Fast evaporation of spreading droplets of colloidal suspensions

Numerical Analysis of the Dispersion and Deposition of Particles in Evaporating Sessile Droplets

Evaporating sessile droplets containing dispersed particles are used in different technological applications, such as 3D printing, biomedicine, and micromanufacturing, where an accurate prediction of both the dispersion and deposition of the particles is important. Furthermore, the interaction between the droplet and the substrate must be taken into account: the motion of the contact line, in particular, must be modeled carefully. To this end, studies have typically been limited to either pinned or moving contact lines to simplify the underlying mathematical models and numerical methods, neglecting the fact that both scenarios are observed during the evaporation process. Here, a numerical algorithm considering both contact line regimes is proposed whereby the regimes are distinguished by predefined threshold contact angles. After a detailed validation, this new algorithm is applied to study the influence of both regimes on the dispersion and deposition of particles in an evaporating sessile droplet. In particular, the presented analysis focuses on the influence of (i) the contact line motion characteristics by varying the limiting contact angle and spreading speed, (ii) the Marangoni number, characterizing the importance of thermocapillarity, (iii) the evaporation number, which quantifies the importance of evaporation, (iv) the Damköhler number, a measure of the particle deposition rate, and (v) the Peclet number, which compares the convection and diffusion of the particle concentration. When thermocapillarity becomes dominant or the limiting contact angle is larger, the particle accumulation near the contact line decreases, which, in turn, means that more particles are deposited near the center of the droplet. In contrast, increasing the evaporation number supports particle accumulation near the contact line, while a larger Damköhler number and/or smaller Peclet number yield more uniform final deposition patterns. Finally, a larger characteristic speed of spreading results in fewer particles being deposited at the center of the droplet.

Quantifying the Microstructure of Dried Deposits Using Height-Height Correlation Function

Colloidal self-assembly has garnered significant attention in recent research, owing to applications in medical and engineering domains. Understanding the arrangement of particles in self-assembled systems is crucial for comprehending the underlying physics and synthesizing complex nano- and microscale structures. In this study, we introduce a novel methodology for analyzing the spatial distribution of particles in colloidal assemblies, focusing specifically on quantifying the microstructure of deposits formed by the evaporation of colloidal particle-laden drops. Utilizing a height-height correlation-function-based approach, we quantify variations in the height profile of deposits in radial and azimuthal directions. This approach enables the classification of the patterns into typical examples encountered in an evaporation-driven assembly. The method is demonstrated to be robust for quantifying synthetic and experimentally obtained deposit patterns, exhibiting excellent agreement in the estimated parameters. The mapping developed between pattern morphology and the quantitative measures introduced in this work may be used in a variety of applications including disease diagnosis as well as in developing pattern recognition tools.

Joint Experimental and Theoretical Study on Deposition Morphologies in Polymer Sessile Droplets

Although past experimental and theoretical research has made substantial progress in understanding evaporation behaviors in various suspensions, the fundamental mechanism for polymer sessile droplets is still lacking. One critical effect is the molecular weight on the evaporation behaviors. Here, systematic experiments are carried out to investigate the evaporation behavior of polymer droplets under the effects of polymer concentration, evaporation rate, and especially molecular weight. We obtain polymer films with various morphologies with molecular weights ranging from 2 orders of magnitude to 4 orders of magnitude and polymer concentration across 4 orders of magnitude. We further develop a theoretical model based on the Onsager principle to explain the evaporation mechanism from a dynamic perspective. Analysis indicates that increasing molecular weight or polymer concentration enhances the contact angle hysteresis and slows down the evaporation, resulting in the transition from multiring to coffee ring and eventually to uniform films. The findings offer a guideline for achieving the desired deposition patterns via droplet processing techniques.

Optical Anisotropy and Dimple Formation on Films Formed after Drying of Gelatinized Starch Solution Droplets

We study the microstructures in the drying droplets of gelatinized starch solutions on a flat substrate. Cryogenic scanning electron microscopy studies on the vertical cross-section of these drying droplets for the first time reveal a relatively thinner solid elastic crust of uniform thickness at the free surface, an intermediate mesh region below the crust, and an inner core of a cellular network structure made of starch nanoparticles. We find that the deposited circular films formed after drying are birefringent and azimuthally symmetric with a dimple at their center. We propose that the dimple formation in our sample occurs due to the evaporation-induced stress on the gel network structure in the drying droplet. The polarizing optical microscopic studies show that these films are optically uniaxial at their center and increasingly biaxial away from the center.

Modeling and Experiments of Droplet Evaporation with Micro or Nano Particles in Coffee Ring or Coffee Splat

Experimental and numerical experiments were carried out to study the coffee rings or coffee splats formed by droplet evaporation with micro or nano polystyrene sphere particles (D_p = 10 μm or 100 nm). Particle image velocimetry (PIV) and a high-resolution camera were used in this experiment, along with a temperature-controlled heater and a data-acquisition computer. The results showed that a nano particle could form a homogeneous coffee splat, instead of the common coffee ring formed when using micro particles. In order to account for this phenomenon, this paper developed a complex multiphase model, one which included the smooth particle hydrodynamics (SPH) fluid model coupled with the van der Waals equation of state for droplet evaporation, the rigid particle model of finite-size micro particles, and the point-particle model of the nanometer particles. The numerical simulation was operated on a GPU-based algorithm and tested by four validation cases. A GPU could calculate 533 times the speed of a single-core CPU for about 300,000 particles. The results showed that, for rigid solid particles, the forms emerged spontaneously on the wall, and their structure was mainly affected by the boundary wettability, and less affected by the fluid flow and thermal condition. When the wall temperature was low, it was easier for the particles to be deposited on the contact line. At high wall temperature, the coffee ring effect would be weakened, and the particles were more likely to be deposited in the droplet center. The hydrophilic surface produced a larger coffee ring compared to the hydrophobic surface. The experimental and numerical results proved that particle size could play a significant role during the particle deposition, which may be a possible route for producing uniform-distributed and nano-structure coatings.

A simple approach for coffee-ring suppression yielding homogeneous drying patterns of ZnO and TiO2 nanoparticles

Evaporation-induced self-assembly in colloidal droplets is a method for organising nanoparticles on substrates, with various resulting patterns. The coffee-ring pattern is among the most common ones, but its non-uniformity limits its applicability, which led to efforts for developing coffee-ring suppression strategies. Considering the wide applicability of ZnO and TiO₂ nanoparticles, there is a high demand for practical means to deposit them as uniform films. Here, we present a simple approach for obtaining highly uniform thin films of ZnO and TiO₂ nanoparticles by drop-coating in ambient conditions, without using surfactants or other surface chemistry modifications. Disc-like films were obtained via a restricted evaporation achieved by covering the droplets with a lid during drying, seconded by the relatively high sedimentation rate of these nanoparticles. To better understand the assembly mechanism, the influence of suspension concentration, type and temperature of the substrate, droplet volume, colloid type, and evaporation rate were studied. The method allows preparing disc-like nanoparticle films with a good control over their diameter and thickness, onto different kinds of substrates (glass, Si, polyethylene terephthalate, polystyrene). By fabricating both two-dimensional lattices and custom disc patterns we highlight the versatility of this drop-coating method and its potential for, e.g., automatized serial production processes.

A facile post-assembly approach for the fabrication of non-close-packed gold nanocrystal arrays from binary nanocrystal superlattices

Here, we demonstrate a novel approach for fabricating non-close-packed gold nanocrystal arrays using facile one-step post-modification of a Cs₄PbBr₆-Au binary nanocrystal superlattice by electron beam etching of the perovskite phase. The proposed methodology can serve as a promising approach for the scalable preparation of a vast library of non-close-packed nanoparticulate superstructures with various morphologies composed of numerous colloidal nanocrystals.

Influence of Surface Roughness on Droplet Evaporation and Absorption: Insights into Experiments from Lubrication-Theory-Based Models

While solid substrates are often idealized as being perfectly smooth, all real surfaces possess some level of topographical and chemical heterogeneity. This heterogeneity can greatly influence droplet dynamics. Mathematical models based on lubrication theory that account for surface roughness reveal how topographical defects induce contact-line pinning and affect the deposition patterns of colloidal particles suspended in the droplet. Contact-line pinning profoundly changes the behavior of droplet evaporation on horizontal and inclined impermeable substrates and droplet absorption on horizontal permeable substrates. Models accounting for surface roughness yield predictions that are qualitatively consistent with experimental observations and also provide insight into the underlying physical mechanisms. These models are a foundation for the exploration of a rich array of problems concerning droplet dynamics which are of both fundamental and practical interest.

Transition from Dendritic to Cell-like Crystalline Structures in Drying Droplets of Fetal Bovine Serum under the Influence of Temperature

The desiccation of biofluid droplets leads to the formation of complex deposits which are morphologically affected by the environmental conditions, such as temperature. In this work, we examine the effect of substrate temperatures between 20 and 40 °C on the desiccation deposits of fetal bovine serum (FBS) droplets. The final dried deposits consist of different zones: a peripheral protein ring, a zone of protein structures, a protein gel, and a central crystalline zone. We focus on the crystalline zone showing that its morphological and topographical characteristics vary with substrate temperature. The area of the crystalline zone is found to shrink with increasing substrate temperature. Additionally, the morphology of the crystalline structures changes from dendritic at 20 °C to cell-like for substrate temperatures between 25 and 40 °C. Calculation of the thermal and solutal Bénard-Marangoni numbers shows that while thermal effects are negligible when drying takes place at 20 °C, for higher substrate temperatures (25-40 °C), both thermal and solutal convective effects manifest within the drying drops. Thermal effects dominate earlier in the evaporation process leading, we believe, to the development of instabilities and, in turn, to the formation of convective cells in the drying drops. Solutal effects, on the other hand, are dominant toward the end of drying, maintaining circulation within the cells and leading to crystallization of salts in the formed cells. The cell-like structures are considered to form because of the interplay between thermal and solutal convection during drying. Dendritic growth is associated with a thicker fluid layer in the crystalline zone compared to cell-like growth with thinner layers. For cell-like structures, we show that the number of cells increases and the area occupied by each cell decreases with temperature. The average distance between cells decreases linearly with substrate temperature.

An experimental and theoretical study of the inward particle drift in contact line deposits

The coffee ring effect, which refers to the formation of a ring-like deposit along the periphery of a dried particle laden sessile drop, is a commonly observed phenomenon. The migration of particles from the interior to the edge of a drying drop as a result of evaporation driven flow directed outwards, is well studied. In this article, we document the inward drift of a coffee stain, which is governed by the descent of the water-air interface of the drying drop due to solvent evaporation. A combination of experimental study and model predictions is undertaken to elucidate the effect of the diameter of particles in the drying drop, the wettability of the substrate on which the drop resides, and the concentration of particles on the inward drift of the coffee stain. This work also suggests a novel method to estimate the coefficient of friction between the particles and the substrate.

Sample-efficient parameter exploration of the powder film drying process using experiment-based Bayesian optimization

Parameter optimization is a long-standing challenge in various production processes. Particularly, powder film forming processes entail multiscale and multiphysical phenomena, each of which is usually controlled by a combination of several parameters. Therefore, it is difficult to optimize the parameters either by numerical-model-based analysis or by “brute force” experiment-based exploration. In this study, we focus on a Bayesian optimization method that has led to breakthroughs in materials informatics. Specifically, we apply this method to exploration of production-process-parameter for the powder film forming process. To this end, a slurry containing a powder, polymer, and solvent was dropped, the drying temperature and time were controlled as parameters to be explored, and the uniformity of the fabricated film was evaluated. Using this experiment-based Bayesian optimization system, we searched for the optimal parameters among 32,768 (8⁵) parameter sets to minimize defects. This optimization converged at 40 experiments, which is a substantially smaller number than that observed in brute-force exploration and traditional design-of-experiments methods. Furthermore, we inferred the mechanism corresponding to the unknown drying conditions discovered in the parameter exploration that resulted in uniform film formation. This demonstrates that a data-driven approach leads to high-throughput exploration and the discovery of novel parameters, which inspire further research.

Droplet evaporation on soft solid substrates

Droplet evaporation on soft solid substrates is relevant to applications such as fabrication of microlenses and controlled particle deposition. Here, we develop a lubrication-theory-based model to advance fundamental understanding of the important limiting case of a planar droplet evaporating on a linear viscoelastic solid. A set of partial differential equations describing the time evolution of the liquid-air and liquid-solid interfaces is derived and solved with a finite-difference method. A disjoining-pressure/precursor-film approach is used to describe contact-line motion, and the one sided model is used to describe solvent evaporation. Parametric studies are conducted to investigate the effect of solid properties (thickness, viscosity, shear modulus, wettability) and evaporation rate on droplet dynamics. Our results indicate that softer substrates speed up droplet evaporation due to prolonged pinning of the contact line. Results from our model are able to qualitatively reproduce some key trends observed in experiments. Due to its systematic formulation, our model can readily be extended to more complex situations of interest such as evaporation of particle-laden droplets on soft solid substrates.

The Effect of Substrate Temperature on the Evaporative Behaviour and Desiccation Patterns of Foetal Bovine Serum Drops

The drying of bio-fluid drops results in the formation of complex patterns, which are morphologically and topographically affected by environmental conditions including temperature. We examine the effect of substrate temperatures between 20 °C and 40 °C, on the evaporative dynamics and dried deposits of foetal bovine serum (FBS) drops. The deposits consist of four zones: a peripheral protein ring, a zone of protein structures, a protein gel, and a central crystalline zone. We investigate the link between the evaporative behaviour, final deposit volume, and cracking. Drops dried at higher substrate temperatures in the range of 20 °C to 35 °C produce deposits of lower final volume. We attribute this to a lower water content and a more brittle gel in the deposits formed at higher temperatures. However, the average deposit volume is higher for drops dried at 40 °C compared to drops dried at 35 °C, indicating protein denaturation. Focusing on the protein ring, we show that the ring volume decreases with increasing temperature from 20 °C to 35 °C, whereas the number of cracks increases due to faster water evaporation. Interestingly, for deposits of drops dried at 40 °C, the ring volume increases, but the number of cracks also increases, suggesting an interplay between water evaporation and increasing strain in the deposits due to protein denaturation.

Evaporation of Binary-Mixture Liquid Droplets: The Formation of Picoliter Pancakelike Shapes

Small multicomponent droplets are of increasing importance in a plethora of technological applications ranging from the fabrication of self-assembled hierarchical patterns to the design of autonomous fluidic systems. While often far away from equilibrium, involving complex and even chaotic flow fields, it is commonly assumed that in these systems with small drops surface tension keeps the shapes spherical. Here, studying picoliter volatile binary-mixture droplets of isopropanol and 2-butanol, we show that the dominance of surface tension forces at small scales can play a dual role: Minute variations in surface tension along the interface can create Marangoni flows that are strong enough to significantly deform the drop, forming micron-thick pancakelike shapes that are otherwise typical of large puddles. We identify the conditions under which these flattened shapes form and explain why, universally, they relax back to a spherical-cap shape toward the end of drop lifetime. We further show that the formation of pancakelike droplets suppresses the "coffee-ring" effect and leads to uniform deposition of suspended particles. The quantitative agreement between theory and experiment provides a predictive capability to modulate the shape of tiny droplets with implications in a range of technologies from fabrication of miniature optical lenses to coating, printing, and pattern deposition.

Controlled Spreading Rates to Distribute Nanoparticles as Uniform Langmuir Films

We report on using a controlled spreading rate to create Langmuir films of nanoparticles with more uniform, macroscale packing. A dispersion of hydrophobic quantum dots in n-hexane was deposited on subphase solutions containing various compositions of water and glycerol. Fluorescence images were captured as the film spread radially. An average spreading rate was defined using film radius and time at maximum expansion. On water with the highest spreading rate, films have an open region surrounded by a coffee ring. At a well-defined slower spreading rate, a distinct inner compact region appears between the open film and coffee ring, now called an outer compact region. As the spreading rate decreases further, the relative position for the open film boundary moves inward while the relative areas for the inner and outer compact regions increase. Films are the smallest in size at the slowest spreading rate on glycerol. The patterns are button-like with a central depleted region (open film), compact inner and outer regions, and a less-dense outer edge region. Normalized radial profiles were used to generate a partition map for the relative radial positions marking each film region at different spreading rates. Area number densities were calculated in the highest-packed regions. The values give no conclusive evidence that nanoparticles stack as multilayers, even the most compactly covered regions. Films spreading on glycerol form the most uniform, circular-shaped, densely packed arrangement of nanoparticles as their final pattern.

Colorimetric Diagnostic Capillary Enabled by Size Sieving in a Porous Hydrogel

Handy and disposable point-of-care diagnostics facilitate the early screening of severe diseases in resource-limited areas. To address urgent needs in inconvenient sites, a simple colorimetric diagnostic device equipped with a capillary tube with porous hydrogel and immunocomplex particles was developed for the rapid detection of biomarkers (16 min). In this device, probe particles attach to capture particles (dp = 40 µm) and form sandwiched immunocomplexes in the presence of target biomarkers, and a red color progressively emerges when the sandwiched immunocomplex particles are blocked by the porous hydrogel embedded inside the glass capillary. Colorimetric aggregation was recorded using a smartphone and analyzed with imaging software. The limit of detection reached 1 ng/mL and showed a maximum of 79% accuracy compared with that obtained through a conventional spectrophotometric technique. The level of a diabetic retinopathy (DR) biomarker, lipocalin-1 (LCN-1), was measured in 1 µL of a human tear sample and used in testing the practicability of the proposed device. All healthy subjects showed lower intensity levels than the other diabetic counterparts (proliferative DR or nonproliferative DR patients), implying the potential of this device in clinical applications. Overall, the diagnostic device facilitates point-of-care-testing and provides a low-cost (~1 USD), compact, and reliable tool for early diagnosis in resource-limited areas.

A thin-film model for droplet spreading on soft solid substrates

The spreading of droplets on soft solid substrates is relevant to applications such as tumor biophysics and controlled droplet condensation and evaporation. In this paper, we apply lubrication theory to advance fundamental understanding of the important limiting case of spreading of a planar droplet on a linear viscoelastic solid. The contact-line region is described by a disjoining-pressure/precursor-film approach, and nonlinear evolution equations describing how the liquid-air and liquid-solid interfaces evolve in space and time are derived and solved numerically. Parametric studies are conducted to investigate the effects of solid thickness, viscosity, shear modulus, and wettability on droplet spreading. Softer substrates are found to speed up spreading for perfectly wetting droplets but slow down spreading for partially wetting droplets. For perfectly wetting droplets, faster spreading is a result of more liquid being pumped toward the contact line due to a larger liquid-film thickness there arising from the repulsive component of the disjoining pressure. In contrast, slower spreading of partially wetting droplets is a result of less liquid being pumped toward the contact line due to a smaller liquid-film thickness there arising from the attractive component of the disjoining pressure. The model predictions for partially wetting droplets are qualitatively consistent with experimental observations, and allow us to disentangle the effects of substrate deformability and wettability on droplet spreading. Due to its systematic formulation, our model can readily be extended to more complex situations involving multiple droplets, substrate inclination, and droplet phase changes.

Crystallization-Driven Flows within Evaporating Aqueous Saline Droplets

Using micro-PIV (particle image velocimetry), we observe for the first time, the direct correlation between crystallization and hydrodynamics in evaporating microliter saline (1 M NaCl) sessile drops. The relationship is demonstrated by a remarkable jet of liquid along the base of the drops, induced by, and directed at the point of nucleation and subsequent crystal growth. Prior to nucleation, the flow is more uniformly outward with the magnitude of the velocity decreasing with time. From calculations and the flow measurements in the two observed stages of evaporation (prior to nucleation and during crystallization), this jet can be explained on the basis of competition between solutal Marangoni convection and mass conservation flow. The jet of fluid leads to vortices on either side of the crystal in which the salt concentration is reduced, providing a potential explanation as to why NaCl deposits as a sequence of discrete crystals rather than as a continuous ring for such drops.

Wetting Properties and Thin-Film Quality in the Wet Deposition of Zeolites

Zeolites are microporous crystalline materials widely used in catalysis and adsorption applications. The fabrication of zeolite thin films and membranes has also opened up the possibility of using zeolites in electronic devices and membrane separations. The existing approach to growing zeolite films involves exposing the substrate to a high-pH environment; however, this process is applicable to only specific types of substrates. Our group has developed the direct wet deposition of zeolites via ultrasonic nozzle spray deposition to address this issue; however, the relationship between wetting properties and thin-film quality has yet to be investigated. In this study, we prepared zeolite CHA (Si:Al:P = 3:10:20) suspensions using different solvents and surfactants in various concentrations. We then examined the relationships among the composition of the cast solution, their wetting behavior on the glass substrate, and the uniformity of the resulting thin films. We found that using ethanol as a solvent with zeolite crystals in low concentrations with added surfactant yielded zeolite films of high quality. We were also able to produce low-haze zeolite coatings on glass. The zeolite coatings with high hydrophilicity and adsorption capacity presented excellent antifogging capability.

Digital Assembly of Colloidal Particles for Nanoscale Manufacturing

From unravelling the most fundamental phenomena to enabling applications that impact our everyday lives, the nanoscale world holds great promise for science, technology and medicine. However, the extent of its practical realization would rely on manufacturing at the nanoscale. Among the various nanomanufacturing approaches being investigated, the bottom-up approach involving assembly of colloidal nanoparticles as building blocks is promising. Compared to a top-down lithographic approach, particle assembly exhibits advantages such as smaller feature size, finer control of chemical composition, less defects, lower material wastage, and higher scalability. The capability to assemble colloidal particles one by one or "digitally" has been heavily sought as it mimics the natural way of making matter and enables construction of nanomaterials with sophisticated architectures. This progress report provides an insight into the tools and techniques for digital assembly of particles, including their working mechanisms and demonstrated particle assemblies. Examples of nanomaterials and nanodevices are presented to demonstrate the strength of digital assembly in nanomanufacturing.

Sessile droplets containing carbon nanotubes: a study of evaporation dynamics and CNT alignment for printed electronics

Carbon nanotubes (CNTs) are 1-dimensional (1D) and flexible nanomaterials with high electric conductivity and a high aspect ratio. These features make CNTs highly suitable materials for the fabrication of flexible electronics. CNTs can also be made into dispersions which can be used as the feedstock material for droplet-based 3D printing technologies, e.g., inkjet printing and aerosol jet printing to fabricate printed electronics. These printing techniques involve several physical processes including deposition of ink droplets on flexible polymeric substrates such as polyimides, evaporation of the solvent and formation of thin films of CNTs, all of which have not been thoroughly investigated. Besides, alignment of the CNTs in the resultant thin films dictates their electrical performance. In this work, we examine the effect of substrate temperature and CNT concentration on the evaporation dynamics and also the alignment in the deposition patterns. Evaporation-driven self-assembly of CNTs and their preferential alignment are observed. Image analysis and Raman spectroscopy are utilised to evaluate the degree of alignment of the CNT network. It is found that the contact line dynamics depends greatly on the CNT concentration. Besides, the substrate temperature plays a significant role in determining the order of the CNTs in the drying deposition pattern. Our findings show the possibility of controlling the film morphology and the degree of alignment of CNTs for printed electronics in the printing process.

Segregation in Drying Binary Colloidal Droplets

When a colloidal suspension droplet evaporates from a solid surface, it leaves a characteristic deposit in the contact region. These deposits are common and important for many applications in printing, coating, or washing. By the use of superamphiphobic surfaces as a substrate, the contact area can be reduced so that evaporation is almost radially symmetric. While drying, the droplets maintain a nearly perfect spherical shape. Here, we exploit this phenomenon to fabricate supraparticles from bidisperse colloidal aqueous suspensions. The supraparticles have a core-shell morphology. The outer region is predominantly occupied by small colloids, forming a close-packed crystalline structure. Toward the center, the number of large colloids increases and they are packed amorphously. The extent of this stratification decreases with decreasing the evaporation rate. Complementary simulations indicate that evaporation leads to a local increase in density, which, in turn, exerts stronger inward forces on the larger colloids. A comparison between experiments and simulations suggest that hydrodynamic interactions between the suspended colloids reduce the extent of stratification. Our findings are relevant for the fabrication of supraparticles for applications in the fields of chromatography, catalysis, drug delivery, photonics, and a better understanding of spray-drying.

Photoluminescence of Drying Droplets with Silicon Nanoparticles

This study is dedicated to the formation of structures during drying of droplets of sols of silicon nanoparticles (SiNPs) in dimethylsulfoxide (DMSO) with a diameter of 1-5 mm on the horizontal glass and mica surfaces. Drying of such droplets with pinning (sticking) of the droplet contact line causes gradual gathering of the SiNPs on its edge with the formation of a thin ring. It has been found that the integral photoluminescence intensity I_PL greatly varies during the drying process. At the initial stage, I_PL monotonically decreases by several orders of magnitude and then abruptly increases several times at the final stage of ring formation. It has been shown that the rate of I_PL decrease is maximal at a very early stage and depends both on the aggregative state (solid film SiNPs/sols of the SiNPs) and volume of the SiNPs sols. It is minimal for the solid film SiNPs and gradually increases as the volume of SiNPs sol in DMSO decreases (optical cell → big droplet → small droplet). The obtained experimental dependencies between the luminescence decrease rate and aggregative state and volumes of the SiNPs sol in DMSO are attributed to the combination of three mechanisms of luminescence quenching: photobleaching, quenching with atmospheric oxygen, and Förster resonance energy transfer quenching. The appearing of the luminescence leap at the final stage of ring formation is associated with the emergence of cracks in the ring.

Modeling solvent evaporation during thin film formation in phase separating polymer mixtures

Preparation of thin films by dissolving polymers in a common solvent followed by evaporation of the solvent has become a routine processing procedure. However, modeling of thin film formation in an evaporating solvent has been challenging due to a need to simulate processes at multiple length and time scales. In this work, we present a methodology based on the principles of linear non-equilibrium thermodynamics, which allows systematic study of various effects such as the changes in the solvent properties due to phase transformation from liquid to vapor and polymer thermodynamics resulting from such solvent transformations. The methodology allows for the derivation of evaporative flux and boundary conditions near each surface for simulations of systems close to the equilibrium. We apply it to study thin film microstructural evolution in phase segregating polymer blends dissolved in a common volatile solvent and deposited on a planar substrate. Effects of the evaporation rates, interactions of the polymers with the underlying substrate and concentration dependent mobilities on the kinetics of thin film formation are studied.

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.

Quantifying vapor transfer into evaporating ethanol drops in a humid atmosphere

A simultaneous evaporation and water intake empirical model for evaporation of organic solvent ethanol drops.

Surface self-assembly of colloidal crystals for micro- and nano-patterning

The controlled patterning of polymeric surfaces at the micro- and nanoscale offers potential in the technological development of small-scale devices, particularly within the fields of photovoltaics, micro-optics and lab- and organ-on-chip, where the topological arrangement of the surface can influence a system's power generation, optical properties or biological function - such as, in the latter case, biomimicking surfaces or topological control of cellular differentiation. One of the most promising approaches in reducing manufacturing costs and complexity is by exploitation of the self-assembling properties of colloidal particles. Self-assembly techniques can be used to produce colloidal crystals onto surfaces, which can act as replicative masks, as has previously been demonstrated with colloidal lithography, or templates in mold-replication methods with resolutions dependent on particle size. Within this context, a particular emerging interest is focused on the use of self-assembled colloidal crystal surfaces in polymer replication methods such as soft lithography, hot and soft embossing and nano-imprint lithography, offering low-cost and high-resolution alternatives to conventional lithographic techniques. However, there are still challenges to overcome for this surface patterning approach to reach a manufacturing reliability and process robustness comparable to competitive technologies already available in the market, as self-assembly processes are not always 100% effective in organizing colloids within a structural pattern onto the surface. Defects often occur during template fabrication. Furthermore, issues often arise mainly at the interface between colloidal crystals and other surfaces and substrates. Particularly when utilized in high-temperature pattern replication processes, poor adhesion of colloidal particles onto the substrate results in degradation of the patterning template. These effects can render difficulties in creating stable structures with little defect that are well controlled such that a large variety of shapes can be reproduced reliably. This review presents an overview of available self-assembly methods for the creation of colloidal crystals, organized by the type of forces governing the self-assembly process: fluidic, physical, external fields, and chemical. The main focus lies on the use of spherical particles, which are favorable due to their high commercial availability and ease of synthesis. However, also shape-anisotropic particle self-assembly will be introduced, since it has recently been gaining research momentum, offering a greater flexibility in terms of patterning. Finally, an overview is provided of recent research on the fabrication of polymer nano- and microstructures by making use of colloidal self-assembled templates.

Drying of Droplets of Colloidal Suspensions on Rough Substrates

In many technological applications, excess solvent must be removed from liquid droplets to deposit solutes onto substrates. Often, the substrates on which the droplets rest may possess some roughness, either intended or unintended. Motivated by these observations, we present a lubrication-theory-based model to study the drying of droplets of colloidal suspensions on a substrate containing a topographical defect. The model consists of a system of one-dimensional partial differential equations accounting for the shape of the droplet and depth-averaged concentration of colloidal particles. A precursor film and disjoining pressure are used to describe the contact-line region, and evaporation is included using the well-known one-sided model. Finite-difference solutions reveal that when colloidal particles are absent, the droplet contact line can pin to a defect for a significant portion of the drying time due to a balance between capillary-pressure gradients and disjoining-pressure gradients. The time-evolution of the droplet radius and contact angle exhibits the constant-radius and constant-contact-angle stages that have been observed in prior experiments. When colloidal particles are present and the defect is absent, the model predicts that particles will be deposited near the center of the droplet in a cone-like pattern. However, when a defect is present, pinning of the contact-line accelerates droplet solidification, leading to particle deposition near the droplet edge in a coffee-ring pattern. These predictions are consistent with prior experimental observations, and illustrate the critical role contact-line pinning plays in controlling the dynamics of drying droplets.

Experimental and Numerical Study of the Evaporation of Water at Low Pressures

Although evaporation is considered to be a surface phenomenon, the rate of molecular transport across a liquid-vapor boundary is strongly dependent on the coupled fluid dynamics and heat transfer in the bulk fluids. Recent experimental thermocouple measurements of the temperature field near the interface of evaporating water into its vapor have begun to show the role of heat transfer in evaporation. However, the role of fluid dynamics has not been explored sufficiently. Here, we have developed a mathematical model to describe the coupling of the heat, mass, and momentum transfer in the fluids with the transport phenomena at the interface. The model was used to understand the experimentally obtained velocity field in the liquid and temperature profiles in the liquid and vapor, in evaporation from a concave meniscus for various vacuum pressures. By using the model, we have shown that an opposing buoyancy flow suppressed the thermocapillary flow in the liquid during evaporation at low pressures in our experiments. As such, in the absence of thermocapillary convection, the evaporation is controlled by heat transfer to the interface, and the predicted behavior of the system is independent of choosing between the existing theoretical expressions for evaporation flux. Furthermore, we investigated the temperature discontinuity at the interface and confirmed that the discontinuity strongly depends on the heat flux from the vapor side, which depends on the geometrical shape of the interface.

Surface freezing and surface coverage as key factors for spontaneous formation of colloidal fibers in vacuum drying of colloidal suspensions

In this study, we investigated vacuum drying of droplets of colloidal suspension. Because of the loss of the latent heat of vaporization, the drying droplet was cooled and then formed ice. Colloidal fibers consisting of packed particles spontaneously formed when the droplet froze from the gas-liquid interface. Conversely, we observed formation of sponge-like porous structures of particles when the whole droplet almost simultaneously froze. However, the freezing mode was not the only factor for formation of colloidal fibers. We found that the surface coverage of particles on the gas-liquid interface was also important. Owing to drying, some particles accumulated at the interface before freezing. When the surface coverage was higher than a threshold value, formation of fibers was severely restricted even in the surface freezing mode. Our results clearly show the important roles of surface freezing and the surface coverage of particles on the gas-liquid interface in formation of colloidal fibers.

Transport of Colloids along Corners: Visualization of Evaporation-Induced Flows beyond the Axisymmetric Condition

Nonhomogeneous evaporation fluxes have been shown to promote the formation of internal currents in sessile droplets, explaining the patterns that suspended particles leave after the droplet has dried out. Although most evaporation experiments have been conducted using spherical-cap-shaped drops, which are essentially in an axisymmetric geometry, here we show an example of nonhomogeneous evaporation in asymmetric geometries, which is visualized by following the motion of colloidal particles along liquid fingers forming a meniscus at square corners. It is found that the particle's velocity increases with the diffusive evaporation factor [Formula: see text] for the three tested fluids: water, isopropyl alcohol (IPA), and ethanol (EtOH). Here, [Formula: see text] is the vapor diffusivity in air, RH is the relative amount of vapor in the atmosphere, and cs is the saturated vapor concentration. We observed that in IPA and EtOH the internal currents promote a 3D spiral motion, whereas in water the particle's trajectory is basically unidirectional. By adding 0.25 critical micelle concentration (CMC) of sodium dodecyl sulfate (SDS) surfactant in water, a velocity blast was observed in the whole circulation flow pattern, going from [Formula: see text] to nearly [Formula: see text] in the longitudinal velocity component. To assess the effect of breaking the axisymmetric condition on the evaporation flux profile, we numerically solved the diffusive equation in model geometries that preserve the value of the contact angle θ but introduce an additional angle ϕ that characterizes the solid substrate. By testing different combinations of θ and ϕ, we corroborated that the evaporation flux increases when the substrate and the gas-liquid curves meet at corners with increasing sharpness.

Self-pinning of a nanosuspension droplet: Molecular dynamics simulations

Results are presented from molecular dynamics simulations of Pb(l) nanodroplets containing dispersed Cu nanoparticles (NPs) and spreading on solid surfaces. Three-dimensional simulations are employed throughout, but droplet spreading and pinning are reduced to two-dimensional processes by modeling cylindrical NPs in cylindrical droplets; NPs have radius R_{NP}≅3nm while droplets have initial R_{0}≅42nm. At low particle loading explored here, NPs in sufficient proximity to the initial solid-droplet interface are drawn into advancing contact lines; entrained NPs eventually bind with the underlying substrate. For relatively low advancing contact angle θ_{adv}, self-pinning on entrained NPs occurs; for higher θ_{adv}, depinning is observed. Self-pinning and depinning cases are compared and forces on NPs at the contact line are computed during a depinning event. Though significant flow in the droplet occurs in close proximity to the particle during depinning, resultant forces are relatively low. Instead, forces due to liquid atoms confined between the particles and substrate dominate the forces on NPs; that is, for the NP size studied here, forces are interface dominated. For pinning cases, a precursor wetting film advances ahead of the pinned contact line but at a significantly slower rate than for a pure droplet. This is because the precursor film is a bilayer of liquid atoms on the substrate surface but it is instead a monolayer film as it crosses over pinning particles; thus, mass delivery to the bilayer structure is impeded.

A mechanistic view of drying suspension droplets

When a dispersion droplet dries, a rich variety of spatial and temporal heterogeneities emerge. Controlling these phenomena is essential for many applications yet requires a thorough understanding of the underlying mechanisms. Although the process of film formation from initially dispersed polymer particles is well documented and is known to involve three main stages - evaporation, particle deformation and coalescence - it is impossible to fully disentangle the effects of particle deformation and coalescence, as these stages are closely linked. We circumvent this problem by studying suspensions of colloidal rubber particles that are incapable of coalescing. Varying the crosslink density allows us to tune the particle deformability in a controlled manner. We develop a theoretical framework of the main regimes and stresses in drying droplets of these suspensions, and validate this framework experimentally. Specifically, we show that changing the particle modulus by less than an order of magnitude can completely alter the stress development and resulting instabilities. Scanning electron microscopy reveals that particle deformability is a key factor in stress mitigation. Our model is the suspension equivalent of the widely used Routh-Russel model for film formation in drying dispersions, with additional focus on lateral nonuniformities such as cracking and wrinkling inherent to the droplet geometry, thus adding a new dimension to the conventional view of particle deformation.

Mathematical modeling of pattern formation caused by drying of colloidal film under a mask

In our model, we simulate an experiment (D.J. Harris, H. Hu, J.C. Conrad, J.A. Lewis, Patterning colloidal films via evaporative lithography, Phys. Rev. Lett. 98, 148301 (2007)). A thin colloidal sessile droplet is allowed to dry out on a horizontal hydrophilic surface. A mask just above the droplet predominantly allows evaporation from the droplet free surface directly beneath the holes in the mask. We consider one special case, when the holes in the mask are arranged so that the system has rotational symmetry of order m . We use a speculative evaporative flux to mimic the real system. Advection, diffusion, and sedimentation are taken into account. FlexPDE is utilized to solve an advection-diffusion equation using the finite element method. The simulation demonstrates that the colloidal particles accumulate below the holes as the solvent evaporates. Diffusion can reduce this accumulation.

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.

Simulation of Latex Film Formation Using a Cell Model in Real Space: Vertical Drying

This paper presents a simulation tool applied to latex film formation by drying, a hybrid between a classical numerical resolution method using finite differences and cellular automata, and making use of object-oriented programming. It consists of dividing real space into cells and applying local physical laws to simulate the exchange of matter between neighboring cells. In a first step, the simulation was applied to the simple case of vertical drying of a latex containing only one population of monodisperse particles and water. Our results show how the distribution of latex particles evolves through the different drying stages due to a combination of diffusion, convection, and particle deformation. While repulsive interactions between the particles tend to favor homogeneous distributions in the first drying stage, concentration gradients that develop in opposite ways can be observed depending on the drying regime. The distributions, calculated in various cases, reproduce and extend several theoretical results and are in qualitative agreement with some experimental findings.

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.