Evaporation of solutions and colloidal dispersions in confined droplets

Emergence and inversion of chirality in hierarchical assemblies of CdS nanocrystal fibers

Arranging semiconducting nanocrystals into ordered superstructures is a promising platform to study fundamental light-matter interactions and develop programmable optical metamaterials. We investigated how the geometrical arrangement of CdS nanocrystals in hierarchical assemblies affects chiroptical properties. To create these structures, we controlled the evaporation of a colloidal CdS nanocrystal solution between two parallel plates. We combined in situ microscopy and computational modeling to establish a formation mechanism involving the shear-induced alignment of nanocrystal fibers and the subsequent mechanical relaxation of the stretched fibers to form Raman noodle-type band textures. The high linear anisotropy in these films shares many similarities with cholesteric liquid crystals. The films deposited on top and bottom surfaces exhibit opposite chirality. The mechanistic insights from this study are consequential to enable future advances in the design and fabrication of programmable optical metamaterials for further development of polarization-based optics toward applications in sensing, hyperspectral imaging, and quantum information technology.

Simple method to measure rheological properties of soft surfaces by a micro-needle contact

We developed a simple method to investigate rheological properties of soft surfaces, such as polymeric liquids and colloidal suspensions, by capturing the images of a metal micro-needle inserted into the surface. At contact, a meniscus-like deformation is formed on the surface. By relating the shape of the deformation to the balance of applied forces, local elasticity and viscosity just inside the surface are obtained. With a facile setup and rapid measurement process, the present method can be implemented to variety of systems, for instance, drying sessile drops and small volume of liquid confined in a capillary.

Tri-templating Synthesis of Multilevel Mesoporous Silica Microspheres with a Complex Interior Structure for Efficient CO2 Capture and Catalysis

Multilevel porous architectures with microscopic shape control and tailor-made complex structures offer great potential for various innovative applications, but their elaborate design and synthesis have remained a scientific and technological challenge. Herein, we report a simple and effective tri-templating method, in which microscale Pickering droplets, nanoscale polystyrene colloids (PS), and molecular cetyltrimethylammonium chloride micelles are synchronously employed, for the fabrication of such micro-nanohierarchical mesoporous silica microspheres. In this protocol, Pickering droplet-directed interfacial sol-gel growth and its spatially confined surfactant assembly-directed sol-gel coating on PS suspensions are coupled together, enabling the successful formation of structured mesoporous silica that consists of numerous nanocompartments enclosed by a permeable shell. By varying the quantity of PS colloidal templates, rational regulation of the complex interior structure is achieved. Also, ascribed to the multilevel arrangement, this peculiar architecture not only shows desirable fast mass transport of external molecules but also possesses easy handling ability. After loading with tetraethylenepentamine or enzyme species, the yielded microspherical CO₂ sorbents or immobilized biocatalysts, respectively, exhibit enhanced CO₂ capture capacity and enzymatic catalysis efficiency. Notably, taking advantage of their microscopic characteristics, the immobilized biocatalysts could be ideally packed in a fixed-bed reactor for long-term continuous-flow enzymatic reactions. This tri-templating strategy provides a new synthetic route to access other multilevel microscopic materials with fascinating complex structures and paves a way to promote their practical applications.

Collective diffusion coefficient of a charged colloidal dispersion: interferometric measurements in a drying drop

In the present work, we use Mach-Zehnder interferometry to thoroughly investigate the drying dynamics of a 2D confined drop of a charged colloidal dispersion. This technique makes it possible to measure the colloid concentration field during the drying of the drop at a high accuracy (about 0.5%) and with a high temporal and spatial resolution (about 1 frame per s and 5 μm per pixel). These features allow us to probe mass transport of the charged dispersion in this out-of-equilibrium situation. In particular, our experiments provide the evidence that mass transport within the drop can be described by a purely diffusive process for some range of parameters for which the buoyancy-driven convection is negligible. We are then able to extract from these experiments the collective diffusion coefficient of the dispersion D(φ) over a wide concentration range φ = 0.24-0.5, i.e. from the liquid dispersed state to the solid glass regime, with a high accuracy. The measured values of D(φ) ≃ 5-12D0 are significantly larger than the simple estimate D0 given by the Stokes-Einstein relation, thus highlighting the important role played by the colloidal interactions in such dispersions.

Evaporation of squeezed water droplets between two parallel hydrophobic/superhydrophobic surfaces

HYPOTHESIS

A liquid droplet is apt to be deformed within a compact space in various applications. The morphological change of a droplet and vapor accumulation in the confined space between two parallel surfaces with different gaps and surface wettability are expected to significantly affect the evaporation dynamics of the squeezed droplet therein.

EXPERIMENTS

Here the evaporation dynamics of a squeezed droplet between two parallel hydrophobic/superhydrophobic surfaces are experimentally explored. By reducing the surface gap from 1000 μm to 400 μm, the evolution of contact angle, contact radius and volume of the evaporating droplet are measured. A diffusion-driven model based on a two-parameter ellipsoidal segment geometry is developed to predict the morphology and volume evolution of a squeezed droplet during evaporation.

FINDINGS

Evaporation dynamics of a squeezed water droplet via the constant contact radius (CCR) mode, the constant contact angle (CCA) mode, or the mixed mode are experimentally observed. Confirmed by our ellipsoidal segment model, the evaporation of the squeezed droplet is significantly depressed with the decreasing surface gap, which is primarily attributed to vapor enrichment in a more confined geometry. A linear scaling law between droplet volume and evaporation time is unveiled, which is verified by a simplified cylindrical model.

Transport dynamics of charged colloidal particles during directional drying of suspensions in a confined microchannel

Directional drying of colloidal suspensions, experimentally observed to exhibit mechanical instabilities, is a nonequilibrium procedure that is susceptible to geometric confinement and the properties of colloidal particles. Here, we develop an advection-diffusion model to characterize the transport dynamics for unidirectional drying of a suspension consisting of charged particles in a confined Hele-Shaw cell. We consider the electrostatic interactions by means of the Poisson-Boltzmann cell approach with the viscous flow confined to the cell. By solving the nonequilibrium transport equations, we clarify how the multiple parameters, such as drying rate, confinement ratio, and the monovalent slat concentration, affect the transport dynamics of charged colloidal particles. We find that the drying front recedes into the cell with linear behavior, while the liquid-solid transition front recedes with power law behaviors. The faster evaporation rate creates a rapid formation of the drying front and produces a thinner transition layer. We show that confinement is equivalent to raising the effective concentration in the cell, and, accordingly, the drying front appears earlier and grows more rapidly. Under geometric confinement, a longer fully dried film is created while the total drying time is shortened. Moreover, we have theoretically illustrated that low salt loadings cause a large collective diffusivity of charged colloidal particles, which results in a colloidal network by aggregation. Thus, the drying behavior alters dramatically as salt loadings decrease, since the resulting compacted clusters of charged particles eventually convert the suspension into a gel-like material instead of a simple fluid. Our model is consistent with the current experiments and provides a simple insight for applications in directional solidification and microfluidics.

Drying-induced stresses before solidification in colloidal dispersions: in situ measurements

We first report an original setup that enables continuous measurements of stresses induced by the drying of confined drops of complex fluids. This setup is mainly based on a precision scale working with an electromagnetic force compensation technique that provides accurate measurements of forces, while allowing simultaneously controlled evaporation rates, in situ microscopic observations, and thus quantitative estimates of normal stresses. We then performed an extensive study of the drying of a charged colloidal dispersion using this setup. Stress measurements clearly show the emergence of large tensile stresses during drying, well-before the solidification stage evidenced by the invasion of the porous colloidal material by air. Combined measurements of solid deformation and concentration profiles (particle tracking, Raman micro-spectroscopy) help us to demonstrate that these stresses are due to the formation of a solid at a low volume fraction, which further undergoes drying-induced shear deformations up to the colloid close-packing, as also supported by large deformation poroelastic modeling. Above all, our results highlight the importance of repulsive colloidal interactions in the build-up of mechanical stresses during drying.

High-resolution patterning of solution-processable materials via externally engineered pinning of capillary bridges

Electronics based on solution-processable materials are promising for applications in many fields which stimulated enormous research interest in liquid-drying and pattern formation. However, assembling of structure with submicrometre/nanometre resolution through liquid process is very challenging. We show a simple method to rapidly generate polymer structures with deep-submicrometre-sized features over large areas. In this method, a solution film is dried on a substrate under a suspended flexible template with groove/ridge surface topography. Upon solvent evaporation, the solution splits in the grooves and forms capillary bridges between the template and substrate, which are firmly pinned by the edges of the template grooves. This groove pinning stabilizes the contact lines, thereby allowing the formation of fine patterned structures with high aspect ratios which were used to fabricate various functional materials and electronic devices. We also produced secondary self-assembled nano-stripe patterns with resolutions of about 50 nm on the primary lines.

Humidity-insensitive water evaporation from molecular complex fluids

We investigated theoretically water evaporation from concentrated supramolecular mixtures, such as solutions of polymers or amphiphilic molecules, using numerical resolutions of a one-dimensional model based on mass transport equations. Solvent evaporation leads to the formation of a concentrated solute layer at the drying interface, which slows down evaporation in a long-time-scale regime. In this regime, often referred to as the falling rate period, evaporation is dominated by diffusive mass transport within the solution, as already known. However, we demonstrate that, in this regime, the rate of evaporation does not also depend on the ambient humidity for many molecular complex fluids. Using analytical solutions in some limiting cases, we first demonstrate that a sharp decrease of the water chemical activity at high solute concentration leads to evaporation rates which depend weakly on the humidity, as the solute concentration at the drying interface slightly depends on the humidity. However, we also show that a strong decrease of the mutual diffusion coefficient of the solution enhances considerably this effect, leading to nearly independent evaporation rates over a wide range of humidity. The decrease of the mutual diffusion coefficient indeed induces strong concentration gradients at the drying interface, which shield the concentration profiles from humidity variations, except in a very thin region close to the drying interface.

Kinetics in directional drying of water that contains deformable non-volatile oil droplets

Herein, we report assessments of the kinetics in directional drying of water that contains non-volatile oil droplets, based on direct observations using a confocal microscope. The water was found to evaporate at a constant rate during the initial stage of drying, after which the evaporation rate decreased. The dispersed oil droplets were compressed and distorted as the surrounding water was lost. Further evaporation of water resulted in coalescence of the oil droplets, with the eventual formation of an oil layer at the drying interface. However, it was apparent that the drying rate decreased even before the formation of this oil layer. We propose that the restricted transport of water via the narrow paths between the distorted oil droplets was responsible for the decreased drying rate. A mathematical model based on foam drainage theory is proposed and describes the experimental data very well. This work also determined that the critical disjoining pressure for the oil droplets is affected by the drying rate, such that higher pressure values are associated with slow drying conditions. The drying kinetics and stability of the dispersed oil droplets are discussed.

Drying paint: from micro-scale dynamics to mechanical instabilities

Charged colloidal dispersions make up the basis of a broad range of industrial and commercial products, from paints to coatings and additives in cosmetics. During drying, an initially liquid dispersion of such particles is slowly concentrated into a solid, displaying a range of mechanical instabilities in response to highly variable internal pressures. Here we summarize the current appreciation of this process by pairing an advection-diffusion model of particle motion with a Poisson-Boltzmann cell model of inter-particle interactions, to predict the concentration gradients in a drying colloidal film. We then test these predictions with osmotic compression experiments on colloidal silica, and small-angle X-ray scattering experiments on silica dispersions drying in Hele-Shaw cells. Finally, we use the details of the microscopic physics at play in these dispersions to explore how two macroscopic mechanical instabilities-shear-banding and fracture-can be controlled.This article is part of the themed issue 'Patterning through instabilities in complex media: theory and applications.'

Confinement-induced alterations in the evaporation dynamics of sessile droplets

Evaporation of sessile droplets has been a topic of extensive research. However, the effect of confinement on the underlying dynamics has not been well explored. Here, we report the evaporation dynamics of a sessile droplet in a confined fluidic environment. Our findings reveal that an increase in the channel length delays the completion of the evaporation process and leads to unique spatio-temporal evaporation flux and internal flow. The evaporation modes (constant contact angle and constant contact radius) during the droplet lifetime however exhibit global similarity when normalized by appropriate length and timescales. These results are explained in light of an increase in vapor concentration inside the channel due to greater accumulation of water vapor on account of increased channel length. We have formulated a theoretical framework which introduces two key parameters namely an enhanced concentration of the vapor field in the vicinity of the confined droplet and a corresponding accumulation lengthscale over which the accumulated vapor relaxes to the ambient concentration. Using these two parameters and modified diffusion based evaporation we are able to show that confined droplets exhibit a universal behavior in terms of the temporal evolution of each evaporation mode irrespective of the channel length. These results may turn out to be of profound importance in a wide variety of applications, ranging from surface patterning to microfluidic technology.

Modeling Flow Coating of Colloidal Dispersions in the Evaporative Regime: Prediction of Deposit Thickness

We investigate flow coating processes, i.e., the formation of dry coatings starting from dilute complex fluids confined between a static blade and a moving substrate. In particular, we focus on the evaporative regime encountered at low substrate velocity, at which the coating flow is driven mainly by solvent evaporation in the liquid meniscus. In this regime, general arguments based on mass conservation show that the thickness of the dry film decreases as the substrate velocity increases, unlike the behavior in the well-known Landau-Levich regime. This work focuses on colloidal dispersions, which deserve special attention. Indeed, flow coating is expected to draw first a solvent-saturated film of densely packed colloids, which further dries fully when air invades the pores of the solid film. We first develop a model based on the transport equations for binary mixtures, which can describe this phenomenon continuously, using appropriate boundary conditions and a criterion to take into account pore-emptying in the colloidal film. Extensive numerical simulations of the model then demonstrate two regimes for the deposit thickness as a function of the process parameters (substrate velocity, evaporation rate, bulk concentration, and particle size). We finally derive an analytical model based on simplified transport equations that can reproduce the output of our numerical simulations very well. This model can predict analytically the two observed asymptotic regimes and therefore unifies the models recently reported in the literature.

Impact of the collective diffusion of charged nanoparticles in the convective/capillary deposition directed by receding contact lines

The motion of electrically charged particles under crowding conditions and subjected to evaporation-driven capillary flow might be ruled by collective diffusion. The concentration gradient developed inside an evaporating drop of colloidal suspension may reduce by diffusion the number of particles transported toward the contact line by convection. Unlike self-diffusion coefficient, the cooperative diffusion coefficient of interacting particles becomes more pronounced in crowded environments. In this work, we examined experimentally the role of the collective diffusion of charge-stabilized nanoparticles in colloidal patterning. To decouple the sustained evaporation from the contact line motion, we conducted evaporating menisci experiments with driven receding contact lines at low capillary number. This allowed us to explore convective assembly at fixed and low bulk concentration, which enabled to develop high concentration gradients. At fixed velocity of receding contact line, we explored a variety of substrate-particle systems where the particle-particle electrostatic interaction was changed (via p H) as well as the substrate receding contact angle and the relative humidity. We found that the particle deposition directed by receding contact lines may be controlled by the interplay between evaporative convection and collective diffusion, particularly at low particle concentration.

Drying with no concentration gradient in large microfluidic droplets

In most situations, drying is accompanied by the development of strong concentration gradients. Here, we evidence theoretically and experimentally that there exist microfluidic geometries for which confined drying becomes homogeneous, i.e., with no concentration gradient regardless of the type of solute involved in the process; ions, molecules, and colloids do concentrate in the same way providing a limited set of assumptions concerning the microfluidic geometry. It thus makes possible the establishment of phase diagrams of multi-component mixtures at the nanoliter scale.

In-plane particle counting at contact lines of evaporating colloidal drops: effect of the particle electric charge

Complete understanding of colloidal assembly is still a goal to be reached. In convective assembly deposition, the concentration gradients developed in evaporating drops or reservoirs are usually significant. However, collective diffusion of charge-stabilized particles has been barely explored. The balance between convective and diffusive flows may dictate the particle dynamics inside evaporating colloidal drops. In this work we performed in situ counting of fluorescent particles in the vicinity of the triple line of evaporating sessile drops by using confocal laser scanning microscopy. We used particles of different sizes, with different charge response over the pH scale and we focused on charged and nearly uncharged particles. Two substrates with different receding contact angles were used. Binary colloidal mixtures were used to illustrate simultaneously the accumulation of particles with two different charge states at the triple line. The deposition rate close to the triple line was different depending on the electric state of the particle, regardless of the substrate used.

Evaporation-induced flows inside a confined droplet of diluted saline solution

Flow patterns inside a droplet of diluted aqueous NaCl solution confined by two flat substrates under natural evaporation were investigated both experimentally and numerically. We focused on natural convection-driven flows inside confined droplets at high Rayleigh numbers (i.e., the ratio of buoyancy to diffusion, Ra), where the convection of solutes is strongly dominant, compared to diffusion. The evaporated water at the free surface of the droplet builds up a concentration gradient inside the solution, which induces the Rayleigh convection flow. Three-dimensional trajectories of tracer particles in the droplet were tracked, and axisymmetric flow motions induced by the Rayleigh convection were experimentally measured by using a digital in-line holographic microscopy technique. In addition, the effects of the confined droplet's aspect ratio and the liquid's molar concentration on the evaporation-induced flows were investigated. The convection velocity is found to be increased as molar concentration increases, because Rayleigh convection becomes significant at high the molar concentration is high (i.e. high Ra). Our numerical simulation based on the Boussinesq approximation fairly well predicted the velocity profiles of evaporating confined droplets at low concentrations. Consequently, evaporation kinetics inside the confined droplets can be controlled with varying droplet's aspect ratio and the liquid's molar concentration, which provides helpful information for the design of biochemical microplating with limited resources and for tuning self-assembly micro/nanoparticle clusters.

Influence of particle shape on bending rigidity of colloidal monolayer membranes and particle deposition during droplet evaporation in confined geometries

We investigate the influence of particle shape on the bending rigidity of colloidal monolayer membranes (CMMs) and on evaporative processes associated with these membranes. Aqueous suspensions of colloidal particles are confined between glass plates and allowed to evaporate. Confinement creates ribbonlike air-water interfaces and facilitates measurement and characterization of CMM geometry during drying. Interestingly, interfacial buckling events occur during evaporation. Extension of the description of buckled elastic membranes to our quasi-2D geometry enables the determination of the ratio of CMM bending rigidity to its Young's modulus. Bending rigidity increases with increasing particle anisotropy, and particle deposition during evaporation is strongly affected by membrane elastic properties. During drying, spheres are deposited heterogeneously, but ellipsoids are not. Apparently, increased bending rigidity reduces contact line bending and pinning and induces uniform deposition of ellipsoids. Surprisingly, suspensions of spheres doped with a small number of ellipsoids are also deposited uniformly.

Solutal convection in confined geometries: enhancement of colloidal transport

We evidence experimentally and theoretically that natural convection driven by solutal density differences in a molecular binary mixture can boost the transport of colloids. We demonstrate that such buoyancy-driven flows have a negligible influence on the gradients that generate them, for moderate Rayleigh numbers in a confined geometry. These flows therefore do not homogenize the binary mixture but can disperse very efficiently large solutes. We illustrate the relevance of such effects thanks to several original experiments: drying of confined droplets, microfluidic evaporation, and interdiffusion in microfluidic flows.