Drying of Droplets of Colloidal Suspensions on Rough Substrates

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.

Pinning-depinning transition of droplets on inclined substrates with a three-dimensional topographical defect

Droplets on inclined substrates can depin and slide freely above a critical substrate inclination angle. Pinning can be caused by topographical defects on the substrate, and understanding the influence of defect geometry on the pinning-depinning transition is important for diverse applications such as fog harvesting, droplet-based microfluidic devices, self-cleaning surfaces, and inkjet printing. Here, we develop a lubrication-theory-based model to investigate the motion of droplets on inclined substrates with a single three-dimensional Gaussian-shaped defect that can be in the form of a bump or a dent. A precursor-film/disjoining-pressure approach is used to capture contact-line motion, and a nonlinear evolution equation is derived which describes droplet thickness as a function of the position along the substrate and time. The evolution equation is solved numerically using an alternating direction implicit finite-difference scheme to study how the defect geometry influences the critical inclination angle and the shape of a pinned droplet. It is found that the critical substrate inclination angle increases as the defect becomes taller/deeper or wider along the direction lateral to the droplet-sliding direction. However, the critical inclination angle decreases as the defect becomes wider along the sliding direction. Below the critical inclination angle, the advancing contact line of the droplet at the droplet centerline is pinned to the defect at the point having maximum negative slope. Simple scaling relations that reflect the influence of defect geometry on the droplet retention force arising from surface tension are able to account for many of the trends observed in the numerical simulations.

Dynamics of individual inkjet printed picoliter droplet elucidated by high speed laser speckle imaging

Inkjet printing is a ubiquitous consumer and industrial process that involves concomitant processes of droplet impact, wetting, evaporation, and imbibement into a substrate as well as consequential substrate rearrangements and remodeling. In this work, we perform a study on the interaction between ink dispersions of different composition on substrates of increasing complexity to disentangle the motion of the liquid from the dynamic response of the substrate. We print three variations of pigmented inks and follow the ensuing dynamics at millisecond and micron time and length scales until complete drying using a multiple scattering technique, laser speckle imaging (LSI). Measurements of the photon transport mean free path, l*, for the printed inks and substrates show that the spatial region of information capture is the entire droplet volume and a depth within the substrate of a few μm beneath the droplet. Within this spatial confinement, LSI is an ideal approach for studying the solid-liquid transition at these small length and time scales by obtaining valid g2 and d2 autocorrelation functions and interpreting these dynamic changes under through kymographs. Our in situ LSI results show that droplets undergo delamination and cracking processes arising during droplet drying, which are confirmed by post mortem SEM imaging.

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.

Structure Formation in Supraparticles Composed of Spherical and Elongated Particles

We studied the evaporation-induced formation of supraparticles from dispersions of elongated colloidal particles using experiments and computer simulations. Aqueous droplets containing a dispersion of ellipsoidal and spherical polystyrene particles were dried on superamphiphobic surfaces at different humidity values that led to varying evaporation rates. Supraparticles made from only ellipsoidal particles showed short-range lateral ordering at the supraparticle surface and random orientations in the interior regardless of the evaporation rate. Particle-based simulations corroborated the experimental observations in the evaporation-limited regime and showed an increase in the local nematic ordering as the diffusion-limited regime was reached. A thin shell of ellipsoids was observed at the surface when supraparticles were made from binary mixtures of ellipsoids and spheres. Image analysis revealed that the supraparticle porosity increased with an increasing aspect ratio of the ellipsoids.

Drying behaviour of nanofluid sessile droplets on self-affine vis-à-vis corrugated nanorough surfaces

In recent years, evaporative self-assembly of sessile droplets has gained considerable attention owing to its wide applicability in many areas. While the phenomenon is well studied for smooth and isotropically rough (self-affine) surfaces, investigations comparing the outcomes on self-affine vis-à-vis corrugated surfaces remains to be done. In this experimental work, we compare the wetting and evaporation dynamics of nano-colloidal microlitre droplets on self-affine and corrugated nanorough surfaces having identical roughnesses and interface properties. The coupled influence of particle size, concentration, and surface structuring has been explored. Differences in wettability and evaporation dynamics are observed, which are explained via the interaction between wetting fluid and anisotropic surface roughness. Our findings exhibit different temporal behaviour of contact radius and angle in the evaporation process of the droplets. Further, the corrugated surface exhibits anisotropic wettability with a monotonic change in droplet shape as evaporation proceeds, finally giving rise to irregular dried patterns. The scaled rim width and crack spacing of the particulate deposits are examined. Our results can inspire fabrication of surfaces that can facilitate direction-dependent droplet motion for specific applications.

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.

Anisotropic nanocluster arrays to a diminished zone: different regimes of surface deposition of gold nanocolloids

Evaporation-induced assembly of nanoparticles has emerged as a versatile technique for the production of large-scale ordered structures and materials with complex features. In this study, we show that a dried particulate of an anisotropic nanocolloid undergoes non-ubiquitous surface morphological transitions at varying particle concentrations. Below 5 nM, deposits reveal the formation of linear arrays of AuNR clusters outside of the coffee ring and an annular CTAB-rich depletion zone in the inner vicinity of the coffee ring. For nanoparticle concentrations ≥5 nM, the outer cluster deposits disappear and a region of reduced AuNR density, sandwiched between the coffee ring and the depletion zone, analogous to the diminished zone, is observed. Within the coffee-ring deposits, nanoscale smectic AuNR assembly occurs via the expulsion of the cetyltrimethyl ammonium bromide (CTAB) bilayer, which contributes to the inward solutal Marangoni flow. An enhanced inward solutal Marangoni flow at high particle concentrations assists in the formation of a wider depletion zone, the emergence of the diminished zone and suppression of the width of the coffee-ring deposits. Through detailed analysis of data from ex situ (scanning electron microscopy, SEM) and in situ (contact angle and confocal imaging) measurements, we establish a direct correlation between the different evaporation modes and the various deposition regimes. A detailed mechanism for the surface morphology modulation of AuNR deposits by tuning the nanoparticle concentration in the drying sessile drop is discussed.

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.

Ordered stripes to crack patterns in dried particulates of DNA-coated gold colloids via modulating nanoparticle-substrate interactions

The surface pattern in dried droplets of nanoparticle suspension possesses direct correlation with the evaporation profile, which apart from the bulk parameters, can also be altered by tuning the nanoscale interactions. Here, we show that, for sessile drops of DNA-coated gold nanoparticle (DNA-AuNP) solution, the alteration in evaporation pathway of TPCL (three-phase contact line) from stick-slip to mixed mode leads to a surface morphological transition from concentric rings with stripes to radial crack formation within the coffee ring deposit. A freshly cleaned silicon substrate offers hydrophilic/favorable substrate-nanoparticle interaction and produces multiple ordered stripes due to stick-slip motion of the TPCL. Using a SiO₂/Si substrate with ∼200 nm of oxide layer leads to an increase in the initial water contact angle θ_i-w by ∼40°, due to increased hydrophobicity of the substrate. Three distinct modes of evaporation are observed - constant contact radius (CCR), constant contact angle (CCA) and mixed mode, resulting in the formation of radial cracks on a thick coffee ring structure. The critical thickness (h_c), beyond which the cracks start to appear, was measured to be ∼600 nm and is in close agreement with the theoretical estimate of ∼510 nm. Through in situ contact angle and ex situ SEM measurements, we provide an understanding of the observed surface morphological transition in the dried particulate at various nanoparticle densities. Further analysis of the coffee ring width (d), linear crack density (σ) and crack spacing (λ) provides insight into the mechanism of crack formation for droplets dried on oxide-coated substrates.

Pinning and Depinning Dynamics of an Evaporating Sessile Droplet Containing Mono- and Bidispersed Colloidal Particles on a Nonheated/Heated Hydrophobic Substrate

The present study is primarily focused on the coupled effects of substrate heating, colloidal dispersion, and particle size variation on the contact line (CL) pinning-depinning dynamics of evaporating droplets containing mono- (3/4.5 μm) and bidispersed (3 and 4.5 μm) polystyrene colloidal particles on poly(dimethylsiloxane) (PDMS) substrates. Experimental techniques such as high-speed visualization, optical microscopy, infrared thermography, and scanning electron microscopy are implemented to discover the plausible causes dictating the underlying physics. In the case of the nonheated substrate, there exists a significant delay in the CL depinning for the evaporating droplets containing bidispersed particles, as opposed to the monodispersed cases. A first-order model is illustrated for the determination of the net horizontal force acting on the particles near the CL. Interestingly, the model's findings revealed that due to the difference of particle size in the case of the bidispersed suspension, the interparticle contact force gets modified, thus enhancing the CL pinning. For the heated substrate cases, droplets with monodispersed particles (3 μm) exhibit a substantial delay in the CL depinning, whereas a nearly complete pinning of the CL is witnessed for the case of bidispersed colloidal suspension droplets. It is mainly due to the augmentation of particle deposition near the CL because of the circulatory thermal Marangoni and outward capillary flows. Thus, the mobility of the CL is inhibited, which is further reinforced by the presence of different-sized particles. Eventually, a ring-like deposition is observed, as opposed to an inner deposit commonly observed from the evaporation of colloidal droplets on hydrophobic substrates.

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.

Size-Dependent Dried Colloidal Deposit and Particle Sorting via Saturated Alcohol Vapor-Mediated Sessile Droplet Spreading

We experimentally and theoretically investigate a distinct problem of spreading, evaporation, and the associated dried deposits of a colloidal particle-laden aqueous sessile droplet on a surface in a saturated alcohol vapor environment. In particular, the effect of particle size on monodispersed suspensions and efficient self-sorting of bidispersed particles have been investigated. The alcohol vapor diffuses toward the droplet's curved liquid-vapor interface from the far field. The incoming vapor mass flux profile assumes a nonuniform pattern across the interface. The alcohol vapor molecules are adsorbed at the liquid-vapor interface, which eventually leads to absorption into the droplet's liquid phase due to the miscibility. This phenomenon triggers a liquid-vapor interfacial tension gradient and causes a reduction in the global surface tension of the droplet. This results in a solutal Marangoni flow recirculation and spontaneous droplet spreading. The interplay between these phenomena gives rise to a complex internal fluid flow within the droplet, resulting in a significantly modified and strongly particle-size-dependent dried colloidal deposit. While the smaller particles form a multiple ring pattern, larger particles form a single ring, and additional "patchwise" deposits emerge. High-speed visualization of the internal liquid-flow revealed that initially, a ring forms at the first location of the contact line. Concurrently, the Marangoni flow recirculation drives a collection of particles at the liquid-vapor interface to form clusters. Thereafter, as the droplet spreads, the smaller particles in the cluster exhibit a "jetlike" outward flow, forming multiple ring patterns. In contrast, the larger particles tend to coalesce together in the cluster, forming the "patchwise" deposits. The widely different response of the different-sized particles to the internal fluid flow enables an efficient sorting of the smaller particles at the contact line from bidispersed suspensions. We corroborate the measurements with theoretical and numerical models wherever possible.

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.

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.

High-speed laser speckle imaging to unravel picoliter drop-on-demand to substrate interaction

Understanding phenomena such as evaporation and imbibition of picoliter droplets into porous substrates is crucial in printing industry to achieve a higher printing quality and print speed. After printing, the residual pigment must remain fixed at the desired location on a substrate and be of a desired volume to yield a high resolution and vibrantly printed page that has become the expectation of modern printing technology. Current research entails not only chemical composition of the ink but also how this links to the dynamics and interactions that occur between the ink and the substrate at every stage of the printed spot formation, including evaporation, wetting, and imbibition. In this paper, we present an instrument that can print on-demand picoliter volume droplets of ink onto substrates and then immediately record on evolution of the resulting dynamics when these two materials interact. This high-speed laser speckle imaging (HS-LSI) technique has been developed to monitor nanometer displacement of the drying and imbibing ink droplet at a high frame rate, up to 20000 Hz, given the short timescales of these interactions. We present the design of the instrument, discuss the related challenges and the theory underlying the LSI technique, specifically how photons non-evasively probe opaque objects in a multiple scattering regime, and show how this technique can unravel the dynamics of drying and imbibition. We will finish giving a validation on the instrument and an example of its usage.

Pattern Formation upon Evaporation of Sessile Droplets of Polyelectrolyte/Surfactant Mixtures on Silicon Wafers

The formation of coffee-ring deposits upon evaporation of sessile droplets containing mixtures of poly(diallyldimethylammonium chloride) (PDADMAC) and two different anionic surfactants were studied. This process is driven by the Marangoni stresses resulting from the formation of surface-active polyelectrolyte–surfactant complexes in solution and the salt arising from the release of counterions. The morphologies of the deposits appear to be dependent on the surfactant concentration, independent of their chemical nature, and consist of a peripheral coffee ring composed of PDADMAC and PDADMAC–surfactant complexes, and a secondary region of dendrite-like structures of pure NaCl at the interior of the residue formed at the end of the evaporation. This is compatible with a hydrodynamic flow associated with the Marangoni stress from the apex of the drop to the three-phase contact line for those cases in which the concentration of the complexes dominates the surface tension, whereas it is reversed when most of the PDADMAC and the complexes have been deposited at the rim and the bulk contains mainly salt.

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.

Further Insights into Patterns from Drying Particle Laden Sessile Drops

The evaporation of colloidal dispersions is an elegant and straightforward route to controlled self-assembly of particles on a solid surface. In particular, the evaporation of particle laden drops placed on solid substrates has received considerable attention for more than two decades. Such particle filled drops upon complete evaporation of the solvent leave behind a residue, commonly called particulate deposit pattern. In these patterns, typically, more particles accumulate at the edge compared to the interior, a feature observed when coffee drops evaporate. Consequently, such evaporative patterns are called coffee stains. In this article, the focus is on the evaporation of highly dilute suspension drops containing particles of larger diameters ranging from 3 to 10 μm drying on solid substrates. This helps us to investigate the combined role of gravity-driven settling of particles and capillary flow-driven particle transport on pattern formation in drying drops. In the highly dilute concentration limit, the evaporative patterns are found to show a transition, from a monolayer deposit that consists of a single layer of particles, to a multilayer deposit as a function of particle diameter and initial concentration of particles in the drying drop. Moreover, the spatial distribution of particles as well as the ordering of particles in the deposit patterns are found to be particle size dependent. It is also seen that the order-disorder transition, a feature associated with the organization of particles at the edge of the deposit, observed typically at moderate particle concentrations, disappears at the highly dilute concentrations considered here. The evaporation of drops containing particles of 10 μm diameter, where the effect of gravity on the particle becomes significant, leads to uniform deposition of particles, i.e, suppression of the coffee-stain effect and to the formation of two-dimensional percolating networks.

Droplet Control Based on Pinning and Substrate Wettability

Pinning of liquid droplets on solid substrates is ubiquitous and plays an essential role in many applications, especially in various areas such as microfluidics and biology. Although pinning can often reduce the efficiency of various applications, a deeper understanding of this phenomenon can actually offer possibilities for technological exploitation. Here, by means of molecular dynamics simulation, we identify the conditions that lead to droplet pinning or depinning and discuss the effects of key parameters in detail, such as the height of the physical pinning barrier and the wettability of the substrates. Moreover, we describe the mechanism of barrier crossing by the droplet upon depinning, identify the driving force of this process, and, also, elucidate the dynamics of the droplet. Not only does our work provide a detailed description of the pinning and depinning processes but also it explicitly highlights how both processes can be exploited in nanotechnology applications to control the droplet motion. Hence, we anticipate that our study will have significant implications for the nanoscale design of substrates in micro- and nanoscale systems and will assist with assessing pinning effects in various applications.

Lattice Boltzmann modeling of heat conduction enhancement by colloidal nanoparticle deposition in microporous structures

Drying of colloidal suspension towards the exploitation of the resultant nanoparticle deposition has been applied in different research and engineering fields. Recent experimental studies have shown that neck-based thermal structure (NTS) by colloidal nanoparticle deposition between microsize filler particle configuration (FPC) can significantly enhance vertical heat conduction in innovative three-dimensional chip stacks [Brunschwiler et al., J. Electron. Packag. 138, 041009 (2016)10.1115/1.4034927]. However, an in-depth understanding of the mechanisms of colloidal liquid drying, neck formation, and their influence on heat conduction is still lacking. In this paper, using the lattice Boltzmann method, we model neck formation in FPCs and evaluate the thermal performances of resultant NTSs. The colloidal liquid is found drying continuously from the periphery of the microstructure to its center with a decreasing drying rate. With drying, more necks of smaller size are formed between adjacent filler particles, while fewer necks of larger size are formed between filler particle and the top/bottom plate of the FPCs. The necks, forming critical throats between the filler particles, are found to improve the heat flux significantly, leading to an overall heat conduction enhancement of 2.4 times. In addition, the neck count, size, and distribution as well as the thermal performance of NTSs are found to be similar for three different FPCs at a constant filler particle volume fraction. Our simulation results on neck formation and thermal performances of NTSs are in good agreement with experimental results. This demonstrates that the current lattice Boltzmann models are accurate in modeling drying of colloidal suspension and heat conduction in microporous structures, and have high potentials to study other problems such as surface coating, salt transport, salt crystallization, and food preserving.

Effect of Particle Concentration on Surfactant-Induced Alteration of the Contact Line Deposition in Evaporating Sessile Droplets

Controlling and suppressing the so-called "coffee-ring effect" (CRE) is an issue of cardinal importance and intense interest in many industries and scientific fields. Here, the combined effect of the particle and surfactant concentration on the CRE is investigated by gradually adding Triton X-100 surfactant to colloidal suspensions of SiO₂ nanoparticles in ethanol for various particle concentrations. First, the effect of particle concentration on the contact line dynamics during the evaporation of a sessile droplet is investigated. It is shown that increasing the particle concentration leads to an increase in pinning time and ring width, whereas the droplet's initial and dynamic contact angle remains unchanged. Afterward, the effect of different concentrations of surfactant is studied for different particle concentrations. It is concluded that the surfactant concentration at which the CRE is suppressed is dependent on the initial particle concentration of the colloid, and it increases as the particle concentration increases. Furthermore, as adding surfactant with a concentration lower than this critical concentration results in an unsuppressed CRE, it is shown that surpassing this concentration will result in a depletion of particles in the contact line. Moreover, it is demonstrated that this critical surfactant concentration has no significant effect on the droplet's geometry and the total evaporation time.

Evaporation-induced alterations in oscillation and flow characteristics of a sessile droplet on a rose-mimetic surface

Strategic control of evaporation dynamics can help control oscillation modes and internal flow field in an oscillating sessile droplet. This article presents the study of an oscillating droplet on a bio-inspired "sticky" surface to better understand the nexus between the modes of evaporation and oscillation. Oscillation in droplets can be characterized by the number of nodes forming on the surface and is referred to as the mode of oscillation. An evaporating sessile droplet under constant periodic perturbation naturally self-tunes between different oscillation modes depending on its geometry. The droplet geometry evolves according to the mode of evaporation controlled by substrate topography. We use a bio-inspired, rose patterned, "sticky" hydrophobic substrate to perpetually pin the contact line of the droplet in order to hence achieve a single mode of evaporation for most of the droplet's lifetime. This allows the prediction of experimentally observed oscillation mode transitions at different excitation frequencies. We present simple scaling arguments to predict the velocity of the internal flow induced by the oscillation. The findings are beneficial to applications which seek to tailor energy and mass transfer rates across liquid droplets by using bio-inspired surfaces.

Evaporation of Sessile Droplets of Polyelectrolyte/Surfactant Mixtures on Silicon Wafers

The wetting and evaporation behavior of droplets of aqueous solutions of mixtures of poly(diallyldimethylammonium chloride) solution, PDADMAC, with two different anionic surfactants, sodium laureth sulfate, SLES, and sodium N-lauroyl N-methyl taurate, SLMT, were studied in terms of the changes of the contact angle θ and contact length L of sessile droplets of the mixtures on silicon wafers at a temperature of 25 °C and different relative humidities in the range of 30–90%. The advancing contact angle θa was found to depend on the surfactant concentration, independent of the relative humidity, with the mixtures containing SLES presenting improved wetting behaviors. Furthermore, a constant droplet contact angle was not observed during evaporation due to pinning of the droplet at the coffee-ring that was formed. The kinetics for the first evaporation stage of the mixture were independent of the relative humidity, with the evaporation behavior being well described in terms of the universal law for evaporation.

Evaporation-driven colloidal cluster assembly using droplets on superhydrophobic fractal-like structures

Microparticles can be considered building units for functional systems, but their assembly into larger structures typically involves complex methods. In this work, we show that a large variety of macro-agglomerate clusters ("supra-particles") can be obtained, by systematically varying the initial particle concentration in an evaporating droplet, spanning more than 3 decades. The key is the use of robust superhydrophobic substrates: in this study we make use of a recently discovered kind of patterned surface with fractal-like microstructures which dramatically reduce the contact of the droplet with the solid substrate. Our results show a clear transition from quasi-2D to 3D clusters as a function of the initial particle concentration, and a clear transition from unstable to stable 3D spheroids as a function of the evaporation rate. The origin of such shape transitions can respectively be found in the dynamic wetting of the fractal-like structure, but also in the enhanced mechanical stability of the particle agglomerate as its particle packing fraction increases.

Toward Controlling Evaporative Deposition: Effects of Substrate, Solvent, and Solute

Understanding evaporative deposition from a colloidal suspension and on-demand control over it are important due to its industrial and biomedical applications. In particular, it is known that interactions among substrate, solute, and solvent have important consequences on evaporative depositions; however, how these are affecting the deposition patterns and at which conditions these interactions are prominent need detailed investigations. Here we report that the total time of deposition (t_d) and the geometric shape of the droplet (L_c = initial footprint diameter/height) have a significant role in determining the evaporative deposition patterns. We have identified four zones based on t_d and L_c, and found that with longer deposition time (high t_d) and larger available space for particle motion within a liquid droplet (high L_c), deposition patterns were governed by the interactions among the substrate, solute, and solvent. We also experimentally demonstrated that the pinned contact line is indispensable for the "coffee ring" effect by comparing the deposition on surfaces with and without hysteresis. The effect of the Marangoni flow is also discussed, and it is shown that by controlling Marangoni flow, one can manipulate the droplet deposition from uniform disk-like to coffee ring with a central deposition.

How coronavirus survives for days on surfaces

Our previous study [R. Bhardwaj and A. Agrawal, "Likelihood of survival of coronavirus in a respiratory droplet deposited on a solid surface," Phys. Fluids 32, 061704 (2020)] showed that the drying time of typical respiratory droplets is on the order of seconds, while the survival time of the coronavirus on different surfaces was reported to be on the order of hours in recent experiments. We attribute the long survival time of the coronavirus on a surface to the slow evaporation of a thin nanometer liquid film remaining after the evaporation of the bulk droplet. Accordingly, we employ a computational model for a thin film in which the evaporating mass rate is a function of disjoining and Laplace pressures inside the film. The model shows a strong dependence on the initial thickness of the film and suggests that the drying time of this nanometric film is on the order of hours, consistent with the survival time of the coronavirus on a surface, seen in published experiments. We briefly examine the change in the drying time as a function of the contact angle and type of surface. The computed time-varying film thickness or volume qualitatively agrees with the measured decay of the coronavirus titer on different surfaces. The present work provides insights on why coronavirus survival is on the order of hours or days on a solid surface under ambient conditions.

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.

Drying Droplets with Soluble Surfactants

We propose a theory for the drying of liquid droplets of surfactant solutions. We show that the added surfactant hinders droplet receding and facilitates droplet spreading, causing a complex behavior of the contact line of an evaporating droplet: the contact line first recedes, then advances, and finally recedes again. We also show that the surfactant can change the deposition pattern from mountain-like to volcano-like and then to coffee-ring-like. Specially, when the contact line motion undergoes a clear receding-advancing transition, a two-ring pattern is formed. The mechanism of the two-ring formation is different from the stick-slip mechanism proposed previously and may be tested experimentally.

Deposition of Colloidal Particles during the Evaporation of Sessile Drops: Dilute Colloidal Dispersions

The deposition of colloidal silica particles during the evaporation of sessile drops on a smooth substrate has been modeled by the simultaneous solution of the Navier–Stokes equations, the convective-diffusive equation for particles, and the diffusion equation for evaporated vapor in the gas phase. Isothermal conditions were assumed. A mapping was created to show the conditions for various deposition patterns for very dilute suspensions. Based on values of the Peclet (Pe) number and Damkholer numbers (Da and Da−1), the effects of adsorption and desorption were discussed according to the map. Simulations were also done for suspensions with a high particle concentration to form a solid phase during the evaporation by using a packing criterion. The simulations predicted the height and width of the ring deposit near the contact line, and the results compared favorably to experimental particle deposition patterns.

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.

From Dot to Ring: The Role of Friction in the Deposition Pattern of a Drying Colloidal Suspension Droplet

The deposition of particles on a substrate by drying a colloidal suspension droplet is at the core of applications ranging from traditional printing on paper to printable electronics or photovoltaic devices. The self-pinning induced by the accumulation of particles at the contact line plays an important role in the formation of a deposit. In this article, we investigate, both numerically and theoretically, the effect of friction between the particles and the substrate on the deposition pattern. Without friction, the contact line shows a stick-slip behavior and a dotlike deposit is left after the droplet is evaporated. By increasing the friction force, we observe a transition from a dotlike to a ringlike deposit. We propose a theoretical model to predict the effective radius of the particle deposit as a function of the friction force. Our theoretical model predicts a critical friction force when self-pinning happens and the effective radius of deposit increases with increasing friction force, confirmed by our simulation results. Our results can find implications for developing active control strategies for the deposition of drying droplets.

Snap evaporation of droplets on smooth topographies

Droplet evaporation on solid surfaces is important in many applications including printing, micro-patterning and cooling. While seemingly simple, the configuration of evaporating droplets on solids is difficult to predict and control. This is because evaporation typically proceeds as a "stick-slip" sequence-a combination of pinning and de-pinning events dominated by static friction or "pinning", caused by microscopic surface roughness. Here we show how smooth, pinning-free, solid surfaces of non-planar topography promote a different process called snap evaporation. During snap evaporation a droplet follows a reproducible sequence of configurations, consisting of a quasi-static phase-change controlled by mass diffusion interrupted by out-of-equilibrium snaps. Snaps are triggered by bifurcations of the equilibrium droplet shape mediated by the underlying non-planar solid. Because the evolution of droplets during snap evaporation is controlled by a smooth topography, and not by surface roughness, our ideas can inspire programmable surfaces that manage liquids in heat- and mass-transfer applications.

Receding Contact Line Motion on Nanopatterned and Micropatterned Polymer Surfaces

Surface properties such as topography and chemistry affect the motion of the three-phase contact line (solid/liquid/air), which in turn affects the contact angle of a liquid moving on a solid surface. In this work, the motion of the receding water contact line was studied on chemically and topographically patterned surfaces obtained from the dewetting of thin polymer films. The patterned surfaces consisted of hydrophilic poly(4-vinylpyridine) (P4VP) bumps, which were either microsized and sparse or nanosized and dense, on top of a hydrophobic polystyrene (PS) background layer. These patterns are designed for atmospheric water capture, for which the easy roll off of water droplets is crucial to their efficient performance. The dynamic receding water contact angle and contact line height of the patterned surfaces were measured by vertically withdrawing the surfaces from a water bath and compared to those of a flat P4VP substrate. For both the micropatterned and nanopatterned surfaces, the height of the dynamic contact lines normalized by the capillary length was characterized by the equilibrium limit that was predicted from static states. The nanopatterned surface had a faster increase in the normalized height as the capillary number increased. The dynamic receding contact angles on all surfaces studied decreased with increasing withdrawing velocity. Surprisingly, even for these patterned surfaces with high hysteresis, the dynamic receding contact angle followed the Cox-Voinov relation at capillary numbers of between 1 × 10^-5 and 5 × 10^-5.