Evaporation and fluid dynamics of a sessile drop of capillary size

Circulating Marangoni flows within droplets in smectic films

We present a theoretical study and numerical simulation of Marangoni convection within ellipsoidal isotropic droplets embedded in free-standing smectic films (FSSFs). The thermocapillary flows are analyzed for both isotropic droplets spontaneously formed in FSSF overheated above the bulk smectic-isotropic transition and oil lenses deposited on the surface of the smectic film. The realistic model for which the upper drop interface is free from the smectic layers, while at the lower drop surface the smectic layering persists is considered in detail. For isotropic droplets and oil lenses this leads effectively to a sticking of fluid motion at the border with a smectic shell. The above mentioned asymmetric configuration is realized experimentally when the temperature of the upper side of the film is higher than at the lower one. The full set of stationary solutions for Stokes stream functions describing the Marangoni convection flows within the ellipsoidal drops are derived analytically. The temperature distribution in the ellipsoidal drop and the surrounding air is determined in the frame of the perturbation theory. As a result, the analytical solutions for the stationary thermocapillary convection are obtained for different droplet ellipticity ratios and the heat conductivity of the liquid crystal and air. In parallel, the numerical hydrodynamic calculations of the thermocapillary motion in drops are made. Both analytical and numerical simulations predict the axially symmetric circulatory convection motion determined by the Marangoni effect at the droplet-free surface. Due to a curvature of the drop interface a temperature gradient along its free surface always exists. Thus, the thermocapillary convection within the ellipsoidal droplets in overheated FSSF is possible for the arbitrarily small Marangoni numbers. Possible experimental observations enabling the checking of our predictions are proposed.

Influence of fluid flows on electric double layers in evaporating colloidal sessile droplets

A model is developed for describing the transport of charged colloidal particles in an evaporating sessile droplet on the electrified metal substrate in the presence of a solvent flow. The model takes into account the electric charge of colloidal particles and small ions produced by electrolytic dissociation of the active groups on the colloidal particles and solvent molecules. We employ a system of self-consistent Poisson and Nernst-Planck equations for electric potential and average concentrations of colloidal particles and ions with the appropriate boundary conditions. The fluid dynamics, temperature distribution and evaporation process are described with the Navier-Stokes equations, equations of heat conduction and vapor diffusion in air, respectively. The developed model is used to carry out a first-principles numerical simulation of charged silica colloidal particle transport in an evaporating aqueous droplet. We find that electric double layers can be destroyed by a sufficiently strong fluid flow.

Controlling Droplet Marangoni Flows to Improve Microscopy-Based TB Diagnosis

In developing countries, the most common diagnostic method for tuberculosis (TB) is microscopic examination sputum smears. Current assessment requires time-intensive inspection across the microscope slide area, and this contributes to its poor diagnostic sensitivity of ≈50%. Spatially concentrating TB bacteria in a smaller area is one potential approach to improve visual detection and potentially increase sensitivity. We hypothesized that a combination of magnetic concentration and induced droplet Marangoni flow would spatially concentrate Mycobacterium tuberculosis on the slide surface by preferential deposition of beads and TB–bead complexes in the center of an evaporating droplet. To this end, slide substrate and droplet solvent thermal conductivities and solvent surface tension, variables known to impact microfluidic flow patterns in evaporating droplets, were varied to select the most appropriate slide surface coating. Optimization in a model system used goniometry, optical coherence tomography, and microscope images of the final deposition pattern to observe the droplet flows and maximize central deposition of 1 μm fluorescent polystyrene particles and 200 nm nanoparticles (NPs) in 2 μL droplets. Rain-X^® polysiloxane glass coating was identified as the best substrate material, with a PBS-Tween droplet solvent. The use of smaller, 200 nm magnetic NPs instead of larger 1 μm beads allowed for bright field imaging of bacteria. Using these optimized components, we compared standard smear methods to the Marangoni-based spatial concentration system, which was paired with magnetic enrichment using iron oxide NPs, isolating M. bovis BCG (BCG) from samples containing 0 and 10³ to 10⁶ bacilli/mL. Compared to standard smear preparation, paired analysis demonstrated a combined volumetric and spatial sample enrichment of 100-fold. With further refinement, this magnetic/Marangoni flow concentration approach is expected to improve whole-pathogen microscopy-based diagnosis of TB and other infectious diseases.

Applying droplets and films in evaporative lithography

This review covers experimental results of evaporative lithography and analyzes existing mathematical models of this method. Evaporating droplets and films are used in different fields, such as cooling of heated surfaces of electronic devices, diagnostics in health care, creation of transparent conductive coatings on flexible substrates, and surface patterning. A method called evaporative lithography emerged after the connection between the coffee ring effect taking place in drying colloidal droplets and naturally occurring inhomogeneous vapor flux densities from liquid-vapor interfaces was established. Essential control of the colloidal particle deposit patterns is achieved in this method by producing ambient conditions that induce a nonuniform evaporation profile from the colloidal liquid surface. Evaporative lithography is part of a wider field known as "evaporative-induced self-assembly" (EISA). EISA involves methods based on contact line processes, methods employing particle interaction effects, and evaporative lithography. As a rule, evaporative lithography is a flexible and single-stage process with such advantages as simplicity, low price, and the possibility of application to almost any substrate without pretreatment. Since there is no mechanical impact on the template in evaporative lithography, the template integrity is preserved in the process. The method is also useful for creating materials with localized functions, such as slipperiness and self-healing. For these reasons, evaporative lithography attracts increasing attention and has a number of noticeable achievements at present. We also analyze limitations of the approach and ways of its further development.

Joint effect of advection, diffusion, and capillary attraction on the spatial structure of particle depositions from evaporating droplets

A simplified model is developed, which allows us to perform computer simulations of the particles transport in an evaporating droplet with a contact line pinned to a hydrophilic substrate. The model accounts for advection in the droplet, diffusion, and particle attraction by capillary forces. On the basis of the simulations, we analyze the physical mechanisms of forming of individual chains of particles inside the annular sediment. The parameters chosen correspond to the experiments of Park and Moon [Langmuir 22, 3506 (2006)LANGD50743-746310.1021/la053450j], where an annular deposition and snakelike chains of colloid particles have been identified. The annular sediment is formed by advection and diffusion transport. We find that the close packing of the particles in the sediment is possible if the evaporation time exceeds the characteristic time of diffusion-based ordering. We show that the chains are formed by the end of the evaporation process due to capillary attraction of particles in the region bounded by a fixing radius, where the local droplet height is comparable to the particle size. At the beginning of the evaporation, the annular deposition is shown to expand faster than the fixing radius moves. However, by the end of the process, the fixing radius rapidly outreaches the expanding inner front of the ring. The snakelike chains are formed at this final stage when the fixing radius moves toward the symmetry axis.

Multiscale assembly of solution-processed organic electronics: the critical roles of confinement, fluid flow, and interfaces

Organic semiconducting small molecules and polymers provide a rich phase space for investigating the fundamentals of molecular and hierarchical assembly. Stemming from weak intermolecular interactions, their assembly sensitively depends on processing conditions, which in turn drastically modulate their electronic properties. Much work has gone into molecular design strategies that maximize intermolecular interactions and encourage close packing. Less understood, however, is the non-equilibrium assembly that occurs during the fabrication process (especially solution coating and printing) which is critical to determining thin film morphology across length scales. This encompasses polymorphism and molecular packing at molecular scale, assembly of π-bonding aggregates at the tens of nanometers scale, and the formation of domains at the micron-millimeter device scale. Here, we discuss three phenomena ubiquitous in solution processing of organic electronic thin films: the confinement effect, fluid flows, and interfacial assembly and the role they play in directing assembly. This review focuses on the mechanistic understanding of how assembly outcomes couple closely to the solution processing environment, supported by salient examples from the recent literature.

Boundary conditions for a one-sided numerical model of evaporative instabilities in sessile drops of ethanol on heated substrates

The work is focused on obtaining boundary conditions for a one-sided numerical model of thermoconvective instabilities in evaporating pinned sessile droplets of ethanol on heated substrates. In the one-sided model, appropriate boundary conditions for heat and mass transfer equations are required at the droplet surface. Such boundary conditions are obtained in the present work based on a derived semiempirical theoretical formula for the total droplet's evaporation rate, and on a two-parametric nonisothermal approximation of the local evaporation flux. The main purpose of these boundary conditions is to be applied in future three-dimensional (3D) one-sided numerical models in order to save a lot of computational time and resources by solving equations only in the droplet domain. Two parameters, needed for the nonisothermal approximation of the local evaporation flux, are obtained by fitting computational results of a 2D two-sided numerical model. Such model is validated here against parabolic flight experiments and the theoretical value of the total evaporation rate. This study combines theoretical, experimental, and computational approaches in convective evaporation of sessile droplets. The influence of the gravity level on evaporation rate and contributions of different mechanisms of vapor transport (diffusion, Stefan flow, natural convection) are shown. The qualitative difference (in terms of developing thermoconvective instabilities) between steady-state and unsteady numerical approaches is demonstrated.

Marangoni Flow Induced Evaporation Enhancement on Binary Sessile Drops

The evaporation processes of pure water, pure 1-butanol, and 5% 1-butanol aqueous solution drops on heated hydrophobic substrates are investigated to determine the effect of temperature on the drop evaporation behavior. The evolution of the parameters (contact angle, diameter, and volume) during evaporation measured using a drop shape analyzer and the infrared thermal mapping of the drop surface recorded by an infrared camera were used in investigating the evaporation process. The pure 1-butanol drop does not show any thermal instability at different substrate temperatures, while the convection cells created by the thermal Marangoni effect appear on the surface of the pure water drop from 50 °C. Because 1-butanol and water have different surface tensions, the infrared video of the 5% 1-butanol aqueous solution drop shows that the convection cells are generated by the solutal Marangoni effect at any substrate temperature. Furthermore, when the substrate temperature exceeds 50 °C, coexistence of the thermal and solutal Marangoni flows is observed. By analyzing the relation between the ratio of the evaporation rate of pure water and 1-butanol aqueous solution drops and the Marangoni number, a series of empirical equations for predicting the evaporation rates of pure water and 1-butanol aqueous solution drops at the initial time as well as the equations for the evaporation rate of 1-butanol aqueous solution drop before the depletion of alcohol are derived. The results of these equations correspond fairly well to the experimental data.

Resolving an ostensible inconsistency in calculating the evaporation rate of sessile drops

This paper resolves an ostensible inconsistency in the literature in calculating the evaporation rate for sessile drops in a quiescent environment. The earlier models in the literature have shown that adapting the evaporation flux model for a suspended spherical drop to calculate the evaporation rate of a sessile drop needs a correction factor; the correction factor was shown to be a function of the drop contact angle, i.e. f(θ). However, there seemed to be a problem as none of the earlier models explicitly or implicitly mentioned the evaporation flux variations along the surface of a sessile drop. The more recent evaporation models include this variation using an electrostatic analogy, i.e. the Laplace equation (steady-state continuity) in a domain with a known boundary condition value, or known as the Dirichlet problem for Laplace's equation. The challenge is that the calculated evaporation rates using the earlier models seemed to differ from that of the recent models (note both types of models were validated in the literature by experiments). We have reinvestigated the recent models and found that the mathematical simplifications in solving the Dirichlet problem in toroidal coordinates have created the inconsistency. We also proposed a closed form approximation for f(θ) which is valid in a wide range, i.e. 8°≤θ≤131°. Using the proposed model in this study, theoretically, it was shown that the evaporation rate in the CWA (constant wetted area) mode is faster than the evaporation rate in the CCA (constant contact angle) mode for a sessile drop.

Following the Assembly of Iron Oxide Nanocubes by Video Microscopy and Quartz Crystal Microbalance with Dissipation Monitoring

We have studied the growth of ordered arrays by evaporation-induced self-assembly of iron oxide nanocubes with edge lengths of 6.8 and 10.1 nm using video microscopy (VM) and quartz crystal microbalance with dissipation monitoring (QCM-D). Ex situ electron diffraction of the ordered arrays demonstrates that the crystal axes of the nanocubes are coaligned and confirms that the ordered arrays are mesocrystals. Time-resolved video microscopy shows that growth of the highly ordered arrays at slow solvent evaporation is controlled by particle diffusion and can be described by a simple growth model. The growth of each mesocrystal depends only on the number of nanoparticles within the accessible region irrespective of the relative time of formation. The mass of the dried mesocrystals estimated from the analysis of the bandwidth-shift-to-frequency-shift ratio correlates well with the total mass of the oleate-coated nanoparticles in the deposited dispersion drop.

Evaporation Flux Distribution of Drops on a Hydrophilic or Hydrophobic Flat Surface by Molecular Simulations

The evaporation flux distribution of sessile drops is investigated by molecular dynamic simulations. Three evaporating modes are classified, including the diffusion dominant mode, the substrate heating mode, and the environment heating mode. Both hydrophilic and hydrophobic drop-substrate interactions are considered. To count the evaporation flux distribution, which is position dependent, we proposed an azimuthal-angle-based division method under the assumption of spherical crown shape of drops. The modeling results show that the edge evaporation, i.e., near the contact line, is enhanced for hydrophilic drops in all the three modes. The surface diffusion of liquid molecular absorbed on solid substrate for hydrophilic cases plays an important role as well as the space diffusion on the enhanced evaporation rate at the edge. For hydrophobic drops, the edge evaporation flux is higher for the substrate heating mode, but lower than elsewhere of the drop for the diffusion dominant mode; however, a nearly uniform distribution is found for the environment heating mode. The evidence shows that the temperature distribution inside drops plays a key role in the position-dependent evaporation flux.

Heat Transfer through a Condensate Droplet on Hydrophobic and Nanostructured Superhydrophobic Surfaces

Understanding the fundamental mechanisms governing vapor condensation on nonwetting surfaces is crucial to a wide range of energy and water applications. In this paper, we reconcile classical droplet growth modeling barriers by utilizing two-dimensional axisymmetric numerical simulations to study individual droplet heat transfer on nonwetting surfaces (90° < θa < 170°). Incorporation of an appropriate convective boundary condition at the liquid-vapor interface reveals that the majority of heat transfer occurs at the three phase contact line, where the local heat flux can be up to 4 orders of magnitude higher than at the droplet top. Droplet distribution theory is incorporated to show that previous modeling approaches underpredict the overall heat transfer by as much as 300% for dropwise and jumping-droplet condensation. To verify our simulation results, we study condensed water droplet growth using optical and environmental scanning electron microscopy on biphilic samples consisting of hydrophobic and nanostructured superhydrophobic regions, showing excellent agreement with the simulations for both constant base area and constant contact angle growth regimes. Our results demonstrate the importance of resolving local heat transfer effects for the fundamental understanding and high fidelity modeling of phase change heat transfer on nonwetting surfaces.

Thermocapillarity in Microfluidics-A Review

This paper reviews the past and recent studies on thermocapillarity in relation to microfluidics. The role of thermocapillarity as the change of surface tension due to temperature gradient in developing Marangoni flow in liquid films and conclusively bubble and drop actuation is discussed. The thermocapillary-driven mass transfer (the so-called Benard-Marangoni effect) can be observed in liquid films, reservoirs, bubbles and droplets that are subject to the temperature gradient. Since the contribution of a surface tension-driven flow becomes more prominent when the scale becomes smaller as compared to a pressure-driven flow, microfluidic applications based on thermocapillary effect are gaining attentions recently. The effect of thermocapillarity on the flow pattern inside liquid films is the initial focus of this review. Analysis of the relation between evaporation and thermocapillary instability approves the effect of Marangoni flow on flow field inside the drop and its evaporation rate. The effect of thermocapillary on producing Marangoni flow inside drops and liquid films, leads to actuation of drops and bubbles due to the drag at the interface, mass conservation, and also gravity and buoyancy in vertical motion. This motion can happen inside microchannels with a closed multiphase medium, on the solid substrate as in solid/liquid interaction, or on top of a carrier liquid film in open microfluidic systems. Various thermocapillary-based microfluidic devices have been proposed and developed for different purposes such as actuation, sensing, trapping, sorting, mixing, chemical reaction, and biological assays throughout the years. A list of the thermocapillary based microfluidic devices along with their characteristics, configurations, limitations, and improvements are presented in this review.

Control of stain geometry by drop evaporation of surfactant containing dispersions

Control of stain geometry by drop evaporation of surfactant containing dispersions is an important topic of interest because it plays a crucial role in many applications such as forming templates on solid surfaces, in ink-jet printing, spraying of pesticides, micro/nano material fabrication, thin film coatings, biochemical assays, deposition of DNA/RNA micro-arrays, and manufacture of novel optical and electronic materials. This paper presents a review of the published articles on the diffusive drop evaporation of pure liquids (water), the surfactant stains obtained from evaporating drops that do not contain dispersed particles and deposits obtained from drops containing polymer colloids and carbon based particles such as carbon nanotubes, graphite and fullerenes. Experimental results of specific systems and modeling attempts are discussed. This review also has some special subtopics such as suppression of coffee-rings by surfactant addition and "stick-slip" behavior of evaporating nanosuspension drops. In general, the drop evaporation process of a surfactant/particle/substrate system is very complex since dissolved surfactants adsorb on both the insoluble organic/inorganic micro/nanoparticles in the drop, on the air/solution interface and on the substrate surface in different extends. Meanwhile, surfactant adsorbed particles interact with the substrate giving a specific contact angle, and free surfactants create a solutal Marangoni flow in the drop which controls the location of the particle deposition together with the rate of evaporation. In some cases, the presence of a surfactant monolayer at the air/solution interface alters the rate of evaporation. At present, the magnitude of each effect cannot be predicted adequately in advance and consequently they should be carefully studied for any system in order to control the shape and size of the final deposit.

Analysis of the effects of evaporative cooling on the evaporation of liquid droplets using a combined field approach

During liquid evaporation, the equations for the vapor concentration in the atmosphere and for the temperature in the liquid are coupled and must be solved in an iterative manner. In the present paper, a combined field approach which unifies the coupled fields into one single hybrid field and thus makes the iteration unnecessary is proposed. By using this approach, the influences of the evaporative cooling on the evaporation of pinned sessile droplets are investigated, and its predictions are found in good agreement with the previous theoretical and experimental results. A dimensionless number Ec which can evaluate the strength of the evaporative cooling is then introduced, and the results show that both the evaporation flux along the droplet surface and the total evaporation rate of the droplet decrease as the evaporative cooling number Ec increases. For drying droplets, there exists a critical value Ec_Crit below which the evaporative cooling effect can be neglected and above which the significance of the effect increases dramatically. The present work may also have more general applications to coupled field problems in which all the fields have the same governing equation.

Monitoring sessile droplet evaporation on a micromechanical device

A bulk acoustic mode micro-electro-mechanical dual resonator platform is utilised to study the evaporation of sub-microliter water droplets from the surface of the resonator. An analytical formulation for the observed frequency shift and the measure dependence of resonant frequency on the modes of evaporation which is consistent with the optically derived data. The resonators access only a thin layer of the liquid through shear contact and, hence, the response is not affected by the bulk mass of the droplet to first order. A relationship between the droplet contact area and the elapsed time was established for the evaporation process and is used to derive a value of the diffusion coefficient of water in air that is found to be in reasonable agreement with literature values. This work introduces a new tool for the electro-mechanical monitoring of droplet evaporation with relevance to applications such as biosensing in liquid samples of sub-microliter volumes.

Temperature distribution along the surface of evaporating droplets

The surface temperature can significantly affect the flow field of drying droplets. Most previous studies assumed a monotonic temperature variation along the droplet surface. However, the present analyses indicate that a nonmonotonic spatial distribution of the surface temperature should occur. Three different patterns of the surface temperature distribution may appear during the evaporation process of liquid droplets: (i) the surface temperature increases monotonically from the center to the edge of the droplet; (ii) the surface temperature exhibits a nonmonotonic spatial distribution along the droplet surface; (iii) the surface temperature decreases monotonically from the center to the edge of the droplet. These surface temperature distributions can be explained by combining the evaporative cooling at the droplet surface and the heat conduction across the substrate and the liquid. Furthermore, a "phase diagram" for the distribution of the surface temperature is introduced and the effect of the spatial temperature distribution along the droplet surface on the flow structure of the droplet is discussed. The results may provide a better understanding of the Marangoni effect of drying droplets and provide a potential way to control evaporation-driven deposition as well as the assembly of colloids and other materials.

Convective flows in evaporating sessile droplets

The evaporation rate and internal convective flows of a sessile droplet with a pinned contact line were formulated and investigated numerically. We developed and analyzed a unified numerical model that includes the effects of temperature, droplet volume, and contact angle on evaporation rate and internal flows. The temperature gradient on the air/liquid interface causes an internal flow due to Marangoni stress, which provides good convective mixing within the droplet, depending upon Marangoni number. As the droplet volume decreases, the thermal gradient becomes smaller and the Marangoni flow becomes negligible. Simultaneously, as the droplet height decreases, evaporation-induced flow creates a large jet-like flow radially toward the contact line. For a droplet containing suspended particles, this jet-like convective flow carries particles toward the contact line and deposits them on the surface, forming the so-called "coffee ring stain". In addition, we reported a simple polynomial correlation for dimensionless evaporation time as a function of initial contact angle of the pinned sessile droplet which agrees well with the previous experimental and numerical results.

Biosensor design based on Marangoni flow in an evaporating drop

Effective point-of-care diagnostics require a biomarker detection strategy that is low-cost and simple-to-use while achieving a clinically relevant limit of detection. Here we report a biosensor that uses secondary flows arising from surface Marangoni stresses in an evaporating drop to concentrate target-mediated particle aggregates in a visually detectable spot. The spot size increases with increasing target concentration within the dynamic range of the assay. The particle deposition patterns are visually detectable and easily measured with simple optical techniques. We use optical coherence tomography to characterize the effect of cross-sectional flow fields on the motion of particles in the presence and absence of target (aggregated and non-aggregated particles, respectively). We show that choice of substrate material and the presence of salts and glycerol in solution promote the Marangoni-induced flows that are necessary to produce signal in the proposed design. These evaporation-driven flows generate signal in the assay on a PDMS substrate but not substrates with greater thermal conductivity like indium tin oxide-coated glass. In this proof-of-concept design we use the M13K07 bacteriophage as a model target and 1 μm-diameter particles surface functionalized with anti-M13 monoclonal antibodies. Using standard microscopy-based techniques to measure the final spot size, the assay has a calculated limit-of-detection of approximately 100 fM. Approximately 80% of the maximum signal is generated within 10 minutes of depositing a 1 μL drop of reacted sample on PDMS enabling a relatively quick time-to-result.

Inkjet patterning of multiline intersections for wirings in printed electronics

Inkjet printed electronics using thermo-curable liquid inks exhibit particular geometrical characteristics in terms of regularity. This article presents a morphological analysis for inkjet printed multi line intersections that are critical structures for building circuits. We studied thin-film structures of silver conductive ink and printed by inkjet technology. Instability of the ink during printing causes the thickness irregularity of vertex, normally with peaks at these areas. We propose the usage of specific patterns for intersections as thickness regularity compensations. The results show that some patterns help to reduce this instability and improve the thickness regularity of intersections morphology.

Fingering inside the coffee ring

Colloidal droplets including micro- and nanoparticles generally leave a ringlike stain, called the "coffee ring," after evaporation. We show that fingering emerges during evaporation inside the coffee ring, resulting from a bidispersed colloidal mixture of micro- and nanoparticles. Microscopic observations suggest that finger formation is driven by competition between the coffee-ring and Marangoni effects, especially when the inward Marangoni flow is overwhelmed by the outward coffee-ring flow. This finding could help to understand the variety of the final deposition patterns of colloidal droplets.

High-resolution epifluorescence and time-of-flight secondary ion mass spectrometry chemical imaging comparisons of single DNA microarray spots

DNA microarray assay performance is commonly compromised by spot-spot probe and signal variations as well as heterogeneity within printed microspots. Accurate metrics for captured DNA target signal rely upon uniform spot distribution of both probe and target DNA to yield reliable hybridized signal. While often presumed, this is neither easily achieved nor often proven experimentally. High-resolution imaging techniques were used to determine spot heterogeneity in identical DNA array microspots comprising varied ratios of unlabeled and dye-labeled DNA probes contact-printed onto commercial arraying surfaces. Epifluorescence imaging data for individual array microspots were correlated with time-of-flight secondary ion mass spectrometry (TOF-SIMS) chemical state imaging of the same spots. Epifluorescence imaging intensity distinguished varying DNA density distributed both within a given spot and from spot to spot. TOF-SIMS chemical analysis confirmed these heterogeneous printed DNA distributions by tracking bound Cy3 dye, DNA base, and phosphate specific ion fragments often correlating to fluorescence patterns within identical spots. TOF-SIMS ion fragments originating from probe DNA and Cy3 dye are enriched in microspot centers, correlating with high fluorescence intensity regions. Both TOF-SIMS and epifluorescence support Marangoni flow effects on spot drying, with high-density DNA-Cy3 located in spot centers and nonhomogeneous DNA distribution within printed spots. Microspot image dimensional analysis results for DNA droplet spreading show differing DNA densities across printed spots. The study directly supports different DNA probe chemical and spatial microenvironments within spots that yield spot-spot signal variations known to affect DNA target hybridization efficiencies and kinetics. These variations critically affect probe-target duplex formation and DNA array signal generation.

Evaporative micro-particle self assembly influenced by capillary evacuation

As evaporation does not incur energy introduction, the droplet coffee-stain patterning approach is attractive for biochemical tests conducted in the field or in third world environments. A practical strategy uses chemically functionalized microbeads for the coffee stain deposition process. From an application perspective, it will be necessary to minimize the coffee stain deposition time, as evaporation, depending on the volume of the droplet, can be a slow process. The introduction of a porous media will generate a capillary flow (or wicking) that removes any remnant liquid in the droplet, thus permitting it to be done inexpensively and in the field. Using optical profilometry, we were able to establish that polystyrene microspheres developed more copious and defined single ring coffee depositions than silica of the same size and concentration in a suspension. In analyzing the droplet capillary evacuation process with a porous media, we found the liquid bridge formed during the later stages to rupture and leave behind some liquid material for a second stage evaporation process. This was responsible for a two ring structure that was more visible with silica microspheres. A high degree of hysteresis of the contact angle was found to develop at the contact line in which values below 5° could be achieved. Dynamic observations showed the copious and dense packing of polystyrene particles to be more resistant to ring break up from the evacuation flow. Nevertheless, erosion of the back array portions of the ring was evident notwithstanding either type of microsphere used.

Hidden cavity formations by nanocrystalline self-assembly on various substrates with different hydrophobicities

The effect of surface hydrophobicity is examined in the formation of hidden complex cavities during evaporation-induced nanocrystalline self-assembly taking place on three different substrates bearing different levels of hydrophobicity, namely, cover glass (CG), a gold thin film (Au), and a polystyrene dish (PS). It turns out that the DLVO theory, the relative thermal conductivities between the substrate and nanofluids, and the relationship between the evaporation and the radial outflow motions of nanoparticles comprehensively explain why the number of cavity cells is proportional to nanoparticle concentration and inversely proportional to surface hydrophobicity.

Controlled orientation and alignment in films of single-walled carbon nanotubes using inkjet printing

An inkjet printing procedure for depositing films of carbon nanotubes (CNTs) that exhibit a very high degree of long-range mutual alignment as well as a controlled orientation with respect to the printed geometry is presented. CNT self-assembly was induced by the intrinsic lyotropic liquid crystallinity of CNT suspensions. Sufficient concentrations are reached by matching the inkjet deposition rate to the numerically modeled local evaporation rate of the printed feature and enable the CNT suspension to be printed using standard inkjet printing. Surface alignment was verified using scanning electron microscopy (SEM) and polarized light microscopy. In addition, the bulk morphology was investigated and found to be composed of stacked planar layers that did not necessarily have the same long-range orientation found on the surface. The bulk morphology was characterized by removing layers through an elastomeric peeling process and by observing cross sections of the films using SEM. CNT concentration and length were spanned experimentally, and it was found that very short and very long CNTs as well as low concentration suspensions did not yield long-range alignment.

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.

X-ray-induced water vaporization

We present quantitative evidence for x-ray-induced water vaporization: water is vaporized at a rate of 5.5 pL/s with the 1-Å-wavelength x-ray irradiation of ~0.1 photons per Å(2); moreover, water vapor is reversibly condensed during pauses in irradiation. This result fundamentally suggests that photoionization induces vaporization. This phenomenon is attributed to surface-tension reduction by ionization and would be universally important in radiological and electrohydrodynamic situations.

Stability of evaporating water when heated through the vapor and the liquid phases

The stability of a water layer of uniform thickness held in a two-dimensional container of finite or semi-infinite extent is examined using linear stability theory. The liquid-vapor interface can be heated both through the liquid and through the vapor, as previously experimentally reported. The need to introduce a heat transfer coefficient is eliminated by introducing statistical rate theory (SRT) to predict the evaporation flux. There are no fitting or undefined parameters in the expression for the evaporation flux. The energy transport is parametrized in terms of the evaporation number, Eev, that for a given experimental circumstance can be predicted. The critical Marangoni number for the finite, Macf, and for the semi-infinite system, Mac(infinity), can be quantitatively predicted. Experiments in which water evaporated from a stainless-steel funnel and from a polymethyl methacrylate (PMMA) funnel into its vapor have been previously reported. Marangoni convection was observed in the experiments that used the stainless-steel funnel but not with the PMMA funnel even though the Marangoni number for the PMMA funnel was more than 27,000. The SRT-based stability theory indicates that the critical value of the Marangoni number for the experiments with the PMMA funnel was greater than the experimental value of the Marangoni number in each case; thus, no Marangoni convection was predicted to result from an instability. The observed convection with the stainless-steel funnel resulted from a temperature gradient imposed along the interface.

Criterion for reversal of thermal Marangoni flow in drying drops

The thermal Marangoni flow induced by nonuniform surface temperature has been widely invoked to interpret the deposition pattern from drying drops. The surface temperature distribution of a drying droplet, although being crucial to the Marangoni flow, is still controversial. In this paper, the surface temperature in the drop central region is analyzed theoretically based on an asymptotic analysis on the heat transfer in such region, and a quantitative criterion is established for the direction of the surface temperature gradient and the direction of the induced Marangoni flow of drying drops. The asymptotic analysis indicates that these two directions will reverse at a critical contact angle, which depends not only on the relative thermal conductivities of the substrate and liquid, but also on the ratio of the substrate thickness to the contact-line radius of the droplet. The theory is corroborated experimentally and numerically, and may provide a potential means to control deposition patterns from drying droplets.