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.     

Effect of nonionic surfactant on wetting behavior of an evaporating drop under a reduced pressure environment

The evaporation of sessile drops at reduced pressure is investigated. The evaporation of water droplets on aluminum and PTFE surfaces at reduced pressure was compared. It was found that water droplets on an aluminum surface exhibit a 'depinning jump' at subatmospheric pressures. This is when a pinned droplet suddenly depins, with an increase in contact angle and a simultaneous decrease in the base width. The evaporation of sessile water droplets with a nonionic surfactant (Triton X-100) added to an aluminum surface was then studied. The initial contact angle exhibited a minimum at 0.001 wt% Triton X-100. A maximum in the evaporation rate was also observed at the same concentration. Droplets with low surfactant concentrations are found to exhibit the 'depinning jump.' It is thought that the local concentration of the surfactant causes a gradient of surface tension. The balance at the contact angle is dictated by complex phenomena, including surfactant diffusion and adsorption processes at interfaces. Due to the strong evaporation near the triple line, an accumulation of the surfactant will lead to a surface tension gradient along the interface. The gradient of surface tension will influence the wetting behavior (Marangoni effect). At low surfactant concentrations the contact line depins under the strong effect of surface tension gradient that develops spontaneously over the droplet interface due to surfactant accumulation near the triple line. The maximum evaporation rate corresponds to a minimum contact angle for a pinned droplet.     

Behavior of evaporating droplets at nonsoluble and soluble surfaces: Modeling with molecular resolution

Liquid droplets in equilibrium with vapor are simulated at solidlike surfaces using the cooperative motion algorithm (CMA). These droplets behave like real droplets, i.e., the densities of the coexistent liquid and vapor phases obey empirical relations such as rho l - rho v proportional, variant (1 - T/Tc)(1/3). Droplet evaporation was studied under various interaction conditions, i.e., nonsoluble and soluble substrates. In the last case, substrate particles migrate toward the liquid-vapor interface to minimize the droplet surface energy. This leads to the formation of a microwell surrounded by a ringlike deposit on the substrate surface. It is shown that the ring formation in the first stages of evaporation results in pinning of the droplet contact area.     

Effect of temperature on ring-shaped-deposit formated at evaporation of droplets of silver-nanoparticle dispersions

The effect of temperature is studied on the geometric parameters and conductivity of ring-shaped deposits formed at evaporation of droplets of dispersions of silver nanoparticles on hydrophilic (glass) and hydrophobic (copper) substrates. It has been shown that increasing temperature leads to substantial changes in the deposit profile. Therewith, the effects of temperature on droplet evaporation on glass and copper substrates are different. It has been found that the lateral conductivity of a ring-shaped deposit formed on a glass substrate increases stepwise similarly to a percolation transition at a droplet-evaporation temperature of 58°C. It has been suggested that the reason for the temperature effect is related to a change in the ratio between the rates of physicochemical processes occurring at different stages of droplet evaporation.     

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.     

Simulation of Sessile Water-Droplet Evaporation on Superhydrophobic Polymer Surfaces

Evaporation of sessile water-droplets on superhydrophobic polymer surfaces has been simulated in recent research. Models based on the ellipsoidal cap geometry and spherical cap geometry, which were originally put forward to describe the profile of a droplet during its evaporation process on a solid surface with a contact angle <90±, are developed to reveal the issue with an initial contact angles larger than 150±. To verify the validity of the model, experiments on superhydrophobic polycarbonate, and °uorinated polyurethane and poly (methyl methacrylate) blend surfaces were carried out. It was observed that the change trends of contact angle and height of the droplet against evaporation time on the superhydrophobic surfaces experimentally are consistent with the simulated results by ellipsoidal and spherical cap models. The ellipsoidal cap model shows the better fits due to the shape distortions of droplets.     

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.     

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.     

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.     

Analysis of the relationship between liquid droplet size and contact angle

The purpose of this paper is to present a consistent theoretical concept that can explain the various physical phenomena associated with the effect of droplet size on contact angle for droplets on solid surfaces, and with the geometry of the liquid/gas/solid contact line in general. Two droplet geometries have been considered: uniformly elongated droplets and axisymmetric droplets. It has been shown that the contact angle for elongated droplets is size-independent and, thus, satisfies the Young equation for constant material and interfacial properties. On the other hand, whereas the contact angle for axisymmetric droplets is size-dependent and does not satisfy the original Young equation, it is shown that this contact angle can still be predicted for any combination of droplet and substrate materials, and a given mass of the droplet. The theoretical work has been combined with the development of numerical schemes of solving the Laplace-Young equation for various droplet geometries. The proposed approach has been applied to different material/substrate combinations and validated against several sets of experimental data. As a result, a method has been developed for predicting the contact angle of both long and axisymmetric sessile droplets of arbitrary sizes for given liquid/solid/gas properties.     

Exceptional superhydrophobicity and low velocity impact icephobicity of acetone-functionalized carbon nanotube films

We present a simple method to produce carbon nanotube-based films with exceptional superhydrophobicity and impact icephobicity by depositing acetone-treated single-walled carbon nanotubes on glass substrates. This method is scalable and can be adopted for any substrate, both flexible and rigid. These films have indicated a high contact angle, in the vicinity of 170°, proved both by static and dynamic analysis processes. The dynamic evaporation studies indicated that a droplet deposited on the treated films evaporated in the constant contact angle mode for more than 80% of the total evaporation time, which is definitely a characteristic of superhydrophobic surfaces. Furthermore, the acetone-functionalized films showed a strong ability to mitigate ice accretion from supercooled water droplets (-8 °C), when the droplets were found to bounce off the films tilted at 30°. The untreated nanotube films did not indicate similar behavior, and the supercooled water droplets remained attached to the films' surfaces. Such studies could be the foundation of highly versatile technologies for both water and ice mitigation.     

Evaporation dynamics of a binary sessile droplet: Theory and comparison with experimental data on a droplet of a sulfuric-acid solution

Diffusion evaporation of a sessile binary droplet in an atmosphere of a noncondensable carrier gas has been considered. For a droplet consisting of two infinitely miscible liquids, a relation between the current values of solution concentration and volume of the droplet has been derived in an explicit form under the ideal solution approximation. It has been shown that the volume of a sessile binary droplet may, as well as the volume of a free binary droplet, vary nonmonotonically with time. The evaporation of a droplet of an aqueous sulfuric-acid solution has been considered in detail taking into account the nonideality of the solution. Time variations in the volume, base area, and contact angle have been experimentally measured for the sessile droplet of an aqueous sulfuric-acid solution on a hydrophobized substrate. The experimental data obtained at different initial humidities of water-vapor and droplet-solution concentrations have been analyzed within the theory of the stationary isothermal diffusion evaporation of a sessile binary droplet.     

Dependence of volatile droplet lifetime on the hydrophobicity of the substrate

In this Article, we demonstrate the dependence of the lifetime of a volatile droplet on the hydrophobicity of the substrate. Ethanol droplets placed on the molecularly smooth surfaces of three polymers, applied to substrates by spin-coating, showed distinct types of behavior depending on the hydrophobicity of the latter. High contact angles, θ, lead to fairly regular recession of the triple line during liquid evaporation at essentially constant θ, whereas low contact angle caused pinning, θ decreasing with time. The latter case leads to shorter drop lifetimes.     

Droplet evaporation study applied to DNA chip manufacturing

DNA chips are potentially powerful technologies for genotyping and gene expression profiling that rely on comparative analyses of up to thousands of "spots of analysis" on a glass support. The spot quality throughout the support influences spot-to-spot variations within an array and the repeatability of data across experiments. For glass slide DNA microarrays, droplets of DNA solution are deposited on functionalized glass slides and left to react through complete evaporation of the droplet. On hydrophobic flat surfaces, different modes of droplet evaporation can be attained. Under atmospheric pressure, water droplets tend to evaporate under two main regimes. Initially, the droplet flattens with a constant contact area, and then the droplet shrinks at a constant contact angle. As a result, the diameter and morphology of thousands of spots on microarrays are not uniform. This leads to poor and unreliable data processing results. In this work, we report the evaporation of an aqueous solution under a constant contact area mode. Evaporation under reduced pressure and the effect of reagent additives to the solution have been investigated. Video microscopy and digital image analysis techniques were applied to monitor the evaporation of the droplets. A mixture of surfactants was developed to maintain a constant area regime during evaporation and to form homogeneous spots. The control of some physicochemical properties (wetting, evaporation rate) of the droplet allows the formation of well-controlled spots compatible with DNA grafting. The influence of surfactant molecules on the mechanisms of evaporation is also discussed.     

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.     

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.     

Mechanisms of depinning accompanying evaporation of colloidal dispersion droplets

Experiments have been performed to clarify the mechanism of depinning, i.e., the onset of the movement of the menisci of evaporating dispersion droplets under the conditions of the formation of ringshaped deposits (the coffee-ring effect). The influence of the nature and concentration of dispersed particles on depinning has been studied. It has been shown that there are three main effects responsible for depinning. The first effect is due to the hysteresis of droplet contact angle, the second one results from the influence of the particles on the surface tension of a dispersion, and the third effect is caused by the formation of a dense gel in the meniscus region. A relation has been revealed between the mechanisms being realized and scenarios of droplet evaporation.     

凹槽状PDMS基底上水滴的挥发及Cassie-Wenzel转变行为

通过在线跟踪水滴在凹槽状聚二甲基硅氧烷(PDMS)基底上的挥发行为, 研究了蒸馏水的挥发规律Cassie-Wenzel转变行为. 结果表明, 初始阶段, 水滴处于Cassie状态, 且在垂直于凹槽方向(V)和平行于凹槽方向(P)上存在显著的各向异性. 水滴的挥发过程依次表现出接触直径不变模式、 接触角不变模式及共同减小模式, 与平滑基底上水滴的挥发规律类似. 在挥发过程中, 发生了Cassie-Wenzel转变, 转变发生的时间与PDMS基底上突起部分的面积分数(即固相率)呈现良好的线性关系. 随着挥发的进行, 水滴的各向异性在接触角不变模式阶段消失, 即挥发导致水滴从开始的椭球缺状变为球缺状.     

Analysis of droplet evaporation on a superhydrophobic surface

The evaporation process for small, 1-2-mm-diameter droplets of water from patterned polymer surfaces is followed and characterized. The surfaces consist of circular pillars (5-15 microm diameter) of SU-8 photoresist arranged in square lattice patterns such that the center-to-center separation between pillars is 20-30 microm. These types of surface provide superhydrophobic systems with theoretical initial Cassie-Baxter contact angles for water droplets of up to 140-167 degrees, which are significantly larger than can be achieved by smooth hydrophobic surfaces. Experiments show that on these SU-8 textured surfaces water droplets initially evaporate in a pinned contact line mode, before the contact line recedes in a stepwise fashion jumping from pillar to pillar. Provided the droplets of water are deposited without too much pressure from the needle, the initial state appears to correspond to a Cassie-Baxter one with the droplet sitting upon the tops of the pillars. In some cases, but not all, a collapse of the droplet into the pillar structure occurs abruptly. For these collapsed droplets, further evaporation occurs with a completely pinned contact area consistent with a Wenzel-type state. It is shown that a simple quantitative analysis based on the diffusion of water vapor into the surrounding atmosphere can be performed, and estimates of the product of the diffusion coefficient and the concentration difference (saturation minus ambient) are obtained.     

Experimental and theoretical investigations of evaporation of sessile water droplet on hydrophobic surfaces

Experiments of sessile water droplet evaporation on both polydimethylsiloxane (PDMS) and Teflon surfaces were conducted. All experiments begin with constant contact area mode (the initial contact angle is greater than 90°), switch to constant contact angle mode and end with mixed mode. Based on the assumptions of spherical droplet and uniform concentration gradient, theoretical analyses for both constant contact area and constant contact angle modes are made and theoretical solutions are derived accordingly, especially a theoretical solution of contact angle is presented first for CCR stage with any value of the initial contact angle. Moreover, comparisons between the theoretical solutions and experimental data of contact angle in CCR stage demonstrate the validity of the theoretical solution and it would help for a better understanding and application of water droplet on solid surfaces, which is quite often encountered in lab-on-a-chip, polymerase chain reaction (PCR) and other micro-fluidics devices.