on-demand control over the impact dynamics of droplets. This paper introduces a new method to actively control the droplet impact onto superhydrophobic and SLIPS surfaces using surface acoustic waves (SAWs). In this study, we designed and fabricated SLIPS on ZnO/aluminum thin-film SAW devices and investigated different scenarios of droplet impact on the surfaces compared to those on similar superhydrophobic-coated surfaces. Our results showed that SAWs have insignificant influences on the impact dynamics of a porous and superhydrophobic surface without an infused oil layer. However, after infusion with oil, SAW energy could be effectively transferred to the droplet, thus modifying its impact dynamics onto the superhydrophobic surface. Results showed that by applying SAWs, the spreading and retraction behaviors of the droplets are altered on the SLIPS surface, leading to a change in a droplet impact regime from deposition to complete rebound with altered rebounding angles. Moreover, the contact time was reduced up to 30% when applying SAWs on surfaces with an optimum oil lubricant thickness of ∼8 μm. Our work offers an effective way of applying SAW technology along with SLIPS to effectively reduce the contact time and alter the droplet rebound angles.

Water evaporation from solute-containing aerosol droplets: Effects of internal concentration and diffusivity profiles and onset of crust formation

The evaporation of droplets is an important process not only in industrial and scientific applications, but also in the airborne transmission of viruses and other infectious agents. We derive analytical and semi-analytical solutions of the coupled heat and mass diffusion equations within a spherical droplet and in the ambient vapor phase that describe the evaporation process of aqueous free droplets containing nonvolatile solutes. Our results demonstrate that the solute-induced water vapor-pressure reduction considerably slows down the evaporation process and dominates the solute-concentration dependence of the droplet evaporation time. The evaporation-induced enhanced solute concentration near the droplet surface, which is accounted for using a two-stage evaporation description, is found to further slow-down the drying process. On the other hand, the presence of solutes is found to produce a lower limit for the droplet size that can be reached by evaporation and, also, to reduce evaporation cooling of the droplet, which tend to decrease the evaporation time. Overall, the first two effects are dominant, meaning that the droplet evaporation time increases in the presence of solutes. Local variation of the water diffusivity inside the droplet near its surface, which is a consequence of the solute-concentration dependence of the diffusion coefficient, does not significantly change the evaporation time. Crust formation on the droplet surface increases the final equilibrium size of the droplet by producing a hollow spherical particle, the outer radius of which is determined as well.

Pattern formation in drying blood drops

Patterns in dried droplets are commonly observed as rings left after spills of dirty water or coffee have evaporated. Patterns are also seen in dried blood droplets and the patterns have been shown to differ from patients afflicted with different medical conditions. This has been proposed as the basis for a new generation of low-cost blood diagnostics. Before these diagnostics can be widely used, the underlying mechanisms leading to pattern formation in these systems must be understood. We analyse the height profile and appearance of dispersions prepared with red blood cells (RBCs) from healthy donors. The red cell concentrations and diluent were varied and compared with simple polystyrene particle systems to identify the dominant mechanistic variables. Typically, a high concentration of non-volatile components suppresses ring formation. However, RBC suspensions display a greater volume of edge deposition when the red cell concentration is higher. This discrepancy is caused by the consolidation front halting during drying for most blood suspensions. This prevents the standard horizontal drying mechanism and leads to two clearly defined regions in final crack patterns and height profile. This article is part of a discussion meeting issue 'A cracking approach to inventing new tough materials: fracture stranger than friction'.

Efficient pesticide formulation and regulation mechanism for improving the deposition of droplets on the leaves of rice (Oryza sativa L.)

BACKGROUND

The effective deposition of pesticide droplets on the target leaf surface is critical for improving the utilization of pesticides. We proposed a new way to enhance the droplet deposition on the target leaf surface by changing the properties of pesticide formulation, and this formulation can be sprayed directly or at a low dilution. In addition, it is a simple method to select a suitable concentration and formulation by evaluating the interfacial dilational rheological properties of pesticide droplets.

RESULTS

The wetting behavior of two types of pesticide formulations prepared by oil-based solvent on the rice leaf surface was investigated based on the surface free energy, surface tension, contact angle, adhesion tension, and adhesion work. The interfacial dilational rheological properties of different pesticide solutions were measured as a function of concentration. This study clearly demonstrates the fact that water-in-oil emulsion has a better wettability than oil-in-water emulsion, especially with the increase of the concentration of the solution, the droplets can be wetted and spread faster on the leaves. Compared with vegetable oil (methyl oleate), mineral oil (solvent oil No. 200) has smaller dilational modulus and surface tension, showing excellent wetting properties.

CONCLUSION

The water-in-oil emulsion prepared with solvent oil No. 200 has the smallest dilational modulus, and the spray droplets spread rapidly to the maximum wetting area on the rice leaves, which can be used in an ultra-low volume spray. The results provide new insights into how to increase the deposition of droplets on superhydrophobic leaf surfaces by screening formulations and concentrations. © 2021 Society of Chemical Industry.

Vibrational Spectroscopic Monitoring of the Gelation Transition in Nafion Ionomer Dispersions

Infrared and Raman spectroscopy techniques were applied to investigate the drying and aggregation behavior of Nafion ionomer particles dispersed in aqueous solution. Gravimetric measurements aided the identification of gel-phase development within a series of time-resolved spectra that tracked transformations of a dispersion sample during solvent evaporation. A spectral band characteristic of ionomer sidechain end group vibration provided a quantitative probe of the dispersion-to-gel change. For sets of attenuated total reflection Fourier transform infrared (ATR FT-IR) spectra, adherence to Beer's law was attributed to the relatively constant refractive index in the frequency region of hydrated -SO 3 - group vibrations as fluorocarbon-rich ionomer regions aggregate in forming the structural framework of membranes and thin films. Although vibrational bands associated with ionomer backbone CF2 stretching vibrations were affected by distortion characteristic of wavelength-dependent refractive index change within a sample, the onset of band distortion signaled gel formation and coincided with ionomer mass % values just below the critical gelation point for Nafion aqueous dispersions. Similar temporal behavior was observed in confocal Raman microscopy experiments that monitored the formation of a thin ionomer film from an individual dispersion droplet. For the ATR FT-IR spectroscopy and confocal Raman microscopy techniques, intensity in the water H-O-H bending vibrational band dropped sharply at the ionomer critical gelation point and displayed a time dependence consistent with changes in water content derived from gravimetric measurements. The reported studies lay groundwork for examining the impact of dispersing solvents and above-ambient temperatures on fluorinated ionomer transformations that influence structural properties of dispersion-cast membranes and thin films.

Chitosan-Alginate-Pectin-coated Suspended-Liquid-Encapsulating (CAPSuLE) marbles for therapeutic agent storage and delivery

Developing a cutting-edge system capable of ensuring long-lasting functionality of therapeutic agents and implementing diverse delivery modes is challenging. A quasi-spherical triple-layered capsule containing suspended liquid droplets and allowing multi-modal delivery of therapeutic agents in the aqueous phase was developed, primarily by adopting the core principles for creating liquid marbles. A naturally derived wettable polysaccharide-pectin-was utilized as a liquid-air interfacial barrier to keep the liquid droplets in the core zone. To tailor the pectin-coated droplet as a therapeutic agent carrier, anionic alginate and cationic chitosan layers were sequentially formed via additional interactions: physically stacking substances with structural chirality (pectin-alginate) and inducing electrostatic association to create the reversible complex coacervates (alginate-chitosan). The resulting system, which is called a Chitosan-Alginate-Pectin-coated Suspended-Liquid-Encapsulating (CAPSuLE) marble, had sufficient mechanical strength to resist external harsh environments and exhibited unique features: ecofriendly sustainability, responsiveness to external stimuli, coacervate-driven coalescence for linking adjacent marbles, and a self-repairing ability. The proposed CAPSuLE system can facilitate the adoption of the liquid-marble concept to biomedical fields, extending its applicability in the fields of biology and applied engineering.

Nanopore-Mediated Spontaneous Dilution of Droplets: When Evaporation Turns to a Dilutor

Droplet evaporation on surfaces is ubiquitous and affects areas as diverse as climate, microbiology, the chemical industry, and materials science. While solute concentration is the universally taken-for-granted behavior in drop evaporation, the present work shows that saline droplets evaporating on nanoporous thin-film surfaces can get diluted rather than concentrated. The driving mechanism of this phenomenon is attributed to the flow drawn from the drop through the nanopores by an annular peripheral evaporation. This fluid transport can continuously collect the salt solution from a concentrated region of the droplet, which is induced by radial microflows during drop evaporation. The coupling of these processes leads to the overall drop dilution effect. The influence of substrate temperature and drop volume was also investigated. This study opens up new perspectives on many natural phenomena and offers alternatives for physicochemical applications in small dimensions as well as for water desalination technologies.

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.

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.

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.

Deposits from evaporating emulsion drops

The processes in which droplets evaporate from solid surfaces, leaving behind distinct deposition patterns, have been studied extensively for variety of solutions. In this work, by combining different microscopy techniques (confocal fluorescence, video and Raman) we investigate pattern formation and evaporation-induced phase change in drying oil-in-water emulsion drops. This combination of techniques allows us to perform drop shape analysis while visualizing the internal emulsion structure simultaneously. We observe that drying of the continuous water phase of emulsion drops on hydrophilic surfaces favors the formation of ring-like zones depleted of oil droplets at the contact line, which originate from geometrical confinement of oil droplets by the meniscus. From such a depletion zone, a “coffee ring” composed of surfactant molecules forms as the water evaporates. On all surfaces drying induces emulsion destabilization by coalescence of oil droplets, commencing at the drop periphery. For hydrophobic surfaces, the coalescence of the oil droplets leads to a uniform oil film spreading out from the initial contact line. The evaporation dynamics of these composite drops indicate that the water in the continuous phase of the emulsion drops evaporates predominantly by diffusion through the vapor, showing no large differences to the evaporation of simple water drops.

Investigation of the Evaporation Rate of Water from Colloidal Unimolecular Polymer (CUP) Systems by Isothermal TGA

Studies of the evaporation of aqueous nanoparticle solutions have been limited due to lack of homogeneity of the solution, difficulties in obtaining reproducible samples and stability of substrates, as well as the effect of other volatile components or contaminants such as surfactants. Colloidal unimolecular polymer (CUP) is a spheroidal nanoparticle with charged hydrophilic groups on the surface, and the particle size ranges from 3 to 9 nm. The large amount of surface water on the CUP surface provides the opportunity to evaluate the evaporation of surface water, which may contribute to the investigation the factors that affect the evaporation rate in solutions of ultra-small particles, like protein, micelle, colloidal, etc. Six CUP systems were evaluated by thermogravimetric analysis (TGA) with respect to time and solids content. The evaporation rate of water was initially enhanced due to the deformation of the air-water interface at low to moderate concentration due to particle charge repulsive forces. At higher concentrations, above 20%, surface charge condensation and increasing viscosity began to dominate. At higher concentration where the CUP reached the gel point the rate of diffusion controlled the evaporation. The final drying point was the loss of three waters of hydration for each carboxylate on the CUP surface.

Probing the temperature profile across a liquid-vapor interface upon phase change

Understanding the temperature profile across a liquid-vapor interface in the presence of phase change is essential for the accurate prediction of evaporation, boiling, and condensation. It has been shown experimentally, from non-equilibrium thermodynamics and using molecular dynamics simulations, the existence of an inverted temperature profile across an evaporating liquid-vapor interface, where the vapor-side interface temperature observes the lowest value and the vapor temperature increases away from the interface, opposite to the direction of heat flow. It is worth noting, however, that an inverted temperature profile is not always the case from other experiments and simulations. In this study, we apply non-equilibrium molecular dynamics simulations to systematically study the temperature profile across a liquid-vapor interface during phase change under various heat fluxes in a two-interface setting consisting of both an evaporating and a condensing interface. The calculated vapor temperature shows different characteristics inside the Knudsen layer and in the bulk vapor. In addition, both the direction and magnitude of the vapor temperature gradient, as well as the temperature jump at the liquid-vapor interface, are functions of the applied heat flux. The interfacial entropy generation rate calculated from the vibrational density of state of the interfacial liquid and vapor molecules shows a positive production during evaporation, and the results qualitatively agree with the predictions from non-equilibrium thermodynamics.

Evaporation and Electrowetting of Sessile Droplets on Slippery Liquid-Like Surfaces and Slippery Liquid-Infused Porous Surfaces (SLIPS)

Sessile droplet evaporation underpins a wide range of applications from inkjet printing to coating. However, drying times can be variable and contact-line pinning often leads to undesirable effects, such as ring stain formation. Here, we show voltage programmable control of contact angles during evaporation on two pinning-free surfaces. We use an electrowetting-on-dielectric approach and Slippery Liquid-Infused Porous (SLIP) and Slippery Omniphobic Covalently Attached Liquid-Like (SOCAL) surfaces to achieve a constant contact angle mode of evaporation. We report evaporation sequences and droplet lifetimes across a broad range of contact angles from 105°-67°. The values of the contact angles during evaporation are consistent with expectations from electrowetting and the Young-Lippman equation. The droplet contact areas reduce linearly in time, and this provides estimates of diffusion coefficients close to the expected literature value. We further find that the total time of evaporation over the broad contact angle range studied is only weakly dependent on the value of the contact angle. We conclude that on these types of slippery surfaces, droplet lifetimes can be predicted and controlled by the droplet's volume and physical properties (density, diffusion coefficient, and vapor concentration difference to the vapor phase) largely independent of the precise value of contact angle. These results are relevant to applications, such as printing, spraying, coating, and other processes, where controlling droplet evaporation and drying is important.

Evaporation of squeezed water droplets between two parallel hydrophobic/superhydrophobic surfaces

HYPOTHESIS

A liquid droplet is apt to be deformed within a compact space in various applications. The morphological change of a droplet and vapor accumulation in the confined space between two parallel surfaces with different gaps and surface wettability are expected to significantly affect the evaporation dynamics of the squeezed droplet therein.

EXPERIMENTS

Here the evaporation dynamics of a squeezed droplet between two parallel hydrophobic/superhydrophobic surfaces are experimentally explored. By reducing the surface gap from 1000 μm to 400 μm, the evolution of contact angle, contact radius and volume of the evaporating droplet are measured. A diffusion-driven model based on a two-parameter ellipsoidal segment geometry is developed to predict the morphology and volume evolution of a squeezed droplet during evaporation.

FINDINGS

Evaporation dynamics of a squeezed water droplet via the constant contact radius (CCR) mode, the constant contact angle (CCA) mode, or the mixed mode are experimentally observed. Confirmed by our ellipsoidal segment model, the evaporation of the squeezed droplet is significantly depressed with the decreasing surface gap, which is primarily attributed to vapor enrichment in a more confined geometry. A linear scaling law between droplet volume and evaporation time is unveiled, which is verified by a simplified cylindrical model.

Modeling Evaporation of Water Droplets as Applied to Survival of Airborne Viruses

Many viruses, such as coronaviruses, tend to spread airborne inside water microdroplets. Evaporation of the microdroplets may result in a reduction of their contagiousness. However, the evaporation of small droplets is a complex process involving mass and heat transfer, diffusion, convection and solar radiation absorption. Virological studies indicate that airborne virus survival is very sensitive to air humidity and temperature. We employ a model of droplet evaporation with the account for the Knudsen layer. This model suggests that evaporation is sensitive to both temperature and the relative humidity (RH) of the ambient air. We also discuss various mechanisms such as the effect of solar irradiation, the dynamic relaxation of moving droplets in ambient air and the gravitational sedimentation of the droplets. The maximum estimate for the spectral radiative flux in the case of cloudless sky showed that the radiation contribution to evaporation of single water droplets is insignificant. We conclude that at small and even at moderately high levels of RH, microdroplets evaporate within dozens of seconds with the convective heat flux from the air being the dominant mechanism in every case. The numerical results obtained in the paper are in good qualitative agreement with both the published laboratory experiments and seasonal nature of many viral infections. Sophisticated experimental techniques may be needed for in situ observation of interaction of viruses with organic particles and living cells within microdroplets. The novel controlled droplet cluster technology is suggested as a promising candidate for such experimental methodology.

Complex Pattern Formation in Solutions of Protein and Mixed Salts Using Dehydrating Sessile Droplets

A sessile droplet of a complex fluid exhibits several stages of drying leading to the formation of a final pattern on the substrate. We report such pattern formation in dehydrating droplets of protein (BSA) and salts (MgCl₂ and KCl) at various concentrations of the two components (protein and salts) as part of a parametric study for the understanding of complex patterns of dehydrating biofluid droplets (blood and urine), which will eventually be used for diagnosis of bladder cancer. The exact analysis of the biofluid patterns will require a rigorous parametric study; however, the current work provides an initial understanding of the effect of the basic components present in a biofluid droplet. Arrangement of the protein and the salts, due to evaporation, leads to the formation of some very distinctive final structures at the end of the droplet lifetime. Furthermore, these structures can be manipulated by varying the initial ratio of the two components in the solution. MgCl₂ forms chains of crystals beyond a threshold initial concentration of protein (>3 wt %). However, the formation of such a crystal is also limited by the maximum concentration of the salt initially present in the droplet (≤1 wt %). On the other hand, KCl forms dendritic and rectangular crystals in the presence of BSA. The formation of these crystals also depends on the relative concentration of salt and protein in the droplet. We also investigated the dried-out patterns in dehydrating droplets of mixed salts (MgCl₂ + KCl) and protein. The patterns can be tuned from a continuous dendritic structure to a snow-flake type structure just by altering the initial ratio of the two salts in the mixture, keeping all other parameters constant.

Investigating the Effect of Antibody-Antigen Reactions on the Internal Convection in a Sessile Droplet via Microparticle Image Velocimetry and DLVO Analysis

The evaporation of antigen-laden sessile droplets on antibody-immobilized PDMS substrates could be used in place of microwells for detection purposes owing to the lesser requirements of analytes and a reduced reaction time. To develop such techniques, the effects of different parameters on the reaction efficiency and on the resulting deposition patterns of antigens on the surface after evaporation need to be well understood. While the resultant deposition patterns from the evaporation of droplets of biological fluids on surfaces are being studied for various biomedical applications, systems where the analyte of interest in the droplet binds to the surface have not been investigated until now. While the effect of temperature on the internal convection within sessile droplets has been studied, the effect of the analyte (antigen in this work) concentration and the analyte-surface (antigen-antibody in this work) binding on the internal convection has not been studied until now. Therefore, to gain insight, the evaporation dynamics of sessile droplets with different concentrations of antigens along with polystyrene microspheres (used as tracers) in phosphate-buffered saline (PBS) on antibody-immobilized PDMS substrates were experimentally studied using microparticle image velocimetry (PIV). It was found that Marangoni flow due to concentration gradients and surface reactions was responsible for the observed velocity field. The antibody-antigen reaction (as compared to the control case of no surface reaction) and higher concentrations of prostate specific antigen (PSA) resulted in increased strength of Marangoni convection. To obtain further insight into the different deposition patterns obtained, the contributions of different particle-particle and particle-substrate forces were determined, and it was observed that the Marangoni forces along with surface tension and DLVO forces create a uniform deposition of the particles present within the droplet. This learning could be used to design biosensors.

Field driven evaporation kinetics of a sessile ferrofluid droplet on a soft substrate

We experimentally investigate the evaporation kinetics of a sessile ferrofluid droplet placed on a soft substrate in the presence of a time-dependent magnetic field. We use both bright field visualization techniques and μ-PIV analysis to gain qualitative as well as quantitative insights into the internal hydrodynamics of the droplet. The results show that the droplet evaporation rate is augmented significantly in the presence of a time-dependent magnetic field, attributed primarily to the enhanced internal flow advection. We show that the motion of the magnetic nanoparticles dictates the overall life-time of the evaporating ferrofluid droplet. At lower frequencies of the magnetic field, the magnetic nanoparticles move towards the magnet and agglomerate into a chain-like cluster formation, oriented according to the magnetic field lines. On the other hand, at higher frequencies, the magnetic nanoparticles do not have sufficient time to travel the whole characteristic length (droplet diameter). Consequently, we observe the presence of a critical frequency at which the perturbation time scale balances the advective time scale of the flow inside the droplet. We show that on account for this balance between the time scales, the droplet experiences a minimum life-time. Finally, we demonstrate that the evaporation kinetics of a ferrofluid droplet in the presence of a time-dependent magnetic field can be described through three distinguishable stages viz., the decreasing contact angle and variable radius zone, the decreasing contact angle and decreasing radius zone and the late mixed zone. The inferences drawn from this study could have far-reaching implications in fields ranging from biomedical engineering to surface patterning.

Theoretical Analysis of a Sessile Evaporating Droplet on a Curved Substrate with an Interfacial Cooling Effect

Sessile droplet evaporation is widely encountered in nature, and it has numerous applications in industrial and scientific communities; therefore, the accurate prediction of droplet evaporation has great significance in practical applications. In this paper, for the first time, a comprehensive theoretical model is built up for diffusion-controlled heat and mass transfer for sessile droplet evaporation on a curved substrate in toroidal coordinates. The evaporative mass transfer is coupled with the heat transfer across the gas-liquid droplet interface, as well as the heat transfer across the solid-liquid interface of the curved substrate. The effects of interfacial cooling and thermal conductivity of the droplet and substrate as well as their initial shapes on the droplet evaporation are provided in details. It is found that the evaporative flux usually increases sharply near the droplet edge due to the short distance for heat conduction from the substrate to the droplet; however, it can be reversed from sharp increasing to decreasing at a low thermal conductivity ratio k_R < 0.3 of the substrate over droplet or large initial droplet contact angle θ > 30°. The interfacial evaporative cooling effect can always suppress the droplet evaporation. The lifetime of evaporative droplet can be prolonged with the decreasing thermal conductivity ratio, increasing evaporative cooling number, and increasing initial droplet contact angle or tangential angle of a curved substrate. These findings may be of great significance in the applications of droplet evaporation on the curved substrate.

Comparing Internal Flow in Freezing and Evaporating Water Droplets Using PIV

The study of evaporation and freezing of droplets is important in, e.g., spray cooling, surface coating, ink-jet printing, and when dealing with icing on wind turbines, airplane wings, and roads. Due to the complex nature of the flow within droplets, a wide range of temperatures, from freezing temperatures to heating temperatures, have to be taken into account in order to increase the understanding of the flow behavior. This study aimed to reveal if natural convection and/or Marangoni convection influence the flow in freezing and evaporating droplets. Droplets were released on cold and warm surfaces using similar experimental techniques and setups, and the internal flow within freezing and evaporating water droplets were then investigated and compared to one another using Particle Image Velocimetry. It was shown that, for both freezing and evaporating droplets, a shift in flow direction occurs early in the processes. For the freezing droplets, this effect could be traced to the Marangoni convection, but this could not be concluded for the evaporating droplets. For both evaporating and freezing droplets, after the shift in flow direction, natural convection dominates the flow. In the end of the freezing process, conduction seems to be the only contributing factor for the flow.

Engineering Micropatterned Surfaces for Controlling the Evaporation Process of Sessile Droplets

Controlling the evaporation process of a droplet is of the utmost importance for a number of technologies. Also, along with the advances of microfabrication, micropatterned surfaces have emerged as an important technology platform to tune the wettability and other surface properties of various fundamental and applied applications. Among the geometrical parameters of these micropatterns, it is of great interest to investigate whether the arrangement of the patterns would affect the evaporation process of a sessile liquid droplet. To address this question, we fabricated four microhole arrays with different arrangements, quantified by the parameter of “eccentricity”. The results suggested that, compared to smooth substrates, the evaporation mode was not only affected by engineering the microhole arrays, but also by the eccentricity of these micropatterns. The values of contact angle hysteresis (CAH) were used to quantify and test this hypothesis. The CAH could partially explain the different evaporation modes observed on the microhole arrays with zero and non-zero values of eccentricity. That is, on microhole arrays with zero eccentricity, CAH of water droplets was comparatively low (less than 20 ° ). Consistently, during the evaporation, around 60% of the life span of the droplet was in the mixed evaporation mode. Increasing the eccentricity of the microhole arrays increases the values of CAH to above 20 ° . Unlike the increasing trend of CAH, the evaporation modes of sessile droplets on the microhole array with non-zero values of eccentricity were almost similar. Over 75% of the life span of droplets on these surfaces was in constant contact line (CCL) mode. Our findings play a significant role in any technology platform containing micropatterned surfaces, where controlling the evaporation mode is desirable.

Making Photonic Crystals via Evaporation of Nanoparticle-Laden Droplets on Superhydrophobic Microstructures

We employed a convenient evaporation approach to fabricate photonic crystals by naturally drying droplets laden with nanoparticles on a superhydrophobic surface. The final drying morphology could be controlled by the concentration of nanoparticles. A dilute droplet resulted in a torus, whereas a quasi-spherical cap with a bottom cavity was made from a concentrated droplet. Remarkably, the nanofluid droplets maintained high contact angles (≳120°) during the entire evaporation process because of inhomogeneous surface wetting. Bottom-view snapshots revealed that during evaporation the color of the contact area changed sequentially from white to red, orange, yellow, and eventually to green. Scanning electron microscopy and Voronoi analysis demonstrated that nanoparticles were self-assembled to a hexagonal pattern. Finally, based on the effects of particle size, material, and volume concentration on the reflected wavelengths, a model has been developed to successfully predict the reflected wavelength peaks from the contact area of evaporating colloidal droplets. Our model can be easily adopted as a manufacturing guide for functional photonic crystals to predict the optimal reflected color made by evaporation-driven self-assembly of photonic crystals.

Cooperative evaporation in two-dimensional droplet arrays

The evaporation of a sessile drop in a gaseous environment may be critical to many practical applications. Evaporation dynamics of interacting sessile droplets is strongly influenced by the proximity of adjacent droplets. We study the effects of droplet-droplet vapor-mediated interactions on the evaporation lifetime of two-dimensional arrays of sessile water droplets. We observe that the presence of neighboring droplets acts as a mode of vapor accumulation which slows down the evaporation process. By considering an arbitrarily configured two-dimensional array of droplets, here we provide a simple generalized theoretical limit to their lifetime in an evaporating state. Using a scaling analysis, we put forward that the sessile droplet lifetime in a two-dimensional array is a linear function of the extent of confinement for various surface wettability and droplet geometric parameters (contact angle and contact radius). Notwithstanding the geometrical and physical complexity of the effective confinement generated due to their cooperative interactions, we show that the consequent evaporation characteristics may be remarkably insensitive to the topographical details of the overall droplet organization for a wide range of droplet-substrate combinations. With subsequent deployment of particle-laden droplets, however, our results lead to the discovery of a unique pathway towards tailoring the internal flows within the collective system by harnessing an exclusive topologically driven symmetry-breaking phenomenon, yielding a strategy of patterning particulate matters around the droplet array.

Nanopore-Enhanced Drop Evaporation: When Cooler or More Saline Water Droplets Evaporate Faster

The evaporation of water droplets on surfaces is a ubiquitous phenomenon in nature and has critical importance in a broad range of technical applications. Here, we show a substantial enhancement of liquid evaporation rate when droplets are on nanoporous thin film surfaces. We also reveal how this nanopore-enhanced evaporation leads to counterintuitive phenomena: cooler or more saline water droplets evaporate faster. We find indeed that, contrary to typical evaporation behavior of sessile droplets on nonporous surfaces, the droplets placed on nanoporous thin films evaporate more rapidly when salt concentration increases or when the temperature decreases. This peculiar droplet evaporation behavior is related to the key role of the steady wetted annulus that is self-generated into the nanopore network in the drop periphery, which leads to an effectively enhanced evaporation area that controls the overall evaporation process. Our results provide the prospect of conceiving fresh scenarios in the evaporation of drops on surfaces in both relevant applications and fundamental insights.

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.

A Study of the Evaporation of Hexane Lenses on an Ionic Liquid Surface: Effect of Wetting Mode

The evaporation of hexane lenses on an ionic liquid (IL) (1-butyl-3-methylimidazolium hexafluorophosphate) surface is studied. The difference between the evaporation processes of the lens on the IL surface and on a distilled water (DW) surface with the same substrate liquid depth (2.6 mm) is primarily analyzed. The variation of the lens contact diameter D_C and the deformation of the IL surface were experimentally observed. The results indicated that the spreading stage of a hexane lens was notably shorter in duration on the IL surface than on the DW surface. A hexane lens was pseudopartially wetted on the DW surface, and the plane position of the lens contact diameter remained level with the water surface throughout the evaporation process. In comparison, a hexane lens was partially wetted on the IL surface, and the plane position of the lens contact diameter was lower than the horizontal surface until the lens evaporated completely. The hexane lens evaporation on the IL surface was calculated by using the diffusion-controlled evaporation model under the constant contact angle mode. The calculated results agreed well with the experimental measurements. Finally, the evaporation of hexane lenses on the DW and the IL surfaces was compared through calculations. Although the maximum lens contact diameter on the DW surface was greater, it took a longer time for the lens to evaporate on the DW surface. This is because the more significant bending of the substrate liquid surface accelerated the lens evaporation. The results of this study offer a new approach for controlling droplet evaporation.

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.

Contactless sensing of liquid marbles for detection, characterisation & computing

Liquid marbles (LMs) are of growing interest in many fields, including microfluidics, microreactors, sensors, and signal carriers. The generation of LMs is generally performed manually, although there has recently been a burst of publications involving 'automatic marble makers'. The characteristics of a LM is dependent on many things, including how it is generated, it is therefore important to be able to characterise LMs once made. Here is presented a novel contactless LM sensor, constructed on a PCB board with a comb-like structure of 36 interlacing electrical traces, 100 μm wide and 100 μm apart. This cheap, scalable, and easy to use sensor exploits the inherent impedance (comprised of the electrical resistance, capacitive reactance and inductive reactance) of different LMs. With it, parameters of a LM can be easily determined, without interfering with the LM. These parameters are (1) particle size of the LM coating, (2) the concentration of a NaCl solution used as the LM core, and (3) the volume of the LM. Additionally, due to the comb-like nature of the sensor, the accurate positioning (down to the inter-trace spacing) of the LM can be ascertained. The new sensor has been shown to work under both static and dynamic (mobile) conditions. The capacitance of a LM was recorded to be 0.10 pF, which compares well with the calculated value of 0.12 pF.

Evaporation of a sessile droplet on a slope

We theoretically examine the drying of a stationary liquid droplet on an inclined surface. Both analytical and numerical approaches are considered, while assuming that the evaporation results from the purely diffusive transport of liquid vapor and that the contact line is a pinned circle. For the purposes of the analytical calculations, we suppose that the effect of gravity relative to the surface tension is weak, i.e. the Bond number (Bo) is small. Then, we express the shape of the drop and the vapor concentration field as perturbation expansions in terms of Bo. When the Bond number is zero, the droplet is unperturbed by the effect of gravity and takes the form of a spherical cap, for which the vapor concentration field is already known. Here, the Young-Laplace equation is solved analytically to calculate the first-order correction to the shape of the drop. Knowing the first-order perturbation to the drop geometry and the zeroth-order distribution of vapor concentration, we obtain the leading-order contribution of gravity to the rate of droplet evaporation by utilizing Green's second identity. The analytical results are supplemented by numerical calculations, where the droplet shape is first determined by minimizing the Helmholtz free energy and then the evaporation rate is computed by solving Laplace's equation for the vapor concentration field via a finite-volume method. Perhaps counter-intuitively, we find that even when the droplet deforms noticeably under the influence of gravity, the rate of evaporation remains almost unchanged, as if no gravitational effect is present. Furthermore, comparison between analytical and numerical calculations reveals that considering only the leading-order corrections to the shape of the droplet and vapor concentration distribution provides estimates that are valid well beyond their intended limit of very small Bo.

Drops That Change Their Mind: Spontaneous Reversal from Spreading to Retraction

A liquid drop may spread faster on surfaces when surfactants are added. Here we show that after some time the spreading in such systems can, under certain conditions, spontaneously reverse to retraction and the droplet pulls itself back, receding from areas it has just recently wetted, elevating its center of mass in a jerklike motion. The duration from drop placement to the onset of retraction ranges from hours to less than a second primarily as a function of surfactant concentration. When the retraction is asymmetric, it results in drop motion, and when it is symmetric, the mass of the drop collects itself on its spot. This phenomenon, which was predicted theoretically in 2014, is apparently a general one for drops with surfactants; however, other factors, such as evaporation and contamination, prevented its observance so far.

1D Roughness Driven Depinning of Self-Assembly of Liquid Droplets

The conventional hexagonal, uniform breath figure pattern formed over smooth substrates and substrates with constraints of the order of 50 μm is distorted when the underlying constraints are down to 1 μm. This paper explores this phenomenon further and concludes that, in addition to topology-based arguments presented by other authors previously, it is necessary to invoke the depinning effects of the three-phase contact line in order to explain the same. The influence of surface constraints on the self-assembly of liquid droplets is investigated. A semiquantitative explanation for large-scale pattern formation consisting of small-scale closely arranged droplets inside the large-scale distorted ring of droplets is presented in this paper. The scale at which the influence of constraints becomes dominant is also determined in this study. It is seen that the underlying roughness has a larger impact than the nature of polymer on pore size. Comparative studies of pore patterns formed on smooth and constrained substrates are reported. The simulated energy-minimized shapes of the droplets on smooth and constrained substrates are obtained using Surface Evolver.