Assessment of water droplet evaporation mechanisms on hydrophobic and superhydrophobic substrates

Unraveling the role of vaporization momentum in self-jumping dynamics of freezing supercooled droplets at reduced pressures

Supercooling of water complicates phase change dynamics, the understanding of which remains limited yet vital to energy-related and aerospace processes. Here, we investigate the freezing and jumping dynamics of supercooled water droplets on superhydrophobic surfaces, induced by a remarkable vaporization momentum, in a low-pressure environment. The vaporization momentum arises from the vaporization at droplet's free surface, progressed and intensified by recalescence, subsequently inducing droplet compression and finally self-jumping. By incorporating liquid-gas-solid phase changes involving vaporization, freezing recalescence, and liquid-solid interactions, we resolve the vaporization momentum and droplet dynamics, revealing a size-scaled jumping velocity and a nucleation-governed jumping direction. A droplet-size-defined regime map is established, distinguishing the vaporization-momentum-dominated self-jumping from evaporative drying and overpressure-initiated levitation, all induced by depressurization and vaporization. Our findings illuminate the role of supercooling and low-pressure mediated phase change in shaping fluid transport dynamics, with implications for passive anti-icing, advanced cooling, and climate physics.

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.

Structure Formation in Supraparticles Composed of Spherical and Elongated Particles

We studied the evaporation-induced formation of supraparticles from dispersions of elongated colloidal particles using experiments and computer simulations. Aqueous droplets containing a dispersion of ellipsoidal and spherical polystyrene particles were dried on superamphiphobic surfaces at different humidity values that led to varying evaporation rates. Supraparticles made from only ellipsoidal particles showed short-range lateral ordering at the supraparticle surface and random orientations in the interior regardless of the evaporation rate. Particle-based simulations corroborated the experimental observations in the evaporation-limited regime and showed an increase in the local nematic ordering as the diffusion-limited regime was reached. A thin shell of ellipsoids was observed at the surface when supraparticles were made from binary mixtures of ellipsoids and spheres. Image analysis revealed that the supraparticle porosity increased with an increasing aspect ratio of the ellipsoids.

Analysis of Evaporation of Droplet Pairs by a Quasi-Steady-State Diffusion Model Coupled with the Evaporative Cooling Effect

Multidroplet evaporation is a common phase-change phenomenon not only in nature but also in many industrial applications, including inkjet printing and spray cooling. The evaporation behavior of these droplets is strongly affected by the distance between neighboring droplets, and in particular, evaporation suppression occurs as the distance decreases. However, further quantitative information, such as the temperature and local evaporation flux, is limited because the analytical models of multidroplet evaporation only treat vapor diffusion, and the effect of the latent heat transfer through the liquid-vapor phase change is ignored. Here, we perform a numerical analysis of evaporating droplet pairs that linked vapor diffusion from the droplet surface and evaporative cooling. Heat transfer through the liquid and gas phases is also considered because the saturation pressure depends on the temperature. The results show an increase in the vapor concentration in the region between the two droplets. Consequently, the local evaporation flux in the proximate region significantly decreases with decreasing separation distance. This means that the latent heat transfer through the phase change is diminished, and an asymmetrical temperature distribution occurs in the liquid and gas phases. These numerical results provide quantitative information about the temperature and local evaporation flux of evaporating droplet pairs, and they will guide further investigation of multiple droplet evaporation.

Melting Process of Frozen Sessile Droplets on Superhydrophobic Surfaces

Superhydrophobic surfaces can exhibit icephobicity in many ways due to their large contact angles and small rolling angles. The melting process of frozen droplets on superhydrophobic surfaces is still unclear, hindering the understanding of surface icephobicity. In this experimental study of the melting process of frozen sessile droplets on superhydrophobic surfaces, we find two types of melting morphologies with opposite vortex directions on a single-scale nanostructured (SN) superhydrophobic substrate and a hierarchical-scale micronanostructured (HMN) superhydrophobic substrate. Melting pattern visualizations and flow field measurements showed Marangoni convection and natural convection occurring in the melting sessile droplets. For the HMN superhydrophobic substrate, the internal flow was found to be dominated by Marangoni convection due to the temperature gradient along the surface of the droplet. For the SN superhydrophobic substrate, Marangoni convection was inhibited by the superhydrophobic particles at the surface of the droplet, which were shed from the fragile superhydrophobic substrate during the freezing-melting process, as confirmed by surface characterizations of the substrate and flow measurements of a water pool. These results will help researchers better understand the melting process of frozen droplets and in designing novel icephobic surfaces for numerous applications.

Hydrophilic and Hydrophobic Surfaces: Features of Interaction with Liquid Drops

The processes of interaction of liquid droplets with solid surfaces have become of interest to many researchers. The achievements of world science should be used for the development of technologies for spray cooling, metal hardening, inkjet printing, anti-icing surfaces, fire extinguishing, fuel spraying, etc. Collisions of drops with surfaces significantly affect the conditions and characteristics of heat transfer. One of the main areas of research into the interaction of drops with solid surfaces is the modification of the latter. Changes in the hydrophilic and hydrophobic properties of surfaces give the materials various functional properties-increased heat transfer, resistance to corrosion and biofouling, anti-icing, etc. This review paper describes methods for obtaining hydrophilic and hydrophobic surfaces. The features of the interaction of liquid droplets with such surfaces are considered. The existing and possible applications of modified surfaces are discussed, as well as topical areas of research.

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.

Advances in Microscale Droplet Generation and Manipulation

Microscale droplet generation and manipulation have widespread applications in numerous fields, from biochemical assays to printing and additive manufacturing. There are several techniques for droplet handling. Most techniques, however, can generate and work with only a limited range of droplet sizes. Furthermore, there are constraints regarding the workable variety of fluid properties (e.g., viscosity, surface tension, mass loading, etc.). Recent works have focused on developing techniques to overcome these limitations. This feature article discusses advances in this area that cover a wide range of droplet sizes from subpicoliter to microliter.

A supraparticle-based biomimetic cascade catalyst for continuous flow reaction

Robust millimeter-sized spherical particles with controlled compositions and microstructures hold promises of important practical applications especially in relation to continuous flow cascade catalysis. However, the efficient fabrication methods for producing such particles remain scare. Here, we demonstrate a liquid marble approach to fabricate robust mm-sized porous supraparticles (SPs) through the bottom-up assembly of silica nanoparticles in the presence of strength additive or surface interactions, without the need for the specific liquid-repellent surfaces used by the existing methods. As the proof of the concept, our method was exemplified by fabricating biomimetic cascade catalysts through assembly of two types of well-defined catalytically active nanoparticles. The obtained SP-based cascade catalysts work well in industrially preferred fixed-bed reactors, exhibiting excellent catalysis efficiency, controlled reaction kinetics, high enantioselectivity (99% ee) and outstanding stability (200~500 h) in the cascades of ketone hydrogenation-kinetic resolution and amine racemization-kinetic resolution. The excellent catalytic performances are attributed to the structural features, reconciling close proximity of different catalytic sites and their sufficient spatial isolation.

Robust millimeter-sized spherical particles with controlled compositions and microstructures hold promises of important practical applications. Here the authors develop a liquid marble method to facilely fabricate robust millimeter-sized supraparticles with controlled microstructures through the bottom-up assembly of silica nanoparticles.

Polyvinyl alcohol microlens array obtained by solvent evaporation from a confined droplet array

In this study, polyvinyl alcohol (PVA) microlens arrays (MLAs) were prepared, and the dynamics of contact lines and contact angles during confined PVA solution droplet evaporation were investigated by in situ optical microscopy. First, hydrophobic layers patterned with hydrophilic microholes array modified substrates were prepared by photolithography and coating methods. The flowing of PVA solution on the substrates formed droplets in each microhole self-assembly. The substrate was then heated to allow evaporation of the solvent. The results showed the contact line of confined droplets pinned at the junction between the hydrophilic and hydrophobic areas during the whole evaporation process. The apparent contact angle decreased nonlinearly during evaporation. The evaporation of PVA solution droplet in each microhole followed a constant contact radius mode, meaning constant contact area and declined contact angle during evaporation. After complete solvent evaporation, PVA formed a convex shape with convergent lens character in each microhole. In sum, the obtained PVA convex arrays with uniform sizes and good focusing properties would have potential applications in wavefront sensing, infrared focal plane detection or CCD array light accumulation, laser array scanning, laser display, optical fiber coupling, and many other optical systems.

Micro/Nanopatterned Superhydrophobic Surfaces Fabrication for Biomolecules and Biomaterials Manipulation and Analysis

Superhydrophobic surfaces display an extraordinary repulsion to water and water-based solutions. This effect emerges from the interplay of intrinsic hydrophobicity of the surface and its morphology. These surfaces have been established for a long time and have been studied for decades. The increasing interest in recent years has been focused towards applications in many different fields and, in particular, biomedical applications. In this paper, we review the progress achieved in the last years in the fabrication of regularly patterned superhydrophobic surfaces in many different materials and their exploitation for the manipulation and characterization of biomaterial, with particular emphasis on the issues affecting the yields of the fabrication processes and the quality of the manufactured devices.

Controlling supraparticle shape and structure by tuning colloidal interactions

HYPOTHESIS

Assembly of colloids in drying colloidal suspensions on superhydrophobic surface is influenced by the colloidal interactions, which determine the shape and interior structure of the assembled supraparticle. The introduction of salt (electrolyte) into the assembly system is expected to influence the colloid interactions and packing during the evaporation process. Hence, both the outer shape and internal structure of supraparticles should be controlled by varying salt concentrations.

EXPERIMENTS

Suspensions of electrostatically stabilized polystyrene particles with specified salt concentrations were chosen as model systems to conduct the evaporation on a superhydrophobic surface. A systematic study was performed by regulating the concentration and valency of salt. The morphology and interior of supraparticles were carefully characterized with electron scanning microscopy, while the colloidal interaction was established using colloidal probe atomic force microscopy.

FINDINGS

Supraparticles displayed a spherical-to-nonspherical shape change due to the addition of salts. The extent of crystallization depended on salt concentration. These changes in shape and structure were correlated with salt-dependent single colloid interaction forces, which were not previously investigated in detail in radially symmetric evaporation geometry. Our findings are crucial for understanding assembly behavior during the drying process and offer guidance for preparing complex supraparticles to meet specific applications requirement.

Buoyancy-driven convection of droplets on hot nonwetting surfaces

The global linear stability of a water drop on hot nonwetting surfaces is studied. The droplet is assumed to have a static shape and the surface tension gradient is neglected. First, the nonlinear steady Boussinesq equation is solved to obtain the axisymmetric toroidal base flow. Then, the linear stability analysis is conducted for different contact angles β=110^{∘} (hydrophobic) and β=160^{∘} (superhydrophobic) which correspond to the experimental study of Dash et al. [Phys. Rev. E 90, 062407 (2014)PLEEE81539-375510.1103/PhysRevE.90.062407]. The droplet with β=110^{∘} is stable while the one with β=160^{∘} is unstable to the azimuthal wave number m=1 mode. This suggests that the experimental observation for a droplet with β=110^{∘} corresponds to the steady toroidal base flow, while for β=160^{∘}, the m=1 instability promotes the rigid body rotation motion. A marginal stability analysis for different β shows that a 3-μL water droplet is unstable to the m=1 mode when the contact angle β is larger than 130^{∘}. A marginal stability analysis for different volumes is also conducted for the two contact angles β=110^{∘} and 160^{∘}. The droplet with β=110^{∘} becomes unstable when the volume is larger than 3.5μL while the one with β=160^{∘} is always unstable to m=1 mode for the considered volume range (2-5μL). In contrast to classical buoyancy driven (Rayleigh-Bénard) problems whose instability is controlled independently by the geometrical aspect ratio and the Rayleigh number, in this problem, these parameters are all linked together with the volume and contact angles.

Gas-Phase Temperature Mapping of Evaporating Microdroplets

Evaporation is a ubiquitous and complex phenomenon of importance to many natural and industrial systems. Evaporation occurs when molecules near the free interface overcome intermolecular attractions with the bulk liquid. As molecules escape the liquid phase, heat is removed, causing evaporative cooling. The influence of evaporative cooling on inducing a temperature difference with the surrounding atmosphere as well as within the liquid is poorly understood. Here, we develop a technique to overcome past difficulties encountered during the study of heterogeneous droplet evaporation by coupling a piezo-driven droplet generation mechanism to a controlled micro-thermocouple to probe microdroplet evaporation. The technique allowed us to probe the gas-phase temperature distribution using a micro-thermocouple (50 μm) in the vicinity of the liquid-vapor interface with high spatial (±10 μm) and temporal (±100 ms) resolution. We experimentally map the temperature gradient formed surrounding sessile water droplets having varying curvature dictated by the apparent advancing contact angle (100° ≲ θ ≲ 165°). The experiments were carried out at temperatures below and above ambient for a range of fixed droplet radii (130 μm ≲ R ≲ 330 μm). Our results provide a primary validation of the centuries-old theoretical framework underpinning heterogeneous droplet evaporation mediated by the working fluid, substrate, and gas thermophysical properties, droplet apparent contact angle, and droplet size. We show that microscale droplets residing on low-thermal-conductivity substrates such as glass absorb up to 8× more heat from the surrounding gas compared to droplets residing on high-thermal-conductivity substrates such as copper. Our work not only develops an experimental understanding of the heat transfer mechanisms governing droplet evaporation but also presents a powerful platform for the study and characterization of liquid-vapor transport at curved interfaces wetting and nonwetting advanced functional surfaces.

Wide Input Dynamic Range Fully Integrated Capacitive Sensor for Life Science Applications

This paper presents a new fully integrated CMOS capacitance sensor chip with a wider input dynamic range (IDR) compared to the state-of-the-art, suitable for a variety of life science applications. With the novel differential capacitance to current conversion topology, it achieves an IDR of about seven times higher compared to the previous charge based capacitive measurement (CBCM) circuits and about three times higher compared to the CBCM with cascode current mirrors. It also features a calibration circuitry consisting of an array of switched capacitors, interdigitated electrodes (IDEs) realized on the topmost metal layer, a current-controlled 300 MHz oscillator, and a counter-serializer to create digital output. The proposed sensor, fabricated in AMS 0.35 μm CMOS technology, enables a high-resolution measurement, equal to 416 aF, of physiochemical changes in the IDE with up to 1.27 pF input offset adjustment range (IOAR). With a measurement speed of 15 μs, this sensor is among the fast CMOS capacitive sensors in the literature. In this paper, we demonstrate its functionality and applicability and present the experimental results for monitoring 2 μL evaporating droplets of chemical solvents. By using samples of solvents with different conductivity and relative permittivity, a wide range of capacitance and resistance variations in the sample-IDE interface electric equivalent model can be created. In addition, the evaporating droplet test has inherently fast dynamic changes. Based on the results, our proposed device addresses the challenge of detecting small capacitance changes despite large parasitic elements caused by the ions in the solution or by remnants deposited on the electrode.

Size-Exclusion Particle Separation Driven by Micro-Flows in a Quasi-Spherical Droplet: Modelling and Experimental Results

Aqueous solution droplets are supported quasi contact-free by superhydrophobic surfaces. The convective flow in evaporating droplets allows the manipulation and control of biological molecules in solution. In previous works, super-hydrophobic drops on nano-patterned substrates have been used to analyze otherwise undetectable species in extremely low concentration ranges. Here, we used particle image velocimetry (PIV) for studying the flow field in water droplets containing polystyrene particles on a pillared silicon super-hydrophobic chip. The particles describe vortex-like motions around the droplet center as long as the evaporating droplet maintains a spherical shape. Simulations by a Finite Element Method (FEM) suggest that the recirculating flow is due to the temperature gradient along the droplet rim, generating a shear stress. Notably, the characteristics of the internal flow can be modulated by varying the intensity of the temperature gradient along the drop. We then used the flow-field determined by experiments and an approximate form of the Langevin equation to examine how particles are transported in the drop as a function of particle size. We found that larger particles with an average size of 36 μm are preferentially transported toward the center of the substrate, differently from smaller particles with a 10-fold lower size that are distributed more uniformly in the drop. Results suggest that solutions of spherical particles on a super-hydrophobic chip can be used to separate soft matter and biological molecules based on their size, similarly to the working principle of a time-of-flight (ToF) mass analyzer, except that the separation takes place in a micro-sphere, with less space, less time, and less solution required for the separation compared to conventional ToF systems.

Droplet Evaporation Dynamics of Low Surface Tension Fluids Using the Steady Method

Droplet evaporation governs many heat- and mass-transfer processes germane in nature and industry. In the past 3 centuries, transient techniques have been developed to characterize the evaporation of sessile droplets. These methods have difficulty in reconciling transient effects induced by the droplet shape and size changes during evaporation. Furthermore, investigation of evaporation of microdroplets residing on wetting substrates, or fluids having low surface tensions (<30 mN/m), is difficult to perform using established approaches. Here, we use the steady method to study the microdroplet evaporation dynamics of low surface tension liquids. We start by employing the steady method to benchmark with water droplets having base radii (20 ≤ R_b ≤ 260 μm), apparent advancing contact angle (45° ≤ θ_a,app ≤ 162°), surface temperature (30 < T_s < 60 °C), and relative humidity (40% < ϕ < 60%). Following validation, evaporation of ethanol (≈22 mN/m), hexane (≈18 mN/m), and dodecane (≈25 mN/m) were studied for 90 ≤ R_b ≤ 400 μm and 10 < T_s < 25 °C. We elucidate the mechanisms governing the observed behavior using heat and mass transport scaling analysis during evaporation, demonstrating our steady technique to be particularly advantageous for microdroplets, where Marangoni and buoyant forces are negligible. Our work not only elucidates the droplet evaporation mechanisms of low surface tension liquids but also demonstrates the steady method as a means to study phase change processes.

Surface temperature transition of a controllable evaporating droplet

Surface temperature is a critical factor affecting the droplet evaporation; however, it is a continuous matter under discussion. We design controllable experiments for sessile ethanol droplet evaporation to investigate the surface temperature distribution evolution. It is found that the evaporation process of a droplet with a constant contact radius can involve five phases: non-wave phase, onset of thermal waves, decrease of thermal waves, transition phase, and final non-wave phase. Under fixed evaporation conditions and a fixed substrate temperature, the phase sequence is solely dependent on the instantaneous contact angle, but independent of the droplet initial volume. Three typical radial temperature distributions are observed at the evaporating droplet surface: a monotonic decrease from the edge to the apex; a nonmonotonic distribution with the highest temperature observed between the edge and the apex; or a monotonic increase from the edge to the apex. The three temperature distributions and the two transitions between them are responsible for the five phases in the evaporation process. However, the early phases may not exist in the sessile droplet with a relatively small initial contact angle. Both the evaporation pressure and the substrate temperature can affect the occurrence of the five phases in the evaporation process. It is noteworthy that the splitting and merging of thermal waves occur simultaneously during evaporation. During the decrease of the thermal waves phase, the number of waves decreases linearly with the contact angle tangent. The decreasing slope is influenced by the evaporation pressure and the substrate temperature.

A droplet reactor on a super-hydrophobic surface allows control and characterization of amyloid fibril growth

Methods to produce protein amyloid fibrils, in vitro, and in situ structure characterization, are of primary importance in biology, medicine, and pharmacology. We first demonstrated the droplet on a super-hydrophobic substrate as the reactor to produce protein amyloid fibrils with real-time monitoring of the growth process by using combined light-sheet microscopy and thermal imaging. The molecular structures were characterized by Raman spectroscopy, X-ray diffraction and X-ray scattering. We demonstrated that the convective flow induced by the temperature gradient of the sample is the main driving force in the growth of well-ordered protein fibrils. Particular attention was devoted to PHF6 peptide and full-length Tau441 protein to form amyloid fibrils. By a combined experimental with the molecular dynamics simulations, the conformational polymorphism of these amyloid fibrils were characterized. The study provided a feasible procedure to optimize the amyloid fibrils formation and characterizations of other types of proteins in future studies.

Zhang et al present an integrated real-time imaging and flow field control platform based on water droplet evaporation on super-hydrophobic substrate (SHS) to enable amyloid fibril aggregation. They apply this methodology to observe structural polymorphism in PHF6 peptide and full length Tau441.

Evaporation of Sessile Water Droplets on Horizontal and Vertical Biphobic Patterned Surfaces

This paper presents an experimental study on thermal transport to single water droplets evaporating on heated biphobic surfaces consisting of a superhydrophobic matrix with a circular hydrophobic pattern with strong contact line pinning. A single water droplet of 8 μL volume is placed on a preheated surface and allowed to evaporate in an open laboratory environment. We investigate the influence of substrate orientation (horizontal and vertical) on evaporation dynamics. Using optical and infrared imaging, we report droplet fluid dynamics and heat transfer characteristics of the evaporating droplet. Overall, evaporation is more efficient on the vertical surface, exhibiting higher total heat transfer rates and up to 10% shorter evaporation times. Counterintuitively, on the vertical surface, the substrate-droplet interfacial heat flux was higher near the lower contact line than in the upper region, despite a high contact angle and an expected wedge effect at the bottom. At the same time, the temperature is colder in the lower part of the droplet. We attribute this apparent anomaly to the competition between sensible heating and evaporation, and a modified convective flow signature (both within the droplet and the gas phase) compared to a horizontal surface. We also show that the thermal signature becomes uniform once the contact angles at the upper and lower contact lines become equal toward the end of the evaporation process. Insights from this work can guide the design of spray cooling devices or be used to alter particle deposition patterns during evaporation-based fabrication techniques and ink-jet printing.

Evaporation-Driven Micromixing in Sessile Droplets for Miniaturized Absorbance-Based Colorimetry

We demonstrate the use of an evaporating, sessile droplet on a nonwetting substrate as a miniature micromixing device to conduct sample-dye reactions for absorbance-based colorimetry. The nonwetting substrate supports buoyancy-induced mixing inside the droplet for rapid completion of the measurement. The Bradford assay is used as a proof of concept, where a protein-containing sample is reacted with a reagent dye to measure the protein concentration. Viability of absorbance measurement through the droplet is first established using droplets in which the reactants are mixed prior to their deposition onto the substrate. In a second set of experiments involving in situ mixing, the reagent is directly added to a sessile droplet of the protein-containing sample, allowing the reactants to mix while the absorbance is being measured. Interplay between buoyancy-induced mixing, protein-reagent reaction, and protein adsorption onto the substrate leads to a complex temporal absorbance measurement signal. Videos corresponding to the signal data show that each of these mechanisms dominates during different phases of droplet evolution, causing a signal pattern containing peaks and valleys having a strong monotonic trend with the protein concentration. Overall, the second absorbance peak at which the reaction nears completion is the most sensitive to sample concentration. Heating of the substrate is demonstrated to dramatically speed up the mixing process. These protein concentration measurements, obtained with a simpler system and low reactant volumes, demonstrate that this droplet micromixing concept is a viable alternative to microtiter plates for colorimetric applications.

Experimental and Theoretical Investigation of Droplet Evaporation on Heated Hydrophilic and Hydrophobic Surfaces

The evaporation characteristics of sessile droplets on heated hydrophobic and hydrophilic surfaces are investigated. Results are reported for the evaporation of water droplet volumes covering a range of shapes dominated by surface tension or gravity and over a range of temperatures between 40 and 60 °C. The weight evolution and total time of evaporation is measured using a novel self-contained heating stage on a high resolution analytical balance, which has advantages over visualization measurement techniques as it allows free choice of the initial droplet size and surface and the ability to record the droplet evaporation right through to the final stages of droplet life. Evaporation is modeled through a combination of a constant contact area and a constant contact angle model with the switch from the former to the latter occurring when the contact angle falls below its predetermined receding value. Theoretical results compare well with the experimental results for the hydrophobic substrate. However, a significant deviation is observed for the hydrophilic substrate due to the combined effects of the droplet surface cooling due to evaporation and buoyancy effects that are not included in the model. The proposed method of using the stick-slip model offers a convenient means of modeling droplet evaporation by mimicking the drying modes based on initial measurements of the static and receding contact angles.

Superhydrophobic Surface Curvature Dependence of Internal Advection Dynamics within Sessile Droplets

Sessile droplets seated on superhydrophobic surfaces are known to exhibit internal circulation patterns. The present article experimentally demonstrates and theoretically confirms, for the very first time, that the nature and velocity of the internal circulation in sessile droplets seated on superhydrophobic surfaces are strongly governed by the curvature of the surface and its directionality. Sessile droplets were rested on concave and convex superhydrophobic surfaces, and both with one curvature (cylindrical) and two curvatures (spherical) and varying droplet diameter to curve diameters were studied. Particle image velocimetry (PIV) was employed for flow visualization and quantification. It was observed that increasing convexity of the surface leads to deterioration in the velocity of advection within the droplet, whereas increasing concavity of the surface augments the velocity of circulation. A scaling model based on the effective curvature-modulated change in wettability has been put forward to predict the phenomenon, but it was found to be weak in deducing the circulation velocities. Consequently, potential flow theory is employed and the curvatures are approximated as equivalent wedges, with the rested droplet engulfing the wedge partly. Based on the curvature of the surface, the equivalent included wedge angle is deduced. Flow theory over wedged structures is employed to deduce the changes in the internal velocity in the presence of curved surfaces. The spatiotemporally averaged experimental velocities are found to conform to predictions from the proposed model, and good agreement between the theoretical predictions and experimental observations is achieved. The present findings may have strong implications in thermofluidic transport phenomena or multiphase transport processes at the interfacial and/or microscale.

Density-Driven Flows in Evaporating Binary Liquid Droplets

In the evaporation of microlitre liquid droplets, the accepted view is that surface tension dominates and the effect of gravity is negligible. We report, through the first use of rotating optical coherence tomography, that a change in the flow pattern and speed occurs when evaporating binary liquid droplets are tilted, conclusively showing that gravitational effects dominate the flow. We use gas chromatography to show that these flows are solutal in nature, and we establish a flow phase diagram demonstrating the conditions under which different flow mechanisms occur.

Effect of Structure Hierarchy for Superhydrophobic Polymer Surfaces Studied by Droplet Evaporation

Super-hydrophobic natural surfaces usually have multiple levels of structure hierarchy. Here, we report on the effect of surface structure hierarchy for droplet evaporation. The two-level hierarchical structures studied comprise micro-pillars superimposed with nanograss. The surface design is fully scalable as structures used in this study are replicated in polypropylene by a fast roll-to-roll extrusion coating method, which allows effective thermoforming of the surface structures on flexible substrates. As one of the main results, we show that the hierarchical structures can withstand pinning of sessile droplets and remain super-hydrophobic for a longer time than their non-hierarchical counterparts. The effect is documented by recording the water contact angles of sessile droplets during their evaporation from the surfaces. The surface morphology is mapped by atomic force microscopy (AFM) and used together with the theory of Miwa et al. to estimate the degree of water impregnation into the surface structures. Finally, the different behavior during the droplet evaporation is discussed in the light of the obtained water impregnation levels.

Liquid Leaks: Dripping Versus Evaporation

Liquid leaks often reveal themselves as pendant drops or drips emanating from a low point on a fluid handling component. For volatile liquids, understanding the contributions of interfacial properties, such as diffusivity of the liquid and wettability of the solid, is crucial to determining leak rates. To estimate the resolution of hydrostatic leak testing, the competing factors of leak and evaporation rates were analyzed. We used drop volumes and contact angles along with intrinsic fluid properties to calculate the detection limit of hydrostatic leak tests. For water and ethanol, we reckon that it is approximately 10^-4 to 10^-5 cm³/s in dry air.

Analytical Model for Diffusive Evaporation of Sessile Droplets Coupled with Interfacial Cooling Effect

Current analytical models for sessile droplet evaporation do not consider the nonuniform temperature field within the droplet and can overpredict the evaporation by 20%. This deviation can be attributed to a significant temperature drop due to the release of the latent heat of evaporation along the air-liquid interface. We report, for the first time, an analytical solution of the sessile droplet evaporation coupled with this interfacial cooling effect. The two-way coupling model of the quasi-steady thermal diffusion within the droplet and the quasi-steady diffusion-controlled droplet evaporation is conveniently solved in the toroidal coordinate system by applying the method of separation of variables. Our new analytical model for the coupled vapor concentration and temperature fields is in the closed form and is applicable for a full range of spherical-cap shape droplets of different contact angles and types of fluids. Our analytical results are uniquely quantified by a dimensionless evaporative cooling number E_o whose magnitude is determined only by the thermophysical properties of the liquid and the atmosphere. Accordingly, the larger the magnitude of E_o, the more significant the effect of the evaporative cooling, which results in stronger suppression on the evaporation rate. The classical isothermal model is recovered if the temperature gradient along the air-liquid interface is negligible ( E_o = 0). For substrates with very high thermal conductivities (isothermal substrates), our analytical model predicts a reversal of temperature gradient along the droplet-free surface at a contact angle of 119°. Our findings pose interesting challenges but also guidance for experimental investigations.

Recent advances in droplet wetting and evaporation

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

Facile Fabrication and Characterization of a PDMS-Derived Candle Soot Coated Stable Biocompatible Superhydrophobic and Superhemophobic Surface

We report a simple, inexpensive, rapid, and one-step method for the fabrication of a stable and biocompatible superhydrophobic and superhemophobic surface. The proposed surface comprises candle soot particles embedded in a mixture of PDMS+n-hexane serving as the base material. The mechanism responsible for the superhydrophobic behavior of the surface is explained, and the surface is characterized based on its morphology and elemental composition, wetting properties, mechanical and chemical stability, and biocompatibility. The effect of %n-hexane in PDMS, the thickness of the PDMS+n-hexane layer (in terms of spin coating speed) and sooting time on the wetting property of the surface is studied. The proposed surface exhibits nanoscale surface asperities (average roughness of 187 nm), chemical compositions of soot particles, very high water and blood repellency along with excellent mechanical and chemical stability and excellent biocompatibility against blood sample and biological cells. The water contact angle and roll-off angle is measured as 160° ± 1° and 2°, respectively, and the blood contact angle is found to be 154° ± 1°, which indicates that the surface is superhydrophobic and superhemophobic. The proposed superhydrophobic and superhemophobic surface offers significantly improved (>40%) cell viability as compared to glass and PDMS surfaces.

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

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

Ultra Water Repellent Polypropylene Surfaces with Tunable Water Adhesion

Polypropylene (PP), including isotactic PP (i-PP) and atactic PP (a-PP) with distinct tacticity, is one of the most widely used general plastics. Herein, ultra water repellent PP coatings with tunable adhesion to water were prepared via a simple casting method. The pure i-PP coating shows a hierarchical morphology with micro/nanobinary structures, exhibiting a water contact angle (CA) larger than 150° and a sliding angle less than 5° (for 5 μL water droplet). In contrast, the pure a-PP coating has a less rough morphology with a water contact angle of about 130°, and the water droplets stick on the coating at any tilted angles. For the composite i-PP/a-PP coatings, however, ultra water repellency with CA > 150° but water adhesion tailorable from slippery to sticky can be realized, depending on the contents of a-PP and i-PP. The different wetting behaviors are due to the various microstructures of the composite coatings resulting from the distinct crystallization ability of a-PP and i-PP. Furthermore, the existence of a-PP in the composite coatings enhances the mechanical properties compared to the i-PP coating. The proposed method is feasible to modify various substrates and potential applications in no-loss liquid transportation, slippery surfaces, and patterned superhydrophobic surfaces are demonstrated.

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.

Marangoni Convection in Evaporating Organic Liquid Droplets on a Nonwetting Substrate

We quantitatively characterize the flow field inside organic liquid droplets evaporating on a nonwetting substrate. A mushroom-structured surface yields the desired nonwetting behavior with methanol droplets, while use of a cooled substrate (5-15 °C) slows the rate of evaporation to allow quasi-static particle image velocimetry. Visualization reveals a toroidal vortex within the droplet that is characteristic of surface tension-driven flow; we demonstrate by means of a scaling analysis that this recirculating flow is Marangoni convection. The velocities in the droplet are on the order of 10-45 mm/s. Thus, unlike in the case of evaporation on wetting substrates where Marangoni convection can be ignored for the purpose of estimating the evaporation rate, advection due to the surface tension-driven flow plays a dominant role in the heat transfer within an evaporating droplet on a nonwetting substrate because of the large height-to-radius aspect ratio of the droplet. We formulate a reduced-order model that includes advective transport within the droplet for prediction of organic liquid droplet evaporation on a nonwetting substrate and confirm that the predicted temperature differential across the height of the droplet matches experiments.

Direct observation of nanoparticle multiple-ring pattern formation during droplet evaporation with dark-field microscopy

Controllable protocols towards nanoparticle self-assembly are important for applications of functional nanomaterials. Evaporation is a simple yet effective method to realize a gold nanoparticle ordered self-assembly, but until now, little attention has been paid to viewing the corresponding assembly process. Herein, with the help of dark-field microscopy, we in situ monitored the whole dynamic process of gold nanorod (GNR) assembly as the solvent evaporated. Differently from the previous coffee-ring effect, rod-shaped hydrophilic GNRs, within certain concentrations, spontaneously assembled into a multiple-ring pattern on a hydrophobic substrate via droplet drying. The self-assembly mechanism is consistent with a diffusion-driven kinetics, and the influencing factors, including the GNR surface modification, the colloid concentration, the surface property of the substrate, and the shape of the nanoparticles, were systematically investigated.

Facile fabrication of a superhydrophobic cage by laser direct writing for site-specific colloidal self-assembled photonic crystal

Micron-sized ablated surface structures with nano-sized 'bumpy' structures were produced by femtosecond (fs) laser ablation of polytetrafluoroethylene (PTFE) film under ambient conditions. Upon just a single step, the processed surface exhibited hierarchical micro/nano morphology. In addition, due to the tribological properties of PTFE, polydimethylsiloxane (PDMS) could be replicated from the laser-ablated PTFE surface without anti-adhesive surface treatment. By controlling the design of the ablated patterns, tunable wettability and superhydrophobicity were achieved on both PTFE and PDMS replica surfaces. Furthermore, using fs laser ablation direct writing, a flexible superhydrophobic PDMS cage formed by superhydrophobic patterns encompassing the unmodified region was demonstrated for aqueous droplet positioning and trapping. Through evaporation-driven colloidal self-assembly in this superhydrophobic cage, a colloidal droplet containing polystyrene (PS) particles dried into a self-assembled photonic crystal, whose optical band gap could be manipulated by the particle size.

Insight into the Evaporation Dynamics of a Pair of Sessile Droplets on a Hydrophobic Substrate

In this work, we have demonstrated three unique regimes in the evaporation lifecycle of a pair of sessile droplets placed in variable proximity on a hydrophobic substrate. For small separation distance, the droplets undergo asymmetric spatiotemporal evaporation leading to contact angle hysteresis and suppressed vaporization. The reduced evaporation has been attributed quantitatively to the existence of a constrained vapor-rich dome between the two droplets. However, a dynamic decrease in the droplet radius due to solvent removal marks a return to symmetry in terms of evaporation and contact angle. We have described the variation in evaporation flux using a universal correction factor. We have also demonstrated the existence of a critical separation distance beyond which the droplets in the droplet pair do not affect each other. The results are crucial to a plethora of applications ranging from surface patterning to lab-on-a-chip devices.

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.