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.     

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.     

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.     

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.     

Dynamics of droplet motion under electrowetting actuation

The static shape of droplets under electrowetting actuation is well understood. The steady-state shape of the droplet is obtained on the basis of the balance of surface tension and electrowetting forces, and the change in the apparent contact angle is well characterized by the Young-Lippmann equation. However, the transient droplet shape behavior when a voltage is suddenly applied across a droplet has received less attention. Additional dynamic frictional forces are at play during this transient process. We present a model to predict this transient behavior of the droplet shape under electrowetting actuation. The droplet shape is modeled using the volume of fluid method. The electrowetting and dynamic frictional forces are included as an effective dynamic contact angle through a force balance at the contact line. The model is used to predict the transient behavior of water droplets on smooth hydrophobic surfaces under electrowetting actuation. The predictions of the transient behavior of droplet shape and contact radius are in excellent agreement with our experimental measurements. The internal fluid motion is explained, and the droplet motion is shown to initiate from the contact line. An approximate mathematical model is also developed to understand the physics of the droplet motion and to describe the overall droplet motion and the contact line velocities.     

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.     

An empirically validated analytical model of droplet dynamics in electrowetting on dielectric devices

Explicit analytical models that describe the capillary force on confined droplets actuated in electrowetting on dielectric devices and the reduction in that force by contact angle hysteresis as a function of the three-dimensional shape of the droplet interface are presented. These models are used to develop an analytical model for the transient position and velocity of the droplet. An order of magnitude analysis showed that droplet motion could be modeled using the driving capillary force opposed by contact angle hysteresis, wall shear, and contact line friction. Droplet dynamics were found to be a function of gap height, droplet radius, surface tension, fluid density, the initial and deformed contact angles, contact angle hysteresis, and friction coefficients pertaining to viscous wall friction and contact line friction. The first four parameters describe the device geometry and fluid properties; the remaining parameters were determined experimentally. Images of the droplet during motion were used to determine the evolution of the shape, position, and velocity of the droplet with time. Comparisons between the measured and predicted results show that the proposed model provides good accuracy over a range of practical voltages and droplet aspect ratios.     

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.     

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.     

Drying of DNA droplets

The evaporation kinetics of droplets containing DNA was studied, as a function of DNA concentration. Drops containing very low DNA concentrations dried by maintaining a constant base, whereas those with high concentration dried with a constant contact angle. To understand this phenomenon, the distribution of the DNA inside the droplet was measured using confocal microscopy. The results indicated that the DNA was condensed mostly on the surface of the droplets. In the case of high concentration droplets, it formed a shell, whereas isolated islands were found for droplets of low DNA concentrations. Rheologic results indicate the formation of a hydro gel in the low concentration drops, whereas phase separation between the self-assembled DNA structures and the water phase occurred at higher concentration.     

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 of water droplets on polymer surfaces

The evaporation of water droplets on polymer surfaces was investigated by using a digital image analysis technique. There were three distinct stages in the water evaporation process: a constant contact area mode, a constant contact angle mode, and a mixed mode that is independent of both the initial quantity of water droplets and the hydrophobic properties of the polymer surfaces. The physical factors influencing the first and second transitions in the evaporation process were found to be the attainment of the receding angle on the polymer surfaces and the Marangoni instability in the evaporating water droplets, which result from the concentration gradient of contaminants. This study also provides qualitative information about the microfluid flows inside the evaporating water droplets and the morphology of drying stains on polymer surfaces. The contaminants were found to be concentrated at the perimeter of the stains, in agreement with the observed outward microfluid flow in the mixed mode of the evaporation process.     

纳米结构表面上冷凝液滴的生长模式及部分润湿液滴的形成机制

分析并计算了纳米结构表面上冷凝液滴按照不同途径长大的过程中液滴能量的增加速率, 并以能量增加最小为判据来确定液滴的生长途径. 结果表明, 纳米结构内形成的冷凝液斑在初期按接触角(CA)增加的模式生长时, 其能量增加速率远低于其它模式, 于是, 初始液斑先按增大接触角、并保持底面积不变的模式生长, 直至液滴达到前进角状态. 此后, 沿接触角增加的模式长大所导致的能量增加速率开始远高于其它生长模式, 于是液滴三相线开始移动, 底面积开始增加, 但接触角保持不变. 液滴所增加的底面积可以呈润湿或复合两种状态, 分别形成Wenzel 液滴及部分润湿液滴, 前者的表观接触角一般小于160°, 而后者则明显大于160°. 液滴的生长模式及其润湿状态均与纳米结构参数密切相关, 仅当纳米柱具有一定高度、且间距较小时, 冷凝液滴才能呈现部分润湿状态. 最后, 本模型对纳米结构表面上冷凝液滴润湿状态的计算结果与绝大部分实测结果相一致, 准确率达到91.9%, 明显高于已有公式的计算准确率.     

Microdroplet growth mechanism during water condensation on superhydrophobic surfaces

By promoting dropwise condensation of water, nanostructured superhydrophobic coatings have the potential to dramatically increase the heat transfer rate during this phase change process. As a consequence, these coatings may be a facile method of enhancing the efficiency of power generation and water desalination systems. However, the microdroplet growth mechanism on surfaces which evince superhydrophobic characteristics during condensation is not well understood. In this work, the sub-10 μm dynamics of droplet formation on nanostructured superhydrophobic surfaces are studied experimentally and theoretically. A quantitative model for droplet growth in the constant base (CB) area mode is developed. The model is validated using optimized environmental scanning electron microscopy (ESEM) imaging of microdroplet growth on a superhydrophobic surface consisting of immobilized alumina nanoparticles modified with a hydrophobic promoter. The optimized ESEM imaging procedure increases the image acquisition rate by a factor of 10-50 as compared to previous research. With the improved imaging temporal resolution, it is demonstrated that nucleating nanodroplets coalesce to create a wetted flat spot with a diameter of a few micrometers from which the microdroplet emerges in purely CB mode. After the droplet reaches a contact angle of 130-150°, its base diameter increases in a discrete steplike fashion. The droplet height does not change appreciably during this steplike base diameter increase, leading to a small decrease of the contact angle. Subsequently, the drop grows in CB mode until it again reaches the maximum contact angle and increases its base diameter in a steplike fashion. This microscopic stick-and-slip motion can occur up to four times prior to the droplet coalescence with neighboring drops. Lastly, the constant contact angle (CCA) and the CB growth models are used to show that modeling formation of a droplet with a 150° contact angle in the CCA mode rather than in the CB mode severely underpredicts both the drop formation time and the average heat transfer rate through the drop.     

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.     

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.     

Evaporation of water droplets on "lock-and-key" structures with nanoscale features

Highly ordered poly(dimethylsiloxane) microbowl arrays (MBAs) and microcap arrays (MCAs) with "lock-and-key" properties are successfully fabricated by self-assembly and electrochemical deposition. The wetting properties and evaporation dynamics of water droplets for both cases have been investigated. For the MBAs case, the wetting radius of the droplets remains unchanged until the portion of the droplet completely dries out at the end of the evaporation process. The pinning state extends for more than 99.5% of the total evaporation time, and the pinning-shrinking transition is essentially prevented whereas in the case of the MCAs the contact radius exhibits distinct stages during evaporation and the contact line retreats significantly in the middle of the evaporation process. We explain the phenomenon by a qualitative energy balance argument based on the different shrinkage types of the nanoscale-folded contact line.     

Picoliter water contact angle measurement on polymers

Water contact angle measurement is the most common method for determining a material's wettability, and the sessile drop approach is the most frequently used. However, the method is generally limited to macroscopic measurements because the base diameter of the droplet is usually greater than 1 mm. Here we report for the first time on a dosing system to dispense smaller individual droplets with control of the position and investigate whether water contact angles determined from picoliter volume water droplets are comparable with those obtained from the conventional microliter volume water droplets. This investigation was conducted on a group of commonly used polymers. To demonstrate the higher spatial resolution of wettability that can be achieved using picoliter volume water droplets, the wettability of a radial plasma polymer gradient was mapped using a 250 microm interval grid.