Evaporative characteristics of sessile nanofluid droplet on micro‐structured heated surface

Micro‐structure patterned substrates attract our attention due to the special and programmable wettabilities. The interaction between the liquid and micro/nano structures gives rise to controllable spreading and thus evaporation. For exploration of the application versatility, the introduction of nanoparticles in liquid droplet results in interaction among particles, liquid and microstructures. In addition, temperature of the substrates strongly affects the spreading of the contact line and the evaporative property. The evaporation of sessile droplets of nanofluids on a micro‐grooved solid surface is investigated in terms of liquid and surface properties. The patterned nickel surface used in the experiments is designed and fabricated with circular and rectangular shaped pillars whose size ratios between interval and pillars is fixed at 5. The behavior is firstly compared between nanofluid and pure liquid on substrates at room temperature. For pure water droplet, the drying time is relatively longer due to the receding of contact line which slows down the liquid evaporation. Higher concentrations of nanoparticles tend to increase the total evaporation time. With varying concentrations of graphite at nano scale from 0.02% to 0.18% with an interval at 0.04% in water droplets and the heating temperature from 22 to 85°C, the wetting and evaporation of the sessile droplets are systematically studied with discussion on the impact parameters and the resulted liquid dynamics as well as the stain. The interaction among the phases together with the heating strongly affects the internal circulation inside the droplet, the evaporative rate and the pattern of particles deposition.     

Evaporation and Marangoni driven convection in small heated water droplets

Evaporation dynamics of small sessile water droplets under microgravity conditions is investigated numerically. The water-air interface is free, and the surrounding air is assumed to be quasisteady. The droplet is described by Navier-Stokes and heat equations and its surrounding water/air gaseous phase with Laplace equation. In the thermodynamic conditions of the simulations presented herein, the evaporative mass flow is nonlinear. It shows a minimum that indicates the existence of qualitative changes in the evaporative regimes although the droplet is sessile. Due to temperature gradients on the free interface, Marangoni motion occurs and generates inside the droplet convection cells that furthermore exhibit small fluctuating motion as evaporation goes on.     

On the lifetime of evaporating sessile droplets

The evaporation of sessile droplets with a constant base radius (pinning mode) and a constant contact angle (depinning mode) has been experimentally observed. Here we analyzed the effect of substrate hydrophobicity on the lifetimes of evaporating droplets for the two modes. Theoretical predictions were obtained and compared with available experimental results. The theoretical analysis and experimental results show that linear methods of extrapolating limited experimental data for a transient droplet contact angle and base radius overpredict the droplet lifetime. Likewise, the linear extrapolation of limited experimental data for transient droplet volume underpredicts the droplet lifetime. Correct methods of extrapolating limited experimental data for transient droplet parameters are described, discussed, and validated. The new methods removed inconsistencies in the previous theory and experimental analysis. Master equations and master curves for the droplet lifetime for the two evaporation modes are obtained and experimentally confirmed.     

Influence of surface orientation on the organization of nanoparticles in drying nanofluid droplets

The influence of droplet orientation on the flow directed organization of nanoparticles in evaporating nanofluid droplets is important for the efficiency of foliar applied fertilizers and contamination adhesion to the exterior of buildings. The so called "coffee ring" deposit resulting from the evaporation of a sessile nanofluid drop on a hydrophilic surface has received much attention in the literature. Deposits forming on hydrophobic surfaces in the pendant drop position (i.e. hanging drop), which are of importance in foliar fertilizer and exterior building contamination, have received much less attention. In this study, the deposit patterns resulting from the evaporation of water droplets containing silica nanoparticles on hydrophobic surfaces orientated in the sessile or pendant configuration are compared. In the case of a sessile drop the well known coffee ring pattern surrounding a thin nanoparticle layer was formed. A deposit consisting of a thin coffee ring surrounding a bump was formed in the pendant position. A mechanism involving flow induced aggregation at the droplet waist, settling, orientation dependant accumulation within the drop and pinning of the contact line is suggested to explain the findings. Differences in the contact area and adhesion of deposits with surface orientation will affect the efficiency and rainfastness of foliar fertilizers and the cleanliness of building exteriors.     

Convective rolls and hydrothermal waves in evaporating sessile drops

Recent experiments on the evaporation of sessile droplets have revealed the spontaneous formation of various patterns including the presence of hydrothermal waves. These waves had previously been observed, in the absence of evaporation, in thin liquid layers subjected to an imposed, uniform temperature gradient. This is in contrast to the evaporating droplet case wherein these gradients arise naturally due to evaporation and are spatially and temporally varying. In the present paper, we present a theory of evaporating sessile droplets deposited on a heated surface and propose a candidate mechanism for the observed pattern formation using a linear stability analysis in the quasi-steady-state approximation. A qualitative agreement with experimental trends is observed.     

Simultaneous spreading and evaporation: Recent developments

The recent progress in theoretical and experimental studies of simultaneous spreading and evaporation of liquid droplets on solid substrates is discussed for pure liquids including nanodroplets, nanosuspensions of inorganic particles (nanofluids) and surfactant solutions. Evaporation of both complete wetting and partial wetting liquids into a nonsaturated vapour atmosphere are considered. However, the main attention is paid to the case of partial wetting when the hysteresis of static contact angle takes place. In the case of complete wetting the spreading/evaporation process proceeds in two stages. A theory was suggested for this case and a good agreement with available experimental data was achieved. In the case of partial wetting the spreading/evaporation of a sessile droplet of pure liquid goes through four subsequent stages: (i) the initial stage, spreading, is relatively short (1–2 min) and therefore evaporation can be neglected during this stage; during the initial stage the contact angle reaches the value of advancing contact angle and the radius of the droplet base reaches its maximum value, (ii) the first stage of evaporation is characterised by the constant value of the radius of the droplet base; the value of the contact angle during the first stage decreases from static advancing to static receding contact angle; (iii) during the second stage of evaporation the contact angle remains constant and equal to its receding value, while the radius of the droplet base decreases; and (iv) at the third stage of evaporation both the contact angle and the radius of the droplet base decrease until the drop completely disappears. It has been shown theoretically and confirmed experimentally that during the first and second stages of evaporation the volume of droplet to power 2/3 decreases linearly with time. The universal dependence of the contact angle during the first stage and of the radius of the droplet base during the second stage on the reduced time has been derived theoretically and confirmed experimentally. The theory developed for pure liquids is applicable also to nanofluids, where a good agreement with the available experimental data has been found. However, in the case of evaporation of surfactant solutions the process deviates from the theoretical predictions for pure liquids at concentration below critical wetting concentration and is in agreement with the theoretical predictions at concentrations above it.     

Evaporation-induced patterns from droplets containing motile and nonmotile bacteria

In this letter, we report the observations of specific pattern formation from the evaporation of aqueous droplets containing motile and nonmotile bacteria. We found that when motile bacteria were present the droplet evaporated into disclike patterned deposits of bacteria. However, when the bacteria were made nonmotile by treatment with liquid nitrogen, the droplet evaporated into ringlike deposits. We also observed that bacteria with higher motility produced more uniformly deposited disclike patterns. Furthermore, we propose a model with numerical simulations to explain the mechanism of formation of these patterns. The model is based on the advective fluid flow from the center of the droplet toward the edge due to enhanced evaporation from the edge of the pinned droplet in comparison to that from the free surface. For the case of motile bacteria, we have added another velocity parameter toward the axis of the droplet and directed against the fluid flow in order to account for the disclike pattern formation. The numerical simulations match the experimental observations well. The present work, by qualitative and quantitative understanding of the evaporation of bacteria droplets, demonstrates that the inherent bacterial motility is primarily responsible for the formation of these differential patterns.     

Use of IR thermography to investigate heated droplet evaporation and contact line dynamics

In this paper we present the results of an experimental study investigating interfacial properties during the evaporation of sessile water droplets on a heated substrate. This study uses infrared thermography to map the droplet interfacial temperature. The measurements evidence nonuniform temperature and gradients that evolve in time during the evaporation process. A general scaling law for the interfacial temperature is deduced from the experimental observations. A theoretical analysis is performed to predict the local evaporation rates and their evolution in time. The use of energy conservation laws enabled us to deduce a general expression for the interfacial temperature. The comparison between the theory and experiments shows good agreement and allows us to rationalize the experimental observations. The thermography analysis also enabled the detection of the three-phase contact line location and its dynamics. To our knowledge, such measurements are performed for the first time using thermography.     

Tritoroidal particle rings formation in open microfluidics induced by standing surface acoustic waves

In this paper, the particle movements in a sessile droplet induced by standing surface acoustic waves (SSAWs) are studied. Tritoroidal particle rings are formed under the interaction of acoustic field and electric field. The experimental results demonstrate that the electric field plays an important role in patterning nanoparticles. The electric field can define the droplet shape due to electrowetting. When the droplet approximates a hemisphere, the acoustic radiation force induced by SSAWs drives the particles to form tritoroidal particle rings. When the droplet approximates a convex plate, the drag force induced by acoustic steaming drives the particle to move. The results will be useful for better understanding the nanoparticle movements in a sessile droplet, which is important to explain the mechanism that SSAWs enhance reaction and crystallization in droplet.     

Modeling of droplet traffic in interconnected microfluidic ladder devices

The problem of controlling the droplet motion in multiphase flows on the microscale has gained increasing attention because the droplet-based microfluidic devices provide great potentials for chemical and biological applications. It is critical to understand the relevant physics on droplet hydrodynamics and thus control the generation, motion, splitting, and coalescence of droplets in complex microfluidic networks. Numerical simulations using the volume of fluid algorithm are conducted to investigate the time-dependent dynamics of droplets in gas-liquid multiphase devices. An analytical model based on the electronic-hydraulic analogy is developed to describe the hydrodynamic behavior of the droplets in interconnected microfluidic ladder devices. It is found that the pressure drop caused by the droplets plays a critical role in the droplet synchronization. A fitted formula for pressure drops in the presence of surfactant is achieved by using numerical simulations. Both the numerical and the theoretical results agree well with the corresponding experimental results.     

Three stages of water microdroplet evaporation on hydrophobized surface: Comparison between steady-state theory and experiment

Three consecutive stages of evaporation of a sessile water microdroplet are studied both theoretically and experimentally under the conditions of contact angle hysteresis. The influence of thermal effects on the dynamics of droplet evaporation is quantitatively investigated on the basis of the obtained experimental results. The features of droplet evolution are analyzed at the final stage, when both the contact angle and the radius of the droplet base decrease with time. It is shown that evaporation at this stage also occurs in a steady-state regime, but the average droplet temperature approaches the ambient temperature.     

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

A sessile drop is an isolated drop which has been deposited on a solid substrate where the wetted area is limited by a contact line and characterized by contact angle, contact radius and drop height. Diffusion-controlled evaporation of a sessile drop in an ambient gas is an important topic of interest because it plays a crucial role in many scientific applications such as controlling the deposition of particles on solid surfaces, in ink-jet printing, spraying of pesticides, micro/nano material fabrication, thin film coatings, biochemical assays, drop wise cooling, deposition of DNA/RNA micro-arrays, and manufacture of novel optical and electronic materials in the last decades. This paper presents a review of the published articles for a period of approximately 120 years related to the evaporation of both sessile drops and nearly spherical droplets suspended from thin fibers. After presenting a brief history of the subject, we discuss the basic theory comprising evaporation of micrometer and millimeter sized spherical drops, self cooling on the drop surface and evaporation rate of sessile drops on solids. The effects of drop cooling, resultant lateral evaporative flux and Marangoni flows on evaporation rate are also discussed. This review also has some special topics such as drop evaporation on superhydrophobic surfaces, determination of the receding contact angle from drop evaporation, substrate thermal conductivity effect on drop evaporation and the rate evaporation of water in liquid marbles.     

The influence of gravity on the distribution of the deposit formed onto a substrate by sessile, hanging, and sandwiched hanging drop evaporation

The focus of the present article is the study of the influence of gravity on the particle deposition profiles on a solid substrate during the evaporation of sessile, hanging and sandwiched hanging drops of colloidal particle suspensions. For concentrations of nanoparticles in the colloidal solutions in the range 0.0001-1 wt.%, highly diluted suspensions will preferentially form rings while concentrated suspensions will preferentially form spots in both sessile and hanging drop evaporation. For intermediary concentrations, the particle deposition profiles will depend on the nanoparticle aggregation dynamics in the suspension during the evaporation process, gravity and on the detailed evaporation geometry. The evaporation of a drop of toluene/carbon nanoparticle suspension hanging from a pendant water drop will leave on the substrate a circular spot with no visible external ring. By contrast, a clear external ring is formed on the substrate by the sessile evaporation of a similar drop of suspension sandwiched between a water drop and the substrate. From the application viewpoint, these processes can be used to create preferential electrical conductive carbon networks and contacts for arrays of self-assembled nanostructures fabricated on solid substrates as well as on flexible polymeric substrates.     

Evaporation of sessile droplets of dilute aqueous solutions containing sodium n-alkylates from polymer surfaces: influences of alkyl length and concentration of solute

The evaporation of sessile droplets placed on polymer surfaces was studied by microscopic observation of the changes in shape of aqueous solution droplets in which the alkyl lengths and the initial concentrations of sodium n-alkylates were varied. Although the initial contact angles of the droplets were not significantly different, the evaporation process varied significantly with the alkyl length of the sodium n-alkylate employed. For the sodium dodecanoate (C 12), showing the highest surface activity, the concentration was found to have a significant effect on the evaporation process of the droplets. In the evaporation of water droplets, variations in the three distinct stages were caused by the different concentration of solutes distributed near or at the air/water interface. It is revealed that the concentration of droplet solute near the air/water interface requires not only solvent evaporation but also some affinity of the solute for the interface. The initial C 12 concentration-dependence of the evaporation of C 12 solution droplets is discussed with particular emphasis on the sudden spreading or sudden contraction of the contact area near the end of evaporation. It is suggested that the cluster formation by C 12 molecules at the air/liquid interface during the evaporation causes Marangoni instability in an evaporating droplet, and the clusters are expected to move dynamically, depending on the droplet concentration of C 12, from the droplet center to the contact line and vice versa, showing Marangoni flow along the air/water interface.     

Stick-slip of evaporating droplets: substrate hydrophobicity and nanoparticle concentration

The dynamics of the three-phase contact line for water and ethanol is experimentally investigated using substrates of various hydrophobicities. Different evolutions of the droplet profile (contact line, R, and contact angle, θ) are found to be dependent on the hydrophobicity of the substrate. A simple theoretical approach based on the unbalanced Young force is used to explain the depinning of the contact line on hydrophilic surfaces or the monotonic slip on hydrophobic substrates. The second part of the article involves the addition of different quantities of titanium oxide nanoparticles to water, and a comparison of the evaporative behavior of these novel fluids with the base liquid (water) on substrates varying in hydrophobicity (i.e., silicon, Cytop, and PTFE) is presented. The observed stick-slip behavior is found to be dependent on the nanoparticle concentration. The evaporation rate is closely related to the dynamics of the contact line. These findings may have an important impact when considering the evaporation of droplets on different substrates and/or those containing nanoparticles.     

Hydrodynamic interactions of evaporating droplet with droplet of nonvolatile substance

The hydrodynamic interactions of freely evaporating or growing droplet (suspended in gaseous medium) in the supersaturated vapor with the droplet of nonvolatile substance or spherical solid particle are theoretically studied with allowance for effects that are linear with respect to the Knudsen number. The process of interaction between the volatile droplet and the infinite plane surface of nonvolatile liquid or solid is considered as a limiting case. Numerical estimates of the velocities of the steady motion of evaporating droplets of water and castor oil are reported. For the droplet of water and spherical solid particle, the effect of the heat conductivity of the latter on the velocity of particle motion is considered. Analogous estimates are obtained for a water droplet that evaporates near the infinite solid surface of castor oil or solid. The effects of the droplet size and the heat conductivity of wall on the rate of the evaporation of water droplet are analyzed.     

Surface-guided templating of particle assemblies inside drying sessile droplets

The particles suspended inside evaporating sessile droplets can be assembled into microscopic objects with long-ranged ordered structure. The air-water droplet interface guides the assembly and determines the shape of the resulting micropatches. We report the results of a systematic study of the mechanism of interface-templated assembly on substrates of controlled contact angle. The kinetics of drying were examined by measurements of droplet profiles, and it was found that the rate matched diffusion-limited evaporation well. The shape of the droplets and of the resulting assemblies was correlated to the dynamics of the receding contact line. The effects of major parameters controlling the process, including contact angle, particle concentration, and electrolyte, were investigated in detail. A variety of micropatch shapes were observed and categorized within the parameter space. The in-depth characterization of the process allowed the optimization of the assembly and the formulation of protocols for the deposition of nanostructured patches of different diameter, thickness, and shape.     

Monte Carlo computer simulations and electron microscopy of colloidal cluster formation via emulsion droplet evaporation

We consider a theoretical model for a binary mixture of colloidal particles and spherical emulsion droplets. The hard sphere colloids interact via additional short-ranged attraction and long-ranged repulsion. The droplet-colloid interaction is an attractive well at the droplet surface, which induces the Pickering effect. The droplet-droplet interaction is a hard-core interaction. The droplets shrink in time, which models the evaporation of the dispersed (oil) phase, and we use Monte Carlo simulations for the dynamics. In the experiments, polystyrene particles were assembled using toluene droplets as templates. The arrangement of the particles on the surface of the droplets was analyzed with cryogenic field emission scanning electron microscopy. Before evaporation of the oil, the particle distribution on the droplet surface was found to be disordered in experiments, and the simulations reproduce this effect. After complete evaporation, ordered colloidal clusters are formed that are stable against thermal fluctuations. Both in the simulations and with field emission scanning electron microscopy, we find stable packings that range from doublets, triplets, and tetrahedra to complex polyhedra of colloids. The simulated cluster structures and size distribution agree well with the experimental results. We also simulate hierarchical assembly in a mixture of tetrahedral clusters and droplets, and find supercluster structures with morphologies that are more complex than those of clusters of single particles.     

Induced detachment of coalescing droplets on superhydrophobic surfaces

Coalescence of a falling droplet with a stationary sessile droplet on a superhydrophobic surface is investigated by a combined experimental and numerical study. In the experiments, the droplet diameter, the impact velocity, and the distance between the impacting droplets were controlled. The evolution of surface shape during the coalescence of two droplets on the superhydrophobic surface is captured using high speed imaging and compared with numerical results. A two-phase volume of fluid (VOF) method is used to determine the dynamics of droplet coalescence, shape evaluation, and contact line movement. The spread length of two coalesced droplets along their original center is also predicted by the model and compared well with the experimental results. The effect of different parameters such as impact velocity, center to center distance, and droplet size on contact time and restitution coefficient are studied and compared to the experimental results. Finally, the wetting and the self-cleaning properties of superhydrophobic surfaces have been investigated. It has been found that impinging water drops with very small amount of kinetic impact energy were able to thoroughly clean these surfaces.     

Fast, high-throughput creation of size-tunable micro/nanoparticle clusters via evaporative self-assembly in picoliter-scale droplets of particle suspension

We report a fast, high-throughput method to create size-tunable micro/nanoparticle clusters via evaporative assembly in picoliter-scale droplets of particle suspension. Mediated by gravity force and surface tension force of a contacting surface, picoliter-scale droplets of the suspension are generated from a nanofabricated printing head. Rapid evaporative self-assembly of the particles on a hydrophobic surface leads to fast clustering of micro/nanoparticles and forms particle clusters of tunable sizes and controlled spacing. The evaporating behavior of the droplet is observed in real-time, and the clustering characteristics of the particles are understood based on the physics of evaporative-assembly. With this method, multiplex printing of various particle clusters with accurate positioning and alignment are demonstrated. Also, size-unifomity of the cluster arrays is thoroughly analyzed by examining the metallic nanoparticle cluster-arrays based on surface-enhanced Raman spectroscopy (SERS).