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.     

Sessile droplet de-pinning: new life for gravimetric data

Using three different types of surfaces as exemplars, we report a gravimetric method as a viable tool for studying the de-pinning process. Namely, the de-pin time, tau(d) (the time required for a horizontal sessile droplet to de-pin at the triple phase line on a given substrate), is estimated without using a time consuming and expensive video imaging system. This is made possible by deciphering the non-linear portion of mass vs time data of an evaporating sessile droplet. Typical gravimetric glass-substrate evaporative mass loss vs time data has two regimes: a long, linear regime followed by a short, non-linear regime. Traditionally, researchers extract only the evaporation rate of a droplet from the linear regime but discard (by truncating the data) or ignore (thus deriving no information from) the non-linear regime. The origin of the linear to non-linear transition, found almost universally in gravimetric data, persists unremarked upon. By constructing three very different types of surfaces and comparing gravimetric data with video imaging data taken simultaneously, we report the transition is correlated to the onset of the de-pinning event in each case. This realization enables us to measure the de-pin time, tau(d), with gravimetric data only; i.e., without the video system, gathering more information from gravimetric data than previously considered. The method has application in estimating the de-pin time of a droplet deposited on a substrate that yields poor top-view contrast for videography, such as a water droplets on silicon wafers or glass substrates. Finally, gravimetric data is more accurate for evaporation modeling when substrate/droplet interaction areas are not circular.     

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.     

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.     

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.     

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.     

Nonstationary evolution of the size,composition, and temperature of microdroplets of nonideal two- and three-component aqueous solutions

Results of numerical solution have been presented for a set of equations describing the nonstationary and nonisothermal growth or evaporation of microdroplets consisting of ethanol and water, sulfuric acid and water, and sulfuric and nitric acids and water. Time dependences of droplet size, temperature, and composition have been determined at low concentrations of a condensable vapor, as compared with the concentration of a carrier gas in an ambient vapor–gas mixture. The calculations have been performed using different initial conditions and approximations for the dependences of saturation vapor pressures, activity coefficients, and partial heats of condensation of the components, as well as average volumes per molecule on droplet composition and temperature. By the examples of ethanol–water and sulfuric acid–water droplets, it has been shown that nonmonotonic variations in the droplet radius are possible. Regimes of nonmonotonic variations in the temperature of a droplet that precede the onset of its stationary growth or evaporation have been revealed for all systems under consideration.     

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.     

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.     

Numerical simulation of water droplet evaporation into vapor–gas medium

Numerical simulation has been employed to consider water droplet evaporation into a vapor–gas medium. An approximate approach has been proposed that makes it possible to take into account the effect of a noncondensable component on the character of variations in the droplet temperature during evaporation. The results of the calculations have been compared with the published experimental data.     

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.     

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.     

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.     

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.     

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.     

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.     

Controlled Directional Water‐Droplet Spreading on a High‐Adhesion Surface

Controlled directional spreading of a droplet on a smart high‐adhesion surface was made possible by simply controlling anodic oxidation. The wettability gradient of the surface was controlled from 0.14 to 3.38° mm^?1 by adjusting the anodic oxidation conditions. When a water droplet made contact with the substrate, the droplet immediately spread in the direction of the wettability gradient but did not move in other directions, such as those perpendicular to the gradient direction, even when the surface was turned upside down. The spreading behavior was mainly controlled by the wettability gradient. Surfaces with a V‐ or inverse‐V‐shaped wettability gradient were also formed by the same method, and two droplets on these surfaces spread either toward or away from one another as designed. This method could be used to oxidize many conductive substrates (e.g., copper, aluminum) to form surfaces with variously shaped wettability gradients. It has potential for application in microfluidic devices.     

Water microdroplets on molecularly tailored surfaces: correlation between wetting hysteresis and evaporation mode switching

The evaporation of water microdroplets from solid surfaces was studied using digital contact angle analysis techniques. An inclusive trend for the evaporation process, that is, a switch from the initial constant contact area to the subsequent constant contact angle mode was observed for all surfaces examined, including mixed self-assembled monolayers (SAMs) on gold and "conventional" surfaces such as silicon wafers, polycarbonate, and Teflon. More importantly, it has been shown that the change in contact angle during the evaporation process (i.e., evaporation hysteresis, delta theta(evap), the difference between the initial and "equilibrated" contact angle) correlates well with the wetting hysteresis determined directly (i.e., measuring the advancing and receding contact angles on these surfaces by changing the drop volume). The comparison between mixed SAM surfaces and conventional solids revealed that the evaporation/wetting hysteresis is dominated by the roughness (from nanometer to micrometer scale) rather than the chemical heterogeneity of the surface. The evaporation rates of water microdroplets on these surfaces were also monitored and modeled.     

Dependence of the structure of ring-shaped deposits resulting from evaporation of dispersion droplets on initial contact angle

Experiments have been performed on the formation of ding-shaped deposits upon the evaporation of dispersion droplets on different substrates accompanied by the coffee ring effect. The main attention has been focused on studying the structure of a formed deposit as depending on the initial contact angle of a droplet. It has been established that the deposit structure may vary from ring-shaped to disc-shaped with a decrease in the contact angle. For certain systems, as the initial contact angle is varied, the scenario of droplet evaporation may change and, in some cases, acquire a combined character. Before the onset of pinning, menisci of droplets that are evaporated on modified polymer substrates may initially move not only toward the droplet center, but also in the opposite direction.     

低黏附耐酸碱水相超疏油铜表面的制备

制备了一种新型的耐酸碱性的水相超疏油铜表面. 在水相中,油滴在其表面上的接触角高达162°,同时极易滚动,表明所得到的表面不但具有水相超疏油特性,同时还表现出较低的黏附性及较强的耐酸碱能力. 在不同pH值（2~12）的水溶液中,这种低黏附超疏油特性依然存在. 研究表明,该表面的水下超疏油及低黏附特性主要源于表面亲水性的化学组成及独特的微纳米等级结构之间的协同作用. 而较强的耐酸碱性则得益于铜材料自身较好的化学稳定性.