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.     

Sessile nanofluid droplet drying

Nanofluid droplet evaporation has gained much audience nowadays due to its wide applications in painting, coating, surface patterning, particle deposition, etc. This paper reviews the drying progress and deposition formation from the evaporative sessile droplets with the suspended insoluble solutes, especially nanoparticles. The main content covers the evaporation fundamental, the particle self-assembly, and deposition patterns in sessile nanofluid droplet. Both experimental and theoretical studies are presented. The effects of the type, concentration and size of nanoparticles on the spreading and evaporative dynamics are elucidated at first, serving the basis for the understanding of particle motion and deposition process which are introduced afterward. Stressing on particle assembly and production of desirable residue patterns, we express abundant experimental interventions, various types of deposits, and the effects on nanoparticle deposition. The review ends with the introduction of theoretical investigations, including the Navier–Stokes equations in terms of solutions, the Diffusion Limited Aggregation approach, the Kinetic Monte Carlo method, and the Dynamical Density Functional Theory. Nanoparticles have shown great influences in spreading, evaporation rate, evaporation regime, fluid flow and pattern formation of sessile droplets. Under different experimental conditions, various deposition patterns can be formed. The existing theoretical approaches are able to predict fluid dynamics, particle motion and deposition patterns in the particular cases. On the basis of further understanding of the effects of fluid dynamics and particle motion, the desirable patterns can be obtained with appropriate experimental regulations.     

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.     

Marangoni effect reverses coffee-ring depositions

We show here both experimentally and theoretically that the formation of "coffee-ring" deposits observed at the edge of drying water droplets requires not only a pinned contact line but also suppression of Marangoni flow. For simple organic fluids, deposition actually occurs preferentially at the center of the droplet, due to a recirculatory flow driven by surface-tension gradients produced by the latent heat of evaporation. The manipulation of this Marangoni flow in a drying droplet should allow one in principle to control and redirect evaporation-driven deposition and assembly of colloids and other materials.     

Passive droplet trafficking at microfluidic junctions under geometric and flow asymmetries

When droplets enter a junction they sort to the channel with the highest flow rate at that instant. Transport is regulated by a discrete time-delayed feedback that results in a highly periodic behavior where specific patterns can continue to cycle indefinitely. Between these highly ordered regimes are chaotic structures where no pattern is evident. Here we develop a model that describes droplet sorting under various asymmetries: branch geometry (length, cross-section), droplet resistance and pressures. First, a model is developed based on the continuum assumption and then, with the assistance of numerical simulations, a discrete model is derived to predict the length and composition of the sorting pattern. Furthermore we derive all unique sequences that are possible for a given distribution and develop a preliminary estimation of why chaotic regimes form. The model is validated by comparing it to numerical simulations and results from microfluidic experiments in PDMS chips with good agreement.     

Controlling the Localization of Liquid Droplets in Polymer Matrices by Evaporative Lithography

Localized inclusions of liquids provide solid materials with many functions, such as self‐healing, secretion, and tunable mechanical properties, in a spatially controlled mode. However, a strategy to control the distribution of liquid droplets in solid matrices directly obtained from a homogeneous solution has not been reported thus far. Herein, we describe an approach to selectively localize liquid droplets in a supramolecular gel directly obtained from its solution by using evaporative lithography. In this process, the formation of droplet‐embedded domains occurs in regions of free evaporation where the non‐volatile liquid is concentrated and undergoes a phase separation to create liquid droplets prior to gelation, while a homogeneous gel matrix is formed in the regions of hindered evaporation. The different regions of a coating with droplet embedment patterns display different secretion abilities, enabling the control of the directional movement of water droplets.     

Microchannel emulsification: from computational fluid dynamics to predictive analytical model

Emulsion droplet formation was investigated in terrace-based microchannel systems that generate droplets through spontaneous Laplace pressure driven snap-off. The droplet formation mechanism was investigated through high-speed imaging and computational fluid dynamics (CFD) simulation, and we found good agreement in the overall shape of the phases during droplet formation. An analytical model was derived from the insights that were gained from the CFD simulations, which describes the droplet diameter as a function of applied pressure. The analytical model covers the influence of both process parameters and geometry of the terrace well and can be used for fast optimization and evaluation studies.     

Unconventional multiple ring structure formation from evaporation-induced self-assembly of polymers

The formation of multiring deposits of poly(2-vinylpyridine) (P2VP) from the evaporation of a P2VP-(2,6-lutidine + water) drop on a glass substrate does not conform to the conventional pinning-depinning mechanism. Instead, ringlike deposits are formed when the droplet undergoes several cycles of spreading and receding where, for each spreading event, a P2VP ridge is formed at the contact line when the polymer flows toward the outward advancing edge. The complex interplay between an outward solutal-Marangoni flow due to a higher concentration of the polymer at the contact line and an inward solvent-Marangoni flow arising from the differences in volatilities and surface tensions of the pure solvent components plays an important role in enhancing the droplet spreading rate. The newly discovered surface patterning mechanism has important implications in the development of novel techniques for inducing self-assembly of functional materials from evaporating drops.     

Evaporation-induced particle microseparations inside droplets floating on a chip

We describe phenomena of colloidal particle transport and separation inside single microdroplets of water floating on the surface of dense fluorinated oil. The experiments were performed on microfluidic chips, where single droplets were manipulated with alternating electric fields applied to arrays of electrodes below the oil. The particles suspended in the droplets were collected in their top region during the evaporation process. Experimental results and numerical simulations show that this microsepration occurs as a result of a series of processes driven by mass and heat transfer. An interfacial tension gradient develops on the surface of the droplet as a result of the nonuniform temperature distribution during the evaporation. This gradient generates an internal convective Marangoni flow. The colloidal particles transported by the flow are collected in the top of the droplets by the hydrodynamic flux, compensating for evaporation through the exposed top surface. The internal flow pattern and temperature distribution within evaporating droplets were simulated using finite element calculations. The results of the simulation were consistent with experiments using tracer particles. Such microseparation processes can be used for on-chip synthesis of advanced particles and innovative microbioassays.     

Encapsulated droplets with metered and removable oil shells by electrowetting and dielectrophoresis

A water-core and oil-shell encapsulated droplet exhibits several advantages including enhanced fluidic manipulation, reduced biofouling, decreased evaporation, and simplified device packaging. However, obtaining the encapsulated droplet with an adjustable water-to-oil volume ratio and a further removable oil shell is not possible by reported techniques using manual pipetting or droplet splitting. We report a parallel-plate device capable of generation, encapsulation, rinsing, and emersion of water and/or oil droplets to achieve three major aims. The first aim of our experiments was to form encapsulated droplets by merging electrowetting-driven water droplets and dielectrophoresis-actuated oil droplets whose volumes were precisely controlled. 25 nL water droplets and 2.5 nL non-volatile silicone oil droplets with various viscosities (10, 100, and 1000 cSt) were individually created from their reservoirs to form encapsulated droplets holding different water-to-oil volume ratios of 10:1 and 2:1. Secondly, the driving voltages, evaporation rates, and biofouling of the precise encapsulated droplets were measured. Compared with the bare and immersed droplets, we found the encapsulated droplets (oil shells with lower viscosities and larger volumes) were driven at a smaller voltage or for a wider velocity range. In the dynamic evaporation tests, at a temperature of 20 ± 1 °C and relative humidity of 45 ± 3%, 10 cSt 10:1 and 2:1 encapsulated droplets were moved at the velocity of 0.25 mm s(-1) for 22 and 35 min until losing 16.6 and 17.5% water, respectively, while bare droplets followed the driving signal for only 6 min when 11.4% water was lost. Evaporation was further diminished at the rate of 0.04% min(-1) for a carefully positioned stationary encapsulated droplet. Biofouling of 5 μg ml(-1) FITC-BSA solution was found to be eliminated by the encapsulated droplet from the fluorescent images. The third aim of our research was to remove the oil shell by dissolving it in an on-chip rinsing reservoir containing hexane. After emersion from the rinsing reservoir, the bare droplet was restored as hexane rapidly evaporated. Removal of the oil shell would not only increase the evaporation of the core droplet when necessary, but also enhance the signal-to-noise ratio in the following detection steps.     

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.     

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.     

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.     

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.     

含盐胶体液滴的蒸发图案形成机理

研究了聚四氟乙烯(PTFE)胶粒与NaCl混合液滴的蒸发过程及其图案形成机理. 结果表明, PTFE颗粒对接触线具有强烈的钉扎作用, 胶体液滴蒸发伴有显著的“咖啡环”效应. 由于液滴中心液相区表面张力法向分力的作用, 使得凝胶区存在辐射状应力, 进而产生从液滴边缘向中心的辐射状裂纹, 裂纹数量随胶粒的体积分数增大而减少. NaCl与PTFE胶粒的混合液滴出现了复杂多样的蒸发图案. 盐的加入抑制了向外的毛细补偿流, 从而有利于获得宏观上厚度均匀的沉积膜. NaCl与PTFE胶粒耦合形成了凹凸不平的枝晶状形貌, 这可能是释放蒸发应力的结果.     

On the effect of marangoni flow on evaporation rates of heated water drops

In this letter we show that the Marangoni flow contribution to the evaporation rate of small heated water droplets resting on hot substrates is negligible. We compare data of evaporating droplet experiments with numerical results and assess the effect of Marangoni flow and its contribution to the evaporation process. We demonstrate that heat conduction inside these water droplets is sufficient to give an accurate estimate of evaporation rates. Although convection in evaporating water droplets remains an open problem, our aim in this study is to demonstrate that these effects can be neglected in the investigation of evaporation rate evaluation. It is worth noting that the presented results apply to volatile heated drops which might differ from spontaneously evaporating cases.     

Plateau Rayleigh instability simulation

The well-known phenomena of Plateau-Rayleigh instability has been simulated using computational fluid dynamics (CFD). The breakup of a liquid film into an array of droplets on a cylindrical element was simulated using a volume-of-fluid (VOF) solver and compared to experimental observations and existing theory. It is demonstrated that the VOF method can correctly predict the breakup of thins films into an array of either axisymmetric droplets or clam-shell droplets, depending on the surface energy. The existence of unrealistically large films is precluded. Droplet spacing was found to show reasonable agreement with theory. Droplet motion and displacement under fluid flow was also examined and compared to that in previous studies. It was found that the presence of air flow around the droplet does not influence the stable film thickness; however, it reduces the time required for droplet formation. Novel relationships for droplet displacement were derived from the results.     

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.     

Velocity of a Molecule Evaporated from a Water Nanodroplet: Maxwell–Boltzmann Statistics versus Non‐Ergodic Events

The velocity of a molecule evaporated from a mass‐selected protonated water nanodroplet is measured by velocity map imaging in combination with a recently developed mass spectrometry technique. The measured velocity distributions allow probing statistical energy redistribution in ultimately small water nanodroplets after ultrafast electronic excitation. As the droplet size increases, the velocity distribution rapidly approaches the behavior expected for macroscopic droplets. However, a distinct high‐velocity contribution provides evidence of molecular evaporation before complete energy redistribution, corresponding to non‐ergodic events.     

流动聚焦型微流控体系中的液滴的图案化排列和转变模式

流体在微流通道中形成剪切流场（低雷诺数）．不同于宏观体系,由于剪切力和表面张力的竞争作用,产生的液滴在微尺度下的微流通道中形成特殊的排列现象---周期性类似“晶格”排列现象．设计了新型流动聚焦型微流控芯片,分析研究在微流体系中液滴周期性图案化排列和转变机理性,液滴排列模式受两方面因素影响：水油两相的流速比值和微通道尺寸．当微通道宽度为250或300 μm时,液滴形成单层分散,双层和单层挤压排列．当微通道宽度为350 μm 时,液滴会形成单层分散到三层排列到双层挤压最后到单层挤压排列．当出口通道宽度增加到400 μm时,甚至出现了液滴四层排列的现象．同时研究了各个液滴排列模式的“转变点”.