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

Numerical Analysis of the Dispersion and Deposition of Particles in Evaporating Sessile Droplets

Evaporating sessile droplets containing dispersed particles are used in different technological applications, such as 3D printing, biomedicine, and micromanufacturing, where an accurate prediction of both the dispersion and deposition of the particles is important. Furthermore, the interaction between the droplet and the substrate must be taken into account: the motion of the contact line, in particular, must be modeled carefully. To this end, studies have typically been limited to either pinned or moving contact lines to simplify the underlying mathematical models and numerical methods, neglecting the fact that both scenarios are observed during the evaporation process. Here, a numerical algorithm considering both contact line regimes is proposed whereby the regimes are distinguished by predefined threshold contact angles. After a detailed validation, this new algorithm is applied to study the influence of both regimes on the dispersion and deposition of particles in an evaporating sessile droplet. In particular, the presented analysis focuses on the influence of (i) the contact line motion characteristics by varying the limiting contact angle and spreading speed, (ii) the Marangoni number, characterizing the importance of thermocapillarity, (iii) the evaporation number, which quantifies the importance of evaporation, (iv) the Damköhler number, a measure of the particle deposition rate, and (v) the Peclet number, which compares the convection and diffusion of the particle concentration. When thermocapillarity becomes dominant or the limiting contact angle is larger, the particle accumulation near the contact line decreases, which, in turn, means that more particles are deposited near the center of the droplet. In contrast, increasing the evaporation number supports particle accumulation near the contact line, while a larger Damköhler number and/or smaller Peclet number yield more uniform final deposition patterns. Finally, a larger characteristic speed of spreading results in fewer particles being deposited at the center of the droplet.

Understanding the Role of Loss Modulus of Viscoelastic Substrates in the Evaporation Dynamics of Sessile Drops

Viscoelastic properties of soft substrates play a crucial role in the evaporation dynamics of sessile drops. Recent studies have revealed that the modification of the viscoelastic properties of substrates changes the dynamics of the three-phase contact line, consequently affecting the evaporation behavior of sessile drops. Notably, these modifications occur without any noticeable changes to the substrate's wetting characteristics or surface topography. However, the individual role of storage (G') and loss (G″) moduli of substrates on drop evaporation dynamics remains unexplored. In this study, we investigate the evaporation dynamics of water drops on two groups of poly(dimethylsiloxane)-based viscoelastic substrates possessing either identical G' with varying G″ or identical G″ with varying G'. Our study reveals that on a substrate with constant shear modulus (G'), a reduction of an order of magnitude in loss modulus shifts the evaporation process from the constant contact radius mode to the constant contact angle mode. We hypothesize that this observed shift in behavior stems from the varying viscoelastic dissipation influenced by the plateau modulus and characteristic relaxation time of polymer gels. Our hypothesis is further supported from the observation that the evaporation process persists on the substrate with constant loss modulus (G″). Our study advances the current understanding of drop evaporation on soft substrates that may find potential applications involving soft composites, biological entities, tissue engineering, and wearable electronics.

Interfacial Effects of Nanostructured Doubly Reentrant Surfaces on the Evolution of Local Concentration and Fluid Flow in an Evaporating Droplet

Surface modification, such as bioinspired nanostructured doubly reentrant surfaces that have presented superhydrophobic wettability even under low-surface-tension liquid, is a very promising technology for controlling droplet dynamics, heat transfer, and evaporation. In this article, we investigate the interfacial effects of nanostructured doubly reentrant surfaces on the flow behaviors and local concentration evolution during the evaporation of an ethanol/water multicomponent droplet. Using particle image velocimetry (PIV) and novel aggregate-induced emission-based (AIE) techniques, the flow patterns and local concentration distributions on both hydrophobic and nanostructured doubly reentrant surfaces were probed and compared. It is found that in addition to the established Marangoni flow-dominated stage, transition stage, and buoyancy-induced flow-dominated stage, a new transition stage and a rolling stage for the nanostructured doubly reentrant surface are detected in the late evaporation period. Differences in the local concentration distribution evolution occur depending on the hydrophobicity of the surface on which the droplet is placed. For the hydrophobic surface, a nonuniform local concentration distribution exists consistently, with a high water fraction in a shell-shaped region near the liquid-air interface and a secondary concentration gradient within this shell-shaped region. The concentration distribution on the nanostructured doubly reentrant surface evolves in a more complex manner, with a strip-shaped region of high water fraction forming in the intermediate stage and then reorganized by rolling flow in the late stage. Finally, theoretical analysis combining PIV and AIE visualization results reveals that the variations in droplet concentration distributions on surfaces with different hydrophobicities exert a significant impact on evaporative behaviors. These behaviors, in turn, affect the evolution of the local concentration distribution.

Evaluation of Evaporation Fluxes for Pesticides and Low Volatile Hazardous Materials Based on Evaporation Kinetics of Net Liquids

Evaporation is the phase transition process that plays a significant role in many spheres of life and science. Volatilization of hazardous materials, pesticides, petroleum spills, etc., impacts the environment and biosphere. Predicting evaporation fluxes under specific environmental conditions is challenging from theoretical and empirical points of view. A new practical method for estimating fluxes is proposed based on our experimental results and previously published data. It is demonstrated that some parameters in theoretical equations for near-equilibrium evaporation can be estimated from experiments, and these formulas can be exploited to predict steady-state evaporation fluxes in the air in a range of 8 orders of magnitude based on a single experiment carried out for nontoxic volatile compounds.

Self-Sustaining Water Microdroplet Resonators Using 3D-Printed Microfluidics

Microdroplet resonators provide an excellent tool for optical studies of water, but water microdroplets are difficult to maintain outside a carefully controlled environment. We present a method for maintaining a water microdroplet resonator on a 3D-printed hydrophobic surface in an ambient environment. The droplet is maintained through a passive microfluidic system that supplies water to the droplet through a vertical channel at a rate equivalent to its evaporation. In this manner, we are able to create and passively maintain water microdroplet resonators with quality factors as high as 3×108.

Liquid Marbles and Drops on Superhydrophobic Surfaces: Interfacial Aspects and Dynamics of Formation: A Review

Liquid marbles (LMs) are droplets encapsulated with powders presenting varied roughness and wettability. These LMs have garnered a lot of attention due to their dual properties of leakage-free and quick transport on both solid and liquid surfaces. These droplets are in a Cassie-Baxter wetting state sitting on both roughness and air pockets existing between particles. They are also reminiscent of the state of a drop on a superhydrophobic (SH) surface. In this review, LMs and bare droplets on SH surfaces are comparatively investigated in terms of two aspects: interfacial and dynamical. LMs present a fascinating class of soft matter due to their superior interfacial activity and their remarkable stability. Inherently hydrophobic powders form stable LMs by simple rolling; however, particles with defined morphologies and chemistries contribute to the varied stability of LMs. The factors contributing to this interesting robustness with respect to bare droplets are then identified by tests of stability such as evaporation and compression. Next, the dynamics of the impact of a drop on a hydrophobic powder bed to form LMs is studied vis-à̀-vis that of drop impact on flat surfaces. The knowledge from drop impact phenomena on flat surfaces is used to build and complement insights to that of drop impact on powder surfaces. The maximum spread of the drop is empirically understood in terms of dimensionless numbers, and their drawbacks are highlighted. Various stages of drop impact-spreading, retraction and rebound, splashing, and final outcome-are systematically explored on both solid and hard surfaces. The implications of crater formation and energy dissipations are discussed in the case of granular beds. While the drop impact on solid surfaces is extensively reviewed, deep interpretation of the drop impact on granular surfaces needs to be improved. Additionally, the applications of each step in the sequence of drop impact phenomena on both substrates are also identified. Next, the criterion for the formation of peculiar jammed LMs was examined. Finally, the challenges and possible future perspectives are envisaged.

Tuning contact line dynamics on slippery silicone oil grafted surfaces for sessile droplet evaporation

Controlling the dynamics of droplet evaporation is critical to numerous fundamental and industrial applications. The three main modes of evaporation so far reported on smooth surfaces are the constant contact radius (CCR), constant contact angle (CCA), and mixed mode. Previously reported methods for controlling droplet evaporation include chemical or physical modifications of the surfaces via surface coating. These often require complex multiple stage processing, which eventually enables similar droplet-surface interactions. By leveraging the change in the physicochemical properties of the outermost surface by different silicone oil grafting fabrication parameters, the evaporation dynamics and the duration of the different evaporation modes can be controlled. After grafting one layer of oil, the intrinsic hydrophilic silicon surface (contact angle (CA) ≈ 60°) is transformed into a hydrophobic surface (CA ≈ 108°) with low contact angle hysteresis (CAH). The CAH can be tuned between 1° and 20° depending on the fabrication parameters such as oil viscosity, volume, deposition method as well as the number of layers, which in turn control the duration of the different evaporation modes. In addition, the occurrence and strength of stick-slip behaviour during evaporation can be additionally controlled by the silicone oil grafting procedure adopted. These findings provide guidelines for controlling the droplet-surface interactions by either minimizing or maximising contact line initial pinning, stick-slip and/or constant contact angle modes of evaporation. We conclude that the simple and scalable silicone oil grafted coatings reported here provide similar functionalities to slippery liquid infused porous surfaces (SLIPSs), quasi-liquid surfaces (QLS), and/or slippery omniphobic covalently attached liquid (SOCAL) surfaces, by empowering pinning-free surfaces, and have great potential for use in self-cleaning surfaces or uniform particle deposition.

Diffusion of Solute Atoms in an Evaporated Liquid Droplet

Controlling the evaporation of a solvent has made it possible to grow crystals, nanoparticles, and microparticles from liquid droplets. At the heart of this process is the evaporation-induced diffusion of solute atoms, causing the liquid solution of the solute atoms to be in a supersaturated state. In this work, we analyze the mass transport in a spherical liquid droplet, which experiences the loss or evaporation of the solvents across the droplet surface. Using a pseudo-steady-state method, two approximate solutions are derived for the moving boundary problem: one is a linear function of the square of radial variable with a constraint to the loss rate of the solvent, and the other is an exponential function of the square of radial variable without any constraint to the loss rate of the solvent. The numerical results obtained from both approximate solutions are in accord with the numerical results from the finite element method, validating the approximate solutions. The results reveal that a small evaporation/loss rate of the solvent is needed to maintain a relatively uniform distribution of solute atoms in a liquid droplet during the solvent evaporation/loss.

Liquid marbles: review of recent progress in physical properties, formation techniques, and lab-in-a-marble applications in microreactors and biosensors

Liquid marbles (LMs) are nonsticking droplets whose surfaces are covered with low-wettability particles. Owing to their high mobility, shape reconfigurability, and widely accessible liquid/particle possibilities, the research on LMs has flourished since 2001. Their physical properties, fabrication mechanisms, and functionalisation capabilities indicate their potential for various applications. This review summarises the fundamental properties of LMs, the recent advances (mainly works published in 2020-2023) in the concept of LMs, physical properties, formation methods, LM-templated material design, and biochemical applications. Finally, the potential development and variations of LMs are discussed.

Strategy for Patterning Titania Dendrites by Gas-Solution Interaction at Droplet Surfaces

Interaction of the solution droplet surface with gaseous components of the environment can lead to the formation of highly ordered patterns, such as dendrites. Here, we show that these structures can be spontaneously created during the open-air interaction of aqueous solution drop of titanium(III) salt with gaseous NH3 at the contact boundary thereof. The conditions have been identified under which radially ordered dendritic patterns can form on the surface of the TiCl3 solution droplet. The formation of these self-organized dendrite patterns can be attributed to the surface instability manifesting in Marangoni thermal flows in a droplet occurring during open-air fabrication. The composition of as-synthesized structures corresponds to coprecipitated crystalline NH4Cl and amorphous TiO2nH2O. After thermal treatment at 450 °C, TiO2 with the anatase crystal lattice is formed; meanwhile, the ordered dendrite patterns are preserved.

Evaporation of alcohol droplets on surfaces in moist air

Droplets of alcohol-based formulations are common in applications from sanitizing sprays to printing inks. However, our understanding of the drying dynamics of these droplets on surfaces and the influence of ambient humidity is still very limited. Here, we report the drying dynamics of picoliter droplets of isopropyl alcohol deposited on a surface under controlled humidity. Condensation of water vapor in the ambient environment onto alcohol droplets leads to unexpectedly complex drying behavior. As relative humidity (RH) increases, we observed a variety of phenomena including enhanced spreading, nonmonotonic changes in the drying time, the formation of pancake-like shapes that suppress the coffee-ring effect, and the formation of water-rich films around an alcohol-rich drop. We developed a lubrication model that accounts for the coupling between the flow field within the drop, the shape of the drop, and the vapor concentration field. The model reproduces many of the experimentally observed morphological and dynamic features, revealing the presence of unusually large spatial compositional gradients within the evaporating droplet and surface-tension-gradient-driven flows arising from water condensation/evaporation at the surface of the droplet. One unexpected feature from the simulation is that water can evaporate and condense concurrently in different parts of the drop, providing fundamental insights that simpler models based on average fluxes lack. We further observed rim instabilities at higher RH that are well-described by a model based on the Rayleigh-Plateau instability. Our findings have implications for the testing and use of alcohol-based disinfectant sprays and printing inks.

Sample preconcentration through airjet-induced liquid phase enrichment

Sample preparation is essential for nucleic acid assays, affecting their sensitivity and reliability. However, this process often results in a significant loss or dilution of the analyte, which becomes a bottleneck that limits downstream assay performance, particularly for assays that accept a limited input sample volume. To overcome this challenge, we present an evaporative-based sample enrichment method that uses an airjet to concentrate analytes within a small, defined volume by reversing the coffee-ring effect. A small, concentrated sample can then be collected for analysis to increase the initial sample load. The effectiveness of the reported airjet enrichment was quantified using qPCR of λ-DNA, HeLa-S3 RNA, and heat-inactivated SARS-CoV-2 samples. Comparisons between airjet enrichment and conventional evaporative concentration methods demonstrated significant advantages of airjet enrichment, including the ability to concentrate a high percentage of analyte within a 1 μL volume. The enrichment method was then integrated and adapted for various fluid volumes commonly found in nucleic acid sample preparation procedures. Here, airjet enrichment reduced the overall Cq by an average of 9.27 cycles for each analyte, resulting in a 600-fold enrichment from the initial concentration. To perform selective enrichment and prevent salt-based interference in downstream analysis, PEG was added to reduce the co-enrichment of salt. In addition, a preliminary study was conducted to explore the integration of airjet enrichment into ELISA using rabbit IgG as a model antigen. These findings demonstrate how airjet enrichment can be easily integrated into existing laboratory protocols with minimal modification and significantly improve the performance of biosensors.

Kinetics of Lipophilic Pesticide Uptake by Living Maize

We report the uptake of a lipophilic fungicide into the cuticle of living leaves of young maize from droplets of a suspension concentrate. The action of a "coffee-ring" effect is demonstrated during fungicide formulation drying, and the fungicide particle distribution is quantified. We develop a simple, two-dimensional model of uptake leading to a "reservoir" of cuticular fungicide. This model allows inferences of physicochemical properties for fungicides inside the cuticular medium. The diffusion coefficient closely agrees with literature penetration experiments (D_cut ≈ 10^-18 m² s^-1). The logarithm of the inferred cuticle-water partition coefficient log₁₀ K_cw = 6.03 ± 0.04 is consistent with ethyl acetate as a model solvent for the maize cuticle. Two limiting kinetic uptake regimes are inferred from the model for short and long times, with the transition resulting from longitudinal saturation of the cuticle beneath the droplet. We discuss the strengths, limitations, and generalizability of our model within the "cuticle reservoir" approximation.

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

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

Inhibiting Cracks in Latte Droplets

Latte is a mixture of coffee and milk and a model of complex fluids containing biomolecules, usually leaving complex deposit patterns after droplet evaporation. Despite the universality and applicability of biofluids, their evaporation and deposition dynamics are not fully understood and controllable because of the complexity of their components. Here we investigate latte droplet evaporation and deposition dynamics, primarily the crack development and inhibition in droplet deposit patterns. With regard to a mixture of milk and coffee, we find that the surfactant-like nature of milk and intermolecular interactions between coffee particles and milk bioparticles are responsible for achieving uniform crack-free deposits. This finding improves our understanding of pattern formation from evaporating droplets with complex biofluids, offering a clue to applications of bioinks with both printability and biocompatibility.

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

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

Construction of an active humidity regulation setup for NMR/MRI-Observation and simulation of the controlled evaporation of sessile water droplets

Controlling and improving processes like for example the production of organic semiconductors via printing depends on understanding the interplay of wetting and evaporation of complex fluids. Therefore, examination of the time dependent composition of complex fluid droplets during wetting or evaporation is of interest. The evaporation rate of sessile droplets containing largely water depends on the vapor pressures of the individual components and on the humidity (or partial pressure) of the surrounding gas phase. Hence, for a complete picture of an evaporation process and the comparability of the results of different measurements, it is essential to measure and control the humidity and temperature in the measurement compartment. Accordingly, climate chambers are available in different scales to fit a variety of techniques like contact angle goniometry to obtain results in a controlled atmosphere. We recently reported the application of MRI (Magnetic Resonance Imaging) and spatially resolved NMR (Nuclear Magnetic Resonance) spectroscopy for the examination of the evaporation of sessile droplets on surfaces in 10 mm NMR tubes. These are considered to be closed compartments. Here, we present an apparatus to a) measure and b) control the relative humidity within the sample compartment of the NMR setup by introducing preconditioned gas into the NMR tube. We monitored the evaporation of water droplets using RARE images and compared the volume decay with a) a simple diffusive evaporation model and b) with detailed FEM (finite element numerical model) simulations using COMSOL for validation. We find three evaporation regimes depending on the flow rate as well as on the distance of the gas outlet and the evaporating droplet. In one of the sample configurations tested the evaporation takes place in such a way that it can be described with the help of the simple diffusive model without convection. Thus, the presented approach opens comparative measurements with other methods as well as the observation of droplet evaporation in very dry or very humid environments with and without the influence of convection. Finally, using PRESS spectra, it is shown that the evaporation rate of water from a water/DMSO droplet can be controlled. This shows how the setup presented here can be used to study the evaporation of droplets of more complex mixtures.

Measurement of the Temperature Decrease in Evaporating Soap Films

Recent advances have demonstrated that evaporation can play a significant role on soap film stability, which is a key concern in many industrial areas but also for children playing with bubbles. Thus, evaporation leads to a film thinning but also to a film cooling, which has been overlooked for soapy objects. Here, we study the temperature variation of an evaporating soap film for different values of relative humidity and glycerol concentrations. We evidence that the temperature of soap films can decrease after their creation up to 8 °C. We propose a model describing the temperature drop of soap films after their formation that is in quantitative agreement with our experiments. We emphasize that this cooling effect is significant and must be carefully considered in future studies on the dynamics of soap films.

Evaporation-driven liquid flow in sessile droplets

The evaporation of a sessile droplet spontaneously induces an internal capillary liquid flow. The surface-tension driven minimisation of surface area and/or surface-tension differences at the liquid-gas interface caused by evaporation-induced temperature or chemical gradients set the liquid into motion. This flow drags along suspended material and is one of the keys to control the material deposition in the stain that is left behind by a drying droplet. Applications of this principle range from the control of stain formation in the printing and coating industry, to the analysis of DNA, to forensic and medical research on blood stains, and to the use of evaporation-driven self-assembly for nanotechnology. Therefore, the evaporation of sessile droplets attracts an enormous interest from not only the fluid dynamics, but also the soft matter, chemistry, biology, engineering, nanotechnology and mathematics communities. As a consequence of this broad interest, knowledge on evaporation-driven flows in drying droplets has remained scattered among the different fields, leading to various misconceptions and misinterpretations. In this review we aim to unify these views, and reflect on the current understanding of evaporation-driven liquid flows in sessile droplets in the light of the most recent experimental and theoretical advances. In addition, we outline open questions and indicate promising directions for future research.

Spontaneous separation and evaporation mechanism of self-rewetting fluid droplets on chemically stripe-patterned surfaces: A lattice Boltzmann study

The evaporation characteristics of self-rewetting fluids have attracted much attention in recent years. However, the evaporation dynamics as well as the underlying evaporation mechanism of self-rewetting fluid droplets has not been well understood. In this paper, we numerically investigate the evaporation performance and the dynamic behavior of self-rewetting fluid droplets on chemically patterned surfaces using a thermal multiphase lattice Boltzmann model with liquid-vapor phase change. First, it is shown that a self-rewetting fluid droplet can spontaneously separate into two droplets during its evaporation on a hydrophilic surface with a hydrophobic stripe, while no separation occurs during the evaporation of a conventional fluid droplet. The positive surface tension gradient of the self-rewetting fluid is found to play an important role in the spontaneous separation of the self-rewetting fluid droplet during the evaporation. Meanwhile, the separation behavior of the self-rewetting fluid droplet can effectively increase the length of the triple-phase contact line, which leads to a significant increase in the evaporation rate as compared with that of a conventional fluid droplet. Moreover, by investigating the evaporation performance of self-rewetting fluid droplets on chemically stripe-patterned surfaces with different values of the widths of the hydrophilic and hydrophobic stripes, it is found that the stripe width and the initial location of the droplet significantly affect the dynamic behavior and the evaporation efficiency of the self-rewetting fluid droplet. For different relative positions between the droplet and the stripes, the droplet may spontaneously separate into two or three droplets and achieve much better evaporation efficiency when the stripe width is within an optimal range.

Preparation of Phase Change Melt Marbles with High Thermal Stability by Spontaneous Shrinkage and Encapsulation

Liquid marbles (LMs) are widely used in the fields of microfluids, gas sensitivity equipment, and microreactors. However, the thermal stability of the encapsulated liquid poses difficulty to the high-temperature stability of LMs. In this study, polar phase-change materials (PCMs) with high melting points were used as the encapsulated liquid of LMs. According to the required temperature, suitable PCMs were selected as the core and encapsulated by hydrophobic SiO₂ particles to form melt marbles (MMs). The types of PCMs used to prepare the MMs include erythritol, elemental sulfur, urea, and molten salts. Based on the premixed melting method, a series of MMs with high melting points and thermal stability were successfully developed. The highest acceptable temperature of the MMs exceeded 323 °C, and the evaporation rate of erythritol MMs was less than 1% at 140 °C in 8 h. Thus, the MMs maintained their excellent stability through multiple phase transitions. In the molten state, the MMs exhibited the properties of bounce ability, cuttability, and deformation resistance. The performance of the PCMs in energy storage and release during phase transition demonstrates their potential applications in the field of heat storage.

One-Step Synthesis of Dynamically Shaped Stiff Nanorods Using Soft Silicone Materials to Control Water Repulsion and Collection

One-dimensional silicone nanostructures, such as filaments, wires, and tubes, have attracted significant attention, owing to their remarkable application capabilities in a large range of material and surface science. However, the soft mechanical properties of silicone cause vulnerability and irregularity in the synthesized structures, which limits their applications. Herein, a simple, solvent-free, and efficient dynamic Droplet Assisted Growth and Shaping (d-DAGS) strategy is proposed for the one-step synthesis and in situ control of the shape of silicone nanostructures. The special designed bamboo-shaped silicone nanorods (SNRs) that are produced by the repetitive dynamic regulation of growth conditions, concomitant with the periodic purging and injection of precursors, exhibit highly-regular and tunable structure with a specific number of segments, indicating that they can be tailor-made according to the requirements of various properties. The enhanced mechanical stiffness and chemical durability strongly support their excellent performances in water-resistance under both static and dynamic wetting conditions. The SNRs significantly promote buoyancy and self-cleaning properties; and exhibit very high water-harvesting efficiency compared with existing designs. Notably, the well-structured ultra-long rods with an ultrahigh aspect ratio (≈176) can also be fabricated by the d-DAGS method, and they can remain standing straight upwards and regular, even though they consist of flexible silicone.

In-vitro evaluation of the evaporation retardation by Meibomian lipids in homogeneous and non-homogeneous evaporation

HYPOTHESIS

An important function of the Tear Film Lipid Layer (TFLL) is the retardation of evaporation. We propose two micro-scaled systems to quantify the influence of the TFLL in evaporation for single patients, which may contribute as an improvement on the diagnosis of Meibomian Gland Dysfunctions (MGD).

EXPERIMENTS

Meibum was extracted from 10 patients with hypersecretory MGD and 9 healthy controls. The lipids were placed over water, and the evaporation was determined in the case of homogeneous evaporation over a surface (pendant drop), and the case where the evaporation depends on a pinned triple contact line (meniscus).

FINDINGS

For the homogeneous case, the presence of Meibum reduced evaporation in 30%, although there was no significant difference between controls and MGD patients. However, evaporation induced by menisci was 25 % higher in MGD patients. Our results contribute to the evidence of the inhibition of evaporation by Meibum. Our study also suggests that the evaporation induced by contact points may be a more relevant model to measure differences in evaporation due to the composition of Meibum. This model may also have connotations in the occurrence of internal stresses in the tear film, inducing its instability.

Use of Heating Configuration to Control Marangoni Circulation during Droplet Evaporation

The present work presents a numerical study of the evaporation of a sessile liquid droplet deposited on a substrate and subjected to different heating configurations. The physical formulation accounts for evaporation, the Marangoni effect, conductive transfer in the support, radiative heating, and diffusion–convection in the droplet itself. The moving interface is solved using the Arbitrary Lagrangian–Eulerian (ALE) method. Simulations were performed using COMSOL Multiphysics. Different configurations were performed to investigate the effect of the heating conditions on the shape and intensity of the Marangoni circulations. A droplet can be heated by the substrate (different natures and thicknesses were tested) and/or by a heat flux supplied at the top of the droplet. The results show that the Marangoni flow can be controlled by the heating configuration. An upward Marangoni flow was obtained for a heated substrate and a downward Marangoni flow for a flux imposed at the top of the droplet. Using both heat sources generated two vortices with an upward flow from the bottom and a downward flow from the top. The position of the stagnation zone depended on the respective intensities of the heating fluxes. Controlling the circulation in the droplet might have interesting applications, such as the control of the deposition of microparticles in suspension in the liquid, the deposition of the solved constituent, and the enhancement of the evaporation rate.

Capillary Bridges on Hydrophobic Surfaces: Analytical Contact Angle Determination

The capillary bridge probe method was introduced previously as a high-accuracy contact angle determination method relying on capillary bridges on hydrophilic and superhydrophilic surfaces [Nagy, N. Langmuir 2019, 35 (15), 5202-5212]. In this work, the behavior of r-ϑ type liquid bridges was studied and the contact angles were determined on hydrophobic surfaces. The equilibrium shape of these liquid bridges often does not contain the neck or haunch region. The unknown neck/haunch radius prevents analytical evaluation of the capillary bridge shape. In this work, the possible incomplete liquid bridge shapes were classified and a novel procedure was developed for the Delaunay's analytical solution-based evaluation of these states. The parameter space of the capillary bridges was visualized and described without using dimensionless variables. As a demonstration, Cyclo Olefin Polymer and PTFE surfaces were investigated, with advancing and receding contact angles determined and compared to the results of sessile drop measurements.

Analytical modeling of the evaporation of sessile drop linear arrays

An analytical model for predicting the competitive evaporation of two and three sessile drops is proposed, based on an analytical solution, in terms of Mehler functions, of the steady species and energy conservation equations for the gaseous phase. The assessment through a comparison with accurate numerical solutions of the species conservation equations is reported in order to quantify the accuracy of the analytical solution. The model is validated against three available sets of experiments on two and three sessile drops on a line array. The decrease of the evaporation rate caused by the vicinity of sessile drops is reported in terms of a screening coefficient given by a relatively simple analytical expression. The influence of wall wettability on the evaporation of pairs of sessile drops is analyzed, and a parameter is proposed to quantify the effect of geometry in a unified way.

Lens Evaporation on Immiscible Liquid Surface with an Interfacial Cooling Effect

A theoretical heat and mass transfer model of volatile liquid lens evaporation on the surface of an immiscible liquid substrate is established in toroidal coordinates. According to the coupled boundary conditions of heat and mass transfer at the lens surface as well as the interfacial cooling effect, the analytical solutions of the temperature field inside the lens and the vapor concentration field around the lens are derived for the first time. Compared with the isothermal model, the change of contact radius calculated by the present model agrees well with the experimental data, especially when the liquid substrate reaches a relatively high temperature. It also reveals that the temperature distribution inside the lens is not uniform, which is similar to the sessile droplet evaporation on a solid substrate surface. In addition, the excess temperature, heat flux, and evaporation flux of the lens-air interface increase monotonically from the lens center to the contact line. Finally, the influences of density ratio and evaporative cooling number E ₀ on lens mass evaporation rate are analyzed, which shows that the lens mass evaporation rate decreases with increasing density ratio and evaporative cooling number.

Microfluidic Droplet Cluster with Distributed Evaporation Rates as a Model for Bioaerosols

Aerosols and microdroplets are known to act as carriers for pathogens or vessels for chemical reactions. The natural occurrence of evaporation of these droplets has implications for the viability of pathogens or chemical processes. For example, it is important to understand how pathogens survive extreme physiochemical conditions such as confinement and osmotic stress induced by evaporation of aerosol droplets. Previously, larger evaporating droplets were proposed as model systems as the processes in the tiny aerosol droplets are difficult to image. In this context, we propose the concept of evaporation of capillary-clustered aqueous microdroplets dispersed in a thin oil layer. The configuration produces spatially segregated evaporation rates. It allows comparing the consequences of evaporation and its rate for processes occurring in droplets. As a proof of concept, we study the consequences of evaporation and its rate using Escherichia coli (E. coli) and Bacillus subtilis as model organisms. Our experiments indicate that the rate of evaporation of microdroplets is an important parameter in deciding the viability of contained microorganisms. With slow evaporation, E. coli could mitigate the osmotic stress by K⁺ ion uptake. Our method may also be applicable to other evaporating droplet systems, for example, microdroplet chemistry to understand the implications of evaporation rates.

An experimental and theoretical study of the inward particle drift in contact line deposits

The coffee ring effect, which refers to the formation of a ring-like deposit along the periphery of a dried particle laden sessile drop, is a commonly observed phenomenon. The migration of particles from the interior to the edge of a drying drop as a result of evaporation driven flow directed outwards, is well studied. In this article, we document the inward drift of a coffee stain, which is governed by the descent of the water-air interface of the drying drop due to solvent evaporation. A combination of experimental study and model predictions is undertaken to elucidate the effect of the diameter of particles in the drying drop, the wettability of the substrate on which the drop resides, and the concentration of particles on the inward drift of the coffee stain. This work also suggests a novel method to estimate the coefficient of friction between the particles and the substrate.

Volatile Aroma Surfactants: The Evaluation of the Adsorption-Evaporation Behavior under Dynamic and Equilibrium Conditions

Multicomponent heterogeneous systems containing volatile amphiphiles are relevant to the fields ranging from drug delivery to atmospheric science. Research presented here discloses the individual interfacial activity and adsorption-evaporation behavior of amphiphilic aroma molecules at the liquid-vapor interface. The surface tension of solutions of nonmicellar volatile surfactants linalool and benzyl acetate, fragrances as such, was compared with that of the conventional surfactant sodium dodecyl sulfate (SDS) under equilibrium as well as under no instantaneous equilibrium, including a fast-adsorbing regime. In open systems, the increase in the surface tension on a time scale of ∼10 min is evaluated using a phenomenological model. The derived characteristic mass transfer constant is shown to be specific to both the desorption mechanism and the chemistry of the volatile amphiphile. Fast-adsorbing behavior disclosed here, as well as the synergetic effect in the mixtures with conventional micellar surfactants, justifies the advantages of volatile amphiphiles as cosurfactants in dynamic interfacial processes. The demonstrated approach to derive specific material parameters of fragrance molecules can be used for an application-targeted selection of volatile cosurfactants, e.g., in emulsification and foaming, inkjet printing, microfluidics, spraying, and coating technologies.

Evaporation and drying characteristics of the sessile ferrofluid droplet under a horizontal magnetic field

In this study, the evaporation characteristics and drying patterns of various sessile ferrofluid droplets on certain substrate under horizontal magnetic fields of controlled intensities are reported. The effects of droplet concentration and magnetic field intensity on the duration of each evaporation stage and drying patterns of droplets have been systematically investigated. It turned out that a plateau appears at the initial stage of evaporation in the absence of magnetic field and it was found that the plateau value is positively correlated with the concentration of ferrofluid droplets. Under the external magnetic field, the evaporation time of droplets decreases, the stage of contact line retreat extends, the stage of late pinning mode shortens, and the deposition area of ferrofluid droplet decreases compared to that of without magnetics field. The deposition area increases gradually and becomes more uniform with the increase of magnetic field. The decrease of friction force which is due to the decrease of the number of nanoparticles at the contact line under external magnetic field is the main reason for the observed phenomena. We found that the coffee ring and the uniform deposition inside the droplet will be destroyed when the magnetic field intensity is higher than a critical value. Our work has a significant reference value for the evaporation of sessile magnetic fluid droplets under the applied magnetic field, especially when the drying pattern needs to be precisely controlled, such as in spray or biomedicine.

Modes of synchrony in self-propelled pentanol drops

We report various modes of synchrony observed for a population of two, three and four pentanol drops in a rectangular channel at the air-water interface. Initially, the autonomous oscillations of a single 1-pentanol drop were studied in a ferroin DI water solution pre-mixed with some volume of pentanol. A pentanol drop performs continuous motion on the air-water interface due to Marangoni forces. A linear channel was prepared to study the uniaxial movement of the drop(s). Thereafter, a systematic study of the self-propelled motion of a 1-pentanol drop was reported as a function of the drop volume. Subsequently, the coupled dynamics were studied for two, three and four drops, respectively. We observed anti-phase oscillations in a pair of pentanol drops. In the case of three drops, relay synchronization was observed, wherein consecutive pairs of drops were exhibiting out-of-phase oscillations and alternate drops were performing in-phase oscillations. Four pentanol drops showed two different modes of synchrony: one was relay synchrony and the other was out-of-phase oscillations between two pairs of drops (within a pair, the drops exhibit in-phase oscillations).

A simple non-contact optical method to quantify in-vivo sweat gland activity and pulsation

OBJECTIVE

Most methods for monitoring sweat gland activity use simple gravimetric methods, which merely measure the average sweat rate of multiple sweat glands over a region of skin. It would be extremely useful to have a method which could quantify individual gland activity in order to improve the treatment of conditions which use sweat tests as a diagnostic tool, such as hyperhidrosis, cystic fibrosis, and peripheral nerve degeneration.

METHODS

An optical method using an infrared camera to monitor the skin surface temperature was developed. A thermodynamics computer model was then implemented to utilize these skin temperature values along with other environmental parameters, such as ambient temperature and relative humidity, to calculate the sweat rates of individual glands using chemically stimulated and unstimulated sweating. The optical method was also used to monitor sweat pulsation patterns of individual sweat glands.

RESULTS

In this preliminary study, the feasibility of the optical approach was demonstrated by measuring sweat rates of individual glands at various bodily locations. Calculated values from this method agree with expected sweat rates given values found in literature. In addition, a lack of pulsatile sweat expulsion was observed during chemically stimulated sweating, and a potential explanation for this phenomenon was proposed.

CONCLUSION

A simple, non-contact optical method to quantify sweat gland activity in-vivo was presented.

SIGNIFICANCE

This method allows researchers and clinicians to investigate several sweat glands simultaneously, which has the potential to provide more accurate diagnoses and treatment as well as increase the potential utility for wearable sweat sensors.

Droplet evaporation on porous fabric materials

Droplet evaporation on porous materials is a complex dynamic that occurs with spontaneous liquid imbibition through pores by capillary action. Here, we explore water dynamics on a porous fabric substrate with in-situ observations of X-ray and optical imaging techniques. We show how spreading and wicking lead to water imbibition through a porous substrate, enhancing the wetted surface area and consequently promoting evaporation. These sequential dynamics offer a framework to understand the alterations in the evaporation due to porosity for the particular case of fabric materials and a clue of how face masks interact with respiratory droplets.

Evaporation-triggered directional transport of asymmetrically confined droplets

HYPOTHESIS

When a liquid droplet is confined between two non-parallel hydrophobic surfaces with dihedral angle α, its behavior is largely influenced by the asymmetric confinement. During evaporation, the droplet morphology under confinement will continuously evolve, leading to the directional transport of the droplet towards the cusp.

EXPERIMENTS AND SIMULATIONS

During the evaporation process, droplets at different initial locations l₀ from the cusp were experimentally observed to transport towards the cusp. A series of simulations using Surface Evolver were performed to obtain the three-dimensional morphologies of the confined droplets. Force and energy analyses were conducted to unveil the mechanisms dominating the evaporation-triggered actuation and transport.

FINDINGS

The asymmetrically confined droplet of volume V would drift towards an equilibrium location of l_e from the cusp with the lowest energy. Its directional motion results from the consecutively decreasing l_e, which is scaled as l_e~α^-1V¹³ during evaporation. Herein, the creeping and slipping modes of transport could be characterized as the quasi-stable and unstable self-relaxation processes of droplet from the stretched regime to the equilibrium regime, respectively. Our findings on the intrinsic mechanism of droplet actuation shed light on a novel approach to manipulating the confined droplet behaviors in a passive and decisive fashion.

Morphology Evolution of a Volatile Liquid Lens on Another Immiscible Liquid Surface Induced by Evaporation

A theoretical model was established to predict the morphology evolution of a volatile liquid lens evaporation on another immiscible liquid substrate surface. The theoretical model considered the dynamic process of contact line motion. On the basis of the boundary conditions established at the contact line, the morphology change of the liquid lens was calculated by numerically solving the Young-Laplace differential equations for the three interfaces. The mass evaporation rate was calculated by the diffusion-controlled evaporation model. Then, an experimental system was established to record the process of a hexane lens evaporation on the surface of an ionic liquid with a depth of 4 mm. The calculated hexane lens radius variation matches well with the experimental measurements, which shows the rationality of the present model. The calculated results show that the evaporation pattern of the liquid lens follows the constant contact-angle evaporation mode for ∼70% of the lifetime. During the later stage of evaporation, the contact angle decreases, accompanied by contraction of the contact line, which is similar to the mixed evaporation mode in the later stage of sessile droplet evaporation on a solid substrate surface. Furthermore, the influences of the initial hexane lens volume and the ionic liquid temperature on the dynamic contact angle were theoretically summarized. This study helps to provide in-depth insights into regulating the lens evaporation process on another immiscible liquid substrate surface to control the particle deposition mode.

Patterns from dried drops as a characterisation and healthcare diagnosis technique, potential and challenges: A review

When particulate-laden droplets evaporate, they leave behind complex patterns on the substrate depending on their composition and the dynamics of their evaporation. Over the past two decades, there has been an increased interest in interpreting these patterns due to their numerous applications in biomedicine, forensics, food quality analysis and inkjet printing. The objective of this review is to investigate the use of patterns from dried drops as a characterisation and diagnosis technique. The patterns left behind by dried drops of various complex fluids are categorised. The potential applications of these patterns are presented, focussing primarily on healthcare, where the future impact could be greatest. A discussion on the limitations which must be overcome and prospective works that may be carried out to allow for widespread implementation of this technique is presented in conclusion.

Evaporation of Sessile Binary Mixture Droplets: Time Dependence of Droplet Shape and Concentration Profile from One-Dimensional Magnetic Resonance Microscopy

Many technological applications like inkjet printing, coating, or cooling processes rely on the evaporation of sessile droplets. Regarding liquid mixtures, the understanding of the underlying physics is still incomplete and process optimization requires trial and error. Our main goal is to establish a novel method in this field, one-dimensional magnetic resonance microscopy, to investigate the evaporation of sessile binary mixture droplets in the microliter range. It allows us not only to determine the droplet volume and shape, including contact angle, but also to measure concentration profiles with a spatial resolution of a few micrometers. These capabilities are demonstrated for a mixture of 1-octanol (OCT) and pentadecafluoro-1-octanol (F-OCT) by combining spatially resolved ¹H and ¹⁹F nuclear magnetic resonance measurements. We clearly observe three evaporation regimes for the OCT/F-OCT mixture. The first and second regimes are characterized by the predominant evaporation of F-OCT and are separated by a depinning event. The third regime starts when no F-OCT is left and, thus, features the evaporation of a pure OCT droplet. During all stages, concentration gradients perpendicular to the substrate are weak in the studied binary droplet.

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.