Evaporation of sessile droplets

Fundamentals and Applications of Surface Wetting

In an era defined by an insatiable thirst for sustainable energy solutions, responsible water management, and cutting-edge lab-on-a-chip diagnostics, surface wettability plays a pivotal role in these fields. The seamless integration of fundamental research and the following demonstration of applications on these groundbreaking technologies hinges on manipulating fluid through surface wettability, significantly optimizing performance, enhancing efficiency, and advancing overall sustainability. This Review explores the behavior of liquids when they engage with engineered surfaces, delving into the far-reaching implications of these interactions in various applications. Specifically, we explore surface wetting, dissecting it into three distinctive facets. First, we delve into the fundamental principles that underpin surface wetting. Next, we navigate the intricate liquid-surface interactions, unraveling the complex interplay of various fluid dynamics, as well as heat- and mass-transport mechanisms. Finally, we report on the practical realm, where we scrutinize the myriad applications of these principles in everyday processes and real-world scenarios.

Crystallization of Poly(l-lactic acid) on Water Surfaces via Controlled Solvent Evaporation and Langmuir-Blodgett Films

Solvent evaporation is one of the most fundamental processes in soft matter. Structures formed via solvent evaporation are often complex yet tunable via the competition between solute diffusion and solvent evaporation time scales. This work concerns the polymer evaporative crystallization on the water surface (ECWS). The dynamic and two-dimensional (2D) nature of the water surface offers a unique way to control the crystallization pathway of polymeric materials. Using poly(l-lactic acid) (PLLA) as the model polymer, we demonstrate that both one-dimensional (1D) crystalline filaments and two-dimensional (2D) lamellae are formed via ECWS, in stark contrast to the 2D Langmuir-Blodgett monolayer systems as well as polymer solution crystallization. Results show that this filament-lamella biphasic structure is tunable via chemical structures such as molecular weight and processing conditions such as temperature and evaporation rate.

Nonequilibrium configurations of swelling polymer brush layers induced by spreading drops of weakly volatile oil

Polymer brush layers are responsive materials that swell in contact with good solvents and their vapors. We deposit drops of an almost completely wetting volatile oil onto an oleophilic polymer brush layer and follow the response of the system upon simultaneous exposure to both liquid and vapor. Interferometric imaging shows that a halo of partly swollen polymer brush layer forms ahead of the moving contact line. The swelling dynamics of this halo is controlled by a subtle balance of direct imbibition from the drop into the brush layer and vapor phase transport and can lead to very long-lived transient swelling profiles as well as nonequilibrium configurations involving thickness gradients in a stationary state. A gradient dynamics model based on a free energy functional with three coupled fields is developed and numerically solved. It describes experimental observations and reveals how local evaporation and condensation conspire to stabilize the inhomogeneous nonequilibrium stationary swelling profiles. A quantitative comparison of experiments and calculations provides access to the solvent diffusion coefficient within the brush layer. Overall, the results highlight the-presumably generally applicable-crucial role of vapor phase transport in dynamic wetting phenomena involving volatile liquids on swelling functional surfaces.

Evaporation-Driven Liquid-Liquid Crystalline Phase Separation in Droplets of Anisotropic Colloids

Drying a colloidal droplet involves complex physics that is often accompanied by evaporation-induced concentration gradients inside of the droplet, offering a platform for fundamental and technological opportunities, including self-assembly, thin film deposition, microfabrication, and DNA stretching. Here, we investigate the drying, liquid crystalline structures, and deposit patterns of colloidal liquid crystalline droplets undergoing liquid-liquid crystalline phase separation (LLCPS) during evaporation. We show that evaporation-induced progressive up-concentration inside the drying droplets makes it possible to cross, at different speeds, various thermodynamic stability states in solutions of amyloid fibril rigid filamentous colloids, thus allowing access to both metastable states, where phase separation occurs via nucleation and growth, as well as to unstable states, where phase separation occurs via the more elusive spinodal decomposition, leading to the formation of liquid crystalline microdroplets (or tactoids) of different shapes. We present the tactoids "phase diagram" as a function of the position within the droplet and elucidate their hydrodynamics. Furthermore, we demonstrate that the presence of the amyloid fibrils not only does not enhance the pinning behavior during droplet evaporation but also slightly suppresses it, thus minimizing the coffee-ring effect. We observed that microsize domains with cholesteric structure emerge in the drying droplet close to the droplet's initial edge, yet such domains are not connected to form a uniform cholesteric dried film. Finally, we demonstrate that a fully cholesteric dried layer can be generated from the drying droplets by regulating the kinetics of the evaporation process.

Counter-Intuitive Evaporation in Nanofluids Droplets due to Stick-Slip Nature

We experimentally investigate the evaporation characteristics of a sessile ethanol droplet containing Al₂O₃ and Cu nanoparticles of sizes 25 and 75 nm on a heated substrate using shadowgraphy and infrared imaging techniques. Our results demonstrate that the droplet contact line dynamics resulting from the presence of various nanoparticles plays a dominant role in the evaporation process. This is in contrast to the widely held assumption that the enhanced evaporation rate observed in sessile nanofluid droplets is due to the higher thermal conductivity of the added nanoparticles. We observe that even though the thermal conductivity of Al₂O₃ is an order of magnitude lower than that of Cu, droplets containing 25-nm-sized Al₂O₃ exhibit pinned contact line dynamics and evaporate much more rapidly than droplets containing Cu nanoparticles of both sizes and 75 nm Al₂O₃ nanoparticles that exhibit stick-slip behavior. We also found that the droplets with different nanoparticles display distinct thermal patterns due to the difference in contact line behavior, which alters the heat transfer inside the droplets. We establish this counter-intuitive observation by analyzing the temporal variations of the perimeter, free surface area, and deposition patterns on the substrate.

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.

Phase separation in evaporating all-aqueous sessile drops

The phase transition and phase distribution in an all-aqueous sessile drop containing polyethylene glycol (PEG) and dextran is studied. Evaporation of water triggers the formation of dextran-rich droplets close to the contact line of the drop that subsequently migrate towards the drop center. The likely reason for the droplet migration is Marangoni convection due to stresses at the interface between the dextran-rich droplets and the surrounding liquid.

Size-Dependent Dried Colloidal Deposit and Particle Sorting via Saturated Alcohol Vapor-Mediated Sessile Droplet Spreading

We experimentally and theoretically investigate a distinct problem of spreading, evaporation, and the associated dried deposits of a colloidal particle-laden aqueous sessile droplet on a surface in a saturated alcohol vapor environment. In particular, the effect of particle size on monodispersed suspensions and efficient self-sorting of bidispersed particles have been investigated. The alcohol vapor diffuses toward the droplet's curved liquid-vapor interface from the far field. The incoming vapor mass flux profile assumes a nonuniform pattern across the interface. The alcohol vapor molecules are adsorbed at the liquid-vapor interface, which eventually leads to absorption into the droplet's liquid phase due to the miscibility. This phenomenon triggers a liquid-vapor interfacial tension gradient and causes a reduction in the global surface tension of the droplet. This results in a solutal Marangoni flow recirculation and spontaneous droplet spreading. The interplay between these phenomena gives rise to a complex internal fluid flow within the droplet, resulting in a significantly modified and strongly particle-size-dependent dried colloidal deposit. While the smaller particles form a multiple ring pattern, larger particles form a single ring, and additional "patchwise" deposits emerge. High-speed visualization of the internal liquid-flow revealed that initially, a ring forms at the first location of the contact line. Concurrently, the Marangoni flow recirculation drives a collection of particles at the liquid-vapor interface to form clusters. Thereafter, as the droplet spreads, the smaller particles in the cluster exhibit a "jetlike" outward flow, forming multiple ring patterns. In contrast, the larger particles tend to coalesce together in the cluster, forming the "patchwise" deposits. The widely different response of the different-sized particles to the internal fluid flow enables an efficient sorting of the smaller particles at the contact line from bidispersed suspensions. We corroborate the measurements with theoretical and numerical models wherever possible.

Evaporation of Water Nanodroplets on Heated Surfaces: Does Nano Matter?

While experiments and continuum models have provided a relatively good understanding of the evaporation of macroscopic water droplets, elucidating how sessile nanodroplets evaporate is an open question critical for advancing nanotechnological applications where nanodroplets can play an essential role. Here, using molecular dynamics simulations, we find that evaporating nanodroplets, in contrast to their macroscopic counterparts, are not always in thermal equilibrium with the substrate and that the vapor concentration on the nanodroplet surface does not reach a steady state. As a result, the evaporative behavior of nanodroplets is significantly different. Regardless of hydrophobicity, nanodroplets do not follow conventional evaporation modes but instead exhibit dynamic wetting behavior characterized by huge, non-equilibrium, isovolumetric fluctuations in the contact angle and contact radius. For hydrophilic nanodroplets, the evaporation rate, controlled by the vapor concentration, decays exponentially over time. Hydrophobic nanodroplets follow stretched exponential kinetics arising from the slower thermalization with the substrate. The evaporative half-lifetime of the nanodroplets is directly related to the thermalization time scale and therefore increases monotonically with the hydrophobicity of the substrate. Finally, the evaporative flux profile along the nanodroplet surface is highly nonuniform but does not diverge at the contact line as the macroscopic continuum models predict.

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'.

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

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

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.

Applying droplets and films in evaporative lithography

This review covers experimental results of evaporative lithography and analyzes existing mathematical models of this method. Evaporating droplets and films are used in different fields, such as cooling of heated surfaces of electronic devices, diagnostics in health care, creation of transparent conductive coatings on flexible substrates, and surface patterning. A method called evaporative lithography emerged after the connection between the coffee ring effect taking place in drying colloidal droplets and naturally occurring inhomogeneous vapor flux densities from liquid-vapor interfaces was established. Essential control of the colloidal particle deposit patterns is achieved in this method by producing ambient conditions that induce a nonuniform evaporation profile from the colloidal liquid surface. Evaporative lithography is part of a wider field known as "evaporative-induced self-assembly" (EISA). EISA involves methods based on contact line processes, methods employing particle interaction effects, and evaporative lithography. As a rule, evaporative lithography is a flexible and single-stage process with such advantages as simplicity, low price, and the possibility of application to almost any substrate without pretreatment. Since there is no mechanical impact on the template in evaporative lithography, the template integrity is preserved in the process. The method is also useful for creating materials with localized functions, such as slipperiness and self-healing. For these reasons, evaporative lithography attracts increasing attention and has a number of noticeable achievements at present. We also analyze limitations of the approach and ways of its further development.

Drop Drying on the Sensor: One More Way for Comparative Analysis of Liquid Media

It is known that the processes of self-organization of the components of drying a liquid drop on a solid substrate are well reproduced under the same external conditions and are determined only by the composition and dispersion of the liquid. If the drop dries on the surface of the sensor device, these processes can be recorded and used as a passport characteristic of the liquid. The first half of the article is devoted to the description of the principles of the method and the proof of the validity of our assumptions. The second half of the article is devoted to the development of a user-friendly version of the device, where the change in the real and imaginary parts of the electrical impedance of the resonator was used as an informative parameter. The measure of the closeness of the relative positions of the hodographs of the compared samples on the complex plane is used as a criterion for the similarity-/-difference of various liquids. The design of a new sensor device and the results of its tests for distinguishing between different brands of alcoholic beverages and reconstituted milk of different concentrations are presented.

Evaporation of Initially Heated Sessile Droplets and the Resultant Dried Colloidal Deposits on Substrates Held at Ambient Temperature

The present study experimentally and numerically investigates the evaporation and resultant patterns of dried deposits of aqueous colloidal sessile droplets when the droplets are initially elevated to a high temperature before being placed on a substrate held at ambient temperature. The system is then released for natural evaporation without applying any external perturbation. Infrared thermography and optical profilometry are used as essential tools for interfacial temperature measurements and quantification of coffee-ring dimensions, respectively. Initially, a significant temperature gradient exists along the liquid-gas interface as soon as the droplet is deposited on the substrate, which triggers a Marangoni stress-induced recirculation flow directed from the top of the droplet toward the contact line along the liquid-gas interface. Thus, the flow is in the reverse direction to that seen in the conventional substrate heating case. Interestingly, this temperature gradient decays rapidly within the first 10% of the total evaporation time and the droplet-substrate system reaches thermal equilibrium with ambient thereafter. Despite the fast decay of the temperature gradient, the coffee-ring dimensions significantly diminish, leading to an inner deposit. A reduction of 50-70% in the coffee-ring dimensions is recorded by elevating the initial droplet temperature from 25 to 75 °C for suspended particle concentration varying between 0.05 and 1.0% v/v. This suppression of the coffee-ring effect is attributed to the fact that the initial Marangoni stress-induced recirculation flow continues until the last stage of evaporation, even after the interfacial temperature gradient vanishes. This is essentially a consequence of liquid inertia. Finally, a finite-element-based two-dimensional modeling in axisymmetric geometry is found to capture the measurements with reasonable fidelity and the hypothesis considered in the present study corroborates well with a first approximation qualitative scaling analysis. Overall, together with a new experimental condition, the present investigation discloses a distinct nature of Marangoni stress-induced flow in a drying droplet and its role in influencing the associated colloidal deposits, which was not explored previously. The insights gained from this study are useful to advance technical applications such as spray cooling, inkjet printing, bioassays, etc.

MRI and localised NMR spectroscopy of sessile droplets on hydrophilic, hydrophobic and superhydrophobic surfaces - Examination of the chemical composition during evaporation

Evaporation of droplets is a process important in many different areas of science, technology and also everyday life. The understanding of droplet evaporation of homogeneous and heterogeneous substance mixtures is important, for example, to explain the formation of coffee stains or to optimize the results in offset printing. For a detailed understanding of the evaporation of complex mixtures from structured surfaces, such as inks used in offset printing, a time-resolved analysis of the droplet composition is essential. Measurement of (local) concentrations may deepen the understanding of wetting phenomena and their connection with transport phenomena. Therefore, we demonstrate in this paper that magnetic resonance methods can be used to (a) image sessile droplets on structured surfaces and (b) investigate their composition in a time-resolved manner. First it is shown that water droplets on superhydrophobic, hydrophobic and hydrophilic surfaces, despite the large liquid/gas interface, can be imaged well and without interfering artefacts using RARE. Further, the signals are examined in localised PRESS NMR spectra with respect to line shape and quantifiability. Finally, it is demonstrated that non-localised NMR spectra can be used to track the droplet composition during evaporation.

Magnetically-Actuated Mixing and Merging of Acid-Base Micro-Droplets on Open Surfaces: Preliminary Study

We present the mixing and merging of two reactive droplets on top of an open surface. A mobile droplet (1.0 M HCl solution + iron oxide particles) is magnetically-actuated to merge with a sessile droplet (1.0 M NaOH + phenolphthalein). The heat from the exothermic reaction is detected by a thermocouple. We vary the droplet volume (1, 5 and 10 μL), the magnet speed (1.86, 2.79, 3.72 and 4.65 mm/s) and the iron oxide concentration (0.010, 0.020 and 0.040 g/mL) to study their influences on the mixing time, peak temperature and cooling time. The sampled recording of these processes are provided as ^{supplementary files}. We observe the following trends. First, the lower volume of droplet and higher speed of magnet lead to shorter mixing time. Second, the peak temperature increases and cooling time decreases at the increasing speed of magnet. Third, the peak temperature is similar for bigger droplets, and they take longer to cool down. Finally, we also discuss the limitations of this preliminary study and propose improvements. These observations could be used to improve the sensitivity of the open chamber system in measuring the exothermic reaction of biological samples.

Evaporation of liquid droplets of nano- and micro-meter size as a function of molecular mass and intermolecular interactions: experiments and molecular dynamics simulations

Transport of heat to the surface of a liquid is a limiting step in the evaporation of liquids into an inert gas. Molecular dynamics (MD) simulations of a two component Lennard-Jones (LJ) fluid revealed two modes of energy transport from a vapour to an interface of an evaporating droplet of liquid. Heat is transported according to the equation of temperature diffusion, far from the droplet of radius R. The heat flux, in this region, is proportional to temperature gradient and heat conductivity in the vapour. However at some distance from the interface, Aλ, (where λ is the mean free path in the gas), the temperature has a discontinuity and heat is transported ballistically i.e. by direct individual collisions of gas molecules with the interface. This ballistic transport reduces the heat flux (and consequently the mass flux) by the factor R/(R + Aλ) in comparison to the flux obtained from temperature diffusion. Thus it slows down the evaporation of droplets of sizes R ∼ Aλ and smaller (practically for sizes from 10³ nm down to 1 nm). We analyzed parameter A as a function of interactions between molecules and their masses. The rescaled parameter, A(k_BT_b/ε₁₁)^1/2, is a linear function of the ratio of the molecular mass of the liquid molecules to the molecular mass of the gas molecules, m₁/m₂ (for a series of chemically similar compounds). Here ε₁₁ is the interaction parameter between molecules in the liquid (proportional to the enthalpy of evaporation) and T_b is the temperature of the gas in the bulk. We tested the predictions of MD simulations in experiments performed on droplets of ethylene glycol, diethylene glycol, triethylene glycol and tetraethylene glycol. They were suspended in an electrodynamic trap and evaporated into dry nitrogen gas. A changes from ∼1 (for ethylene glycol) to approximately 10 (for tetraethylene glycol) and has the same dependence on molecular parameters as obtained for the LJ fluid in MD simulations. The value of x = A(k_BT_b/ε₁₁)^1/2 is of the order of 1 (for water x = 1.8, glycerol x = 1, ethylene glycol x = 0.4, tetraethylene glycol x = 2.1 evaporating into dry nitrogen at room temperature and for Lennard-Jones fluids x = 2 for m₁/m₂ = 1 and low temperature).

Dynamics of a Water Droplet over a Sessile Oil Droplet: Compound Droplets Satisfying a Neumann Condition

We report the dynamics of compound droplets with a denser liquid (water) droplet over a less dense sessile droplet (mineral oil) that satisfies the Neumann condition. For a fixed size of an oil droplet, depending on the size of the water droplet, either it attains the axisymmetric position or tends to migrate toward the edge of the oil droplet. For a water droplet-to-oil droplet at volume ratio V_w/V_o ≥ 0.05, stable axisymmetric configuration is achieved; for V_w/V_o < 0.05, migration of water droplet is observed. The stability and migration of water droplets of size above and below critical size, respectively, are explained using the force balance at the three-phase contact line and film tension. The larger and smaller droplets that initially attain the axisymmetric position or some radial position, respectively, evaporate continuously and thus migrate toward the edge of the oil droplet. The radial location and migration of the water droplets of different initial sizes with respect to time are studied. Experiments with water droplets on a flat oil-air interface did not show migration, which signified the role of the curved oil-air interface for droplet migration. Finally, coalescence of water droplets of size above the critical size at the axisymmetric position is demonstrated. Our compound droplet studies could be beneficial for applications involving droplet transport where contamination due to direct contact and pinning of droplets on solid surfaces is of concern. Migration and coalescence of water droplets on curved oil-air interfaces could open new frontiers in chemical and biological applications including multiphase processing and biological interaction of cells and atmospheric chemistry.

Pinning-Depinning Mechanism of the Contact Line during Evaporation on Chemically Patterned Surfaces: A Lattice Boltzmann Study

In this paper, the pinning and depinning mechanism of the contact line during droplet evaporation on chemically stripe-patterned surfaces is numerically investigated using a thermal multiphase lattice Boltzmann (LB) model with liquid-vapor phase change. A local force balance in the context of diffuse interfaces is introduced to explain the equilibrium states of droplets on chemically patterned surfaces. It is shown that when the contact line is pinned on a hydrophobic-hydrophilic boundary, different contact angles can be interpreted as the variation of the length of the contact line occupied by each component. The stick-slip-jump behavior of evaporating droplets on chemically patterned surfaces is well captured by the LB simulations. Particularly, a slow movement of the contact line is clearly observed during the stick (pinning) mode, which shows that the pinning of the contact line during droplet evaporation on chemically stripe-patterned surfaces is actually a dynamic pinning process and the dynamic equilibrium is achieved by the self-adjustment of the contact lines occupied by each component. Moreover, it is shown that when the surface tension varies with the temperature, the Marangoni effect has an important influence on the depinning of the contact line, which occurs when the horizontal component (toward the center of the droplet) of the force caused by the Marangoni stress overcomes the unbalanced Young's force toward the outside.

Drying Mechanisms in Plasticized Latex Films: Role of Horizontal Drying Fronts

This article presents studies on the drying kinetics of latexes with particles made progressively softer by adding increasing amounts of a plasticizer, in relation to speeds of horizontal drying fronts and particle deformation mechanisms. Global drying rates were measured by gravimetry, and speeds of the horizontal fronts were recorded using a video camera and image processing. Particle deformation mechanisms were inferred using the deformation map established by Routh and Russel (RR). This required precise measurements of the rheological properties of the polymers using a piezorheometer. The results show that latexes with softer particles dry slowly, but in our systems, this is not due to skin formation. A correlation between global drying rates and speeds of horizontal fronts could be established and interpreted in terms of the evolution of mass transfer coefficients of water in different areas of the drying system. The speeds of the horizontal drying fronts were compared with the RR model. A remarkable qualitative agreement of the curve shapes was observed; however, the fit could not be considered good. These results call for further research efforts in modeling and simulation.

Evaporation of Ethanol-Water Binary Mixture Sessile Liquid Marbles

Liquid marble is a liquid droplet coated with particles. Recently, the evaporation process of a sessile liquid marble using geometric measurements has attracted great attention from the research community. However, the lack of gravimetric measurement limits further insights into the physical changes of a liquid marble during the evaporation process. Moreover, the evaporation process of a marble containing a liquid binary mixture has not been reported before. The present paper investigates the effective density and the effective surface tension of an evaporating liquid marble that contains aqueous ethanol at relatively low concentrations. The effective density of an evaporating liquid marble is determined from the concurrent measurement of instantaneous mass and volume. Density measurements combined with surface profile fitting provide the effective surface tension of the marble. We found that the density and surface tension of an evaporating marble are significantly affected by the particle coating.

Stick-Jump (SJ) Evaporation of Strongly Pinned Nanoliter Volume Sessile Water Droplets on Quick Drying, Micropatterned Surfaces

We present an experimental study of stick-jump (SJ) evaporation of strongly pinned nanoliter volume sessile water droplets drying on micropatterned surfaces. The evaporation is studied on surfaces composed of photolithographically micropatterned negative photoresist (SU-8). The micropatterning of the SU-8 enables circular, smooth, trough-like features to be formed which causes a very strong pinning of the three phase (liquid-vapor-solid) contact line of an evaporating droplet. This is ideal for studying SJ evaporation as it contains sequential constant contact radius (CCR) evaporation phases during droplet evaporation. The evaporation was studied in nonconfined conditions, and forced convection was not used. Micropatterned concentric circles were defined having an initial radius of 1000 μm decreasing by a spacing ranging from 500 to 50 μm. The droplet evaporates, successively pinning and depinning from circle to circle. For each pinning radius, the droplet contact angle and volume are observed to decrease quasi-linearly with time. The experimental average evaporation rates were found to decrease with decreasing pining radii. In contrast, the experimental average evaporation flux is found to increase with decreasing droplet radii. The data also demonstrate the influence of the initial contact angle on evaporation rate and flux. The data indicate that the total evaporation time of a droplet depends on the specific micropattern spacing and that the total evaporation time on micropatterned surfaces is always less than on flat, homogeneous surfaces. Although the surface patterning is observed to have little effect on the average droplet flux-indicating that the underlying evaporation physics is not significantly changed by the patterning-the total evaporation time is considerably modified by patterning, up to a factor or almost 2 compared to evaporation on a flat, homogeneous surface. The closely spaced concentric circle pinning maintains a large droplet radius and small contact angle from jump to jump; the result is a large evaporation rate leading to faster evaporation.

Thermocapillarity in Microfluidics-A Review

This paper reviews the past and recent studies on thermocapillarity in relation to microfluidics. The role of thermocapillarity as the change of surface tension due to temperature gradient in developing Marangoni flow in liquid films and conclusively bubble and drop actuation is discussed. The thermocapillary-driven mass transfer (the so-called Benard-Marangoni effect) can be observed in liquid films, reservoirs, bubbles and droplets that are subject to the temperature gradient. Since the contribution of a surface tension-driven flow becomes more prominent when the scale becomes smaller as compared to a pressure-driven flow, microfluidic applications based on thermocapillary effect are gaining attentions recently. The effect of thermocapillarity on the flow pattern inside liquid films is the initial focus of this review. Analysis of the relation between evaporation and thermocapillary instability approves the effect of Marangoni flow on flow field inside the drop and its evaporation rate. The effect of thermocapillary on producing Marangoni flow inside drops and liquid films, leads to actuation of drops and bubbles due to the drag at the interface, mass conservation, and also gravity and buoyancy in vertical motion. This motion can happen inside microchannels with a closed multiphase medium, on the solid substrate as in solid/liquid interaction, or on top of a carrier liquid film in open microfluidic systems. Various thermocapillary-based microfluidic devices have been proposed and developed for different purposes such as actuation, sensing, trapping, sorting, mixing, chemical reaction, and biological assays throughout the years. A list of the thermocapillary based microfluidic devices along with their characteristics, configurations, limitations, and improvements are presented in this review.

Effect of a triple contact line on the thermokinetics of dropwise condensation on an immiscible liquid surface

An extended thermokinetic model is developed for liquid-substrate-induced condensation by considering the collective influence of the line tension and the two mechanisms of molecular transport.

Simulation of Latex Film Formation Using a Cell Model in Real Space: Vertical Drying

This paper presents a simulation tool applied to latex film formation by drying, a hybrid between a classical numerical resolution method using finite differences and cellular automata, and making use of object-oriented programming. It consists of dividing real space into cells and applying local physical laws to simulate the exchange of matter between neighboring cells. In a first step, the simulation was applied to the simple case of vertical drying of a latex containing only one population of monodisperse particles and water. Our results show how the distribution of latex particles evolves through the different drying stages due to a combination of diffusion, convection, and particle deformation. While repulsive interactions between the particles tend to favor homogeneous distributions in the first drying stage, concentration gradients that develop in opposite ways can be observed depending on the drying regime. The distributions, calculated in various cases, reproduce and extend several theoretical results and are in qualitative agreement with some experimental findings.

Combined effects of underlying substrate and evaporative cooling on the evaporation of sessile liquid droplets

The evaporation of pinned, sessile droplets resting on finite thickness substrates was investigated numerically by extending the combined field approach to include the thermal properties of the substrate. By this approach, the combined effects of the underlying substrate and the evaporative cooling were characterized. The results show that the influence of the substrate on the droplet evaporation depends largely on the strength of the evaporative cooling. When the evaporative cooling is weak, the influence of substrate is also weak. As the strength of evaporative cooling increases, the influence of the substrate becomes more and more pronounced. Further analyses indicated that it is the cooling at the droplet surface and the temperature dependence of the saturation vapor concentration that relate the droplet evaporation to the underlying substrate. This indicates that the evaporative cooling number, Ec, can be used to identify the influence of the substrate on the droplet evaporation. The theoretical predictions by the present model are compared and found to be in good agreement with the experimental measurements. The present work may contribute to the body of knowledge concerning droplet evaporation and may have applications in a wide range of industrial and scientific processes.

Analysis of the effects of evaporative cooling on the evaporation of liquid droplets using a combined field approach

During liquid evaporation, the equations for the vapor concentration in the atmosphere and for the temperature in the liquid are coupled and must be solved in an iterative manner. In the present paper, a combined field approach which unifies the coupled fields into one single hybrid field and thus makes the iteration unnecessary is proposed. By using this approach, the influences of the evaporative cooling on the evaporation of pinned sessile droplets are investigated, and its predictions are found in good agreement with the previous theoretical and experimental results. A dimensionless number Ec which can evaluate the strength of the evaporative cooling is then introduced, and the results show that both the evaporation flux along the droplet surface and the total evaporation rate of the droplet decrease as the evaporative cooling number Ec increases. For drying droplets, there exists a critical value Ec_Crit below which the evaporative cooling effect can be neglected and above which the significance of the effect increases dramatically. The present work may also have more general applications to coupled field problems in which all the fields have the same governing equation.