We study the evaporation-induced stratification of a mixture of short and long polymer chains in a drying droplet using molecular simulations. We systematically investigate the effects of hydrodynamic interactions (HI) on this process by comparing hybrid simulations accounting for HI between polymers through the multiparticle collision dynamics technique with free-draining Langevin dynamics simulations neglecting the same. We find that the dried supraparticle morphologies are homogeneous when HI are included but are stratified in core--shell structures (with the short polymers forming the shell) when HI are neglected. The simulation methodology unambiguously attributes this difference to the treatment of the solvent in the two models. We rationalize the presence (or absence) of stratification by measuring phenomenological multicomponent diffusion coefficients for the polymer mixtures. The diffusion coefficients show the importance of not only solvent backflow but also HI between polymers in controlling the dried supraparticle morphology.
Nonequilibrium molecular dynamics simulations are used to investigate the influence of hydrodynamic interactions on vertical segregation (stratification) in drying mixtures of long and short polymer chains. In agreement with previous computer simulations and theoretical modeling, the short polymers stratify on top of the long polymers at the top of the drying film when hydrodynamic interactions between polymers are neglected. However, no stratification occurs at the same drying conditions when hydrodynamic interactions are incorporated through an explicit solvent model. Our analysis demonstrat…
We report the optical and structural properties of starch films formed on drying droplets of starch solutions on a flat substrate. The starch films formed after drying are circular in shape and have an azimuthally symmetric "M-shaped" height profile along their diameter. These films are found to be semi-crystalline in nature and transparent in visible light. Our experimental results show that these films are optically uniaxial at their center but biaxial away from the center. The variation of birefringence along the radial direction is studied for the films formed after drying droplets with di…
The size-dependent contact angle and the drying and wetting morphological transition are studied with respect to the volume change for a spherical cap-shaped droplet placed on a spherical substrate. The line-tension effect is included using the rigorous formula for the Helmholtz free energy in the droplet capillary model. A morphological drying transition from a cap-shaped to a spherical droplet occurs when the substrate is hydrophobic and the droplet volume is small, similar to the transition predicted on a flat substrate. In addition, a morphological wetting transition from a cap-shaped to a…
When a liquid film of colloidal solution consisting of particles of different sizes is dried on a substrate, the colloids often stratify, where smaller colloids are laid upon larger colloids. This phenomenon is counter intuitive because larger colloids which have smaller diffusion constant are expected to remain near the surface during the drying process, leaving the layer of larger colloids on top of smaller colloids. Here we show that the phenomenon is caused by the interaction between the colloids, and can be explained by the diffusion model which accounts for the interaction between the co…
We present a study of patterns, formed in drying drops of aqueous gelatin solution containing sodium sulphate. The patterns are highly complex, consisting of a hierarchical sequence of rings which form concentric bands as well as dendritic crystalline aggregates. When the preparation of the complex fluid is done by mixing an aqueous solution of the salt with an aqueous solution of gelatin prepared separately, another feature is observed in the pattern on the dried out drop. This is a viscous fingering pattern, superposed on the series of rings. We try to explain the origin of these two feature…
A colloidal particle placed in an inhomogeneous solution of smaller non-adsorbing polymers will move towards regions of lower polymer concentration, in order to reduce the free energy of the interface between the surface of the particle and the solution. This phenomenon is known as diffusiophoresis. Treating the polymer as penetrable hard spheres, as in the Asakura-Oosawa model, a simple analytic expression for the diffusiophoretic drift velocity can be obtained. In the context of drying films we show that diffusiophoresis by this mechanism can lead to stratification under easily accessible ex…
A potential strategy for controlling stratification in a drying suspension of bidisperse particles is studied using molecular dynamics simulations. When the suspension is maintained at a constant temperature during fast drying, it can exhibit "small-on-top" stratification with an accumulation (depletion) of smaller (larger) particles in the top region of the drying film, consistent with the prediction of current theories based on diffusiophoresis. However, when only the region near the substrate is thermalized at a constant temperature, a negative temperature gradient develops in the suspensio…
The process of drying is a simple physical mechanism that drives a system to relax from one equilibrium point to another. The native states of the constituent particles in the droplets can be linked to the emergent morphological patterns via this drying process. This paper explores the interplay between different initial concentrations of a globular protein lysozyme ($ϕ_p$) and the salts ($ϕ_s$) in the phosphate buffer saline (PBS). The $ϕ_s$ = 0 wt% embodies the lysozyme solution prepared in de-ionized water. The samples at $ϕ_s$ = 0.9 wt% display a dark texture in the central region. We exam…
Exploring the role of hydrodynamic interactions in spherically-confined drying colloidal suspensions
Auburn University（奥本大学）；Leibniz-Institut für Polymerforschung Dresden e.V.（德累斯顿莱布尼茨聚合物研究所）；Technische Universität Dresden（德累斯顿工业大学）；Johannes Gutenberg University Mainz（美因茨约翰内斯·古腾堡大学）
A bio-colloidal drying droplet can be used as a pre-diagnostic technique. However, a successful clinical setting requires a fundamental understanding of the final morphology and the way it is related to the initial state of the constituents present in the droplet. This chapter focuses on the physics associated with different pattern formations in the globular protein, bovine serum albumin (BSA) at different phosphate-buffered saline concentrations. The study reports that the first-order statistics (FOS) and the gray level co-occurrence matrix (GLCM) analysis are capable of capturing structural…
Drying colloidal droplets have a wide range of applications from medical diagnostics to coatings for industries. This paper explores the effects of the substrate temperature (ranging from $25$ to $55 ^{\circ}$C) and various initial concentrations ($ϕ$) of $1$ to $20$ wt% of lysozyme in an aqueous solution on its drying and final dried film state using bright-field optical microscopy. The $ϕ$ is divided into three regimes, ultra-concentrated ($20$ $<$ $ϕ$ $\leq$ $17$ wt%), concentrated ($17$ $<$ $ϕ$ $\leq$ $9$ wt%) and diluted ($9$ $<$ $ϕ$ $\leq$ $1$ wt%). Increasing $ϕ$ in these regimes finds …
We present an optical study that reveals the bulk dynamics of the stratification process in drying colloidal dispersions. Terahertz time-domain spectroscopy has been used to measure in situ solventborne and waterborne paint layers as a function of drying time. The dynamic behavior of the dry top layer and wet bottom layer thickness, as well as the bulk thickness, reflect the principal processes of the established drying mechanism. In addition, the results demonstrate stratification only when the drying process is in the evaporation controlled regime, whereas the coating is shown to remain a si…
I model the drying of a liquid film containing small and big colloid particles. Fortini et al. [A. Fortini et al, Phys. Rev. Lett. 116, 118301 (2016)] studied these films with both computer simulation and experiment. They found that at the end of drying the mixture had stratified with a layer of the smaller particles on top of the big particles. I develop a simple model for this process. The model has two ingredients: arrest of the diffusion of the particles at high density, and diffusiophoretic motion of the big particles due to gradients in the concentration of the small particles. The model…
In simulations and experiments, we study the drying of films containing mixtures of large and small colloidal particles in water. During drying, the mixture stratifies into a layer of the larger particles at the bottom with a layer of the smaller particles on top. We developed a model to show that a gradient in osmotic pressure, which develops dynamically during drying, is responsible for the segregation mechanism behind stratification.
We develop a dynamical density functional theory based model for the drying of colloidal films on planar surfaces. We consider mixtures of two different sizes of hard-sphere colloids. Depending on the solvent evaporation rate and the initial concentrations of the two species, we observe varying degrees of stratification in the final dried films. Our model predicts the various structures described in the literature previously from experiments and computer simulations, in particular the small-on-top stratified films. Our model also includes the influence of adsorption of particles to the interfa…
Drying a droplet of colloidal dispersion can result in complex pattern formation due to both development and deformation of a skin at the drop surface. The present study focus on the drying process of droplets of colloidal dispersions in a confined geometry where direct observations of the skin thickness are allowed. During the drying, a buckling process is followed by a single depression growth inside the drop. The deformation of the droplet is found to be generic and is studied for various colloidal dispersions. The final shape can be partly explained by simple energy analysis based on the c…
We propose a theory for the multi-ring pattern of the deposits that are formed when droplets of suspension are dried on a substrate. Assuming a standard model for the stick-slip motion of the contact line, we show that as droplets evaporate, many concentric rings of deposits are formed, but are taken over by a solid-circle pattern in the final stage of drying. An analytical expression is given to indicate when ring-pattern changes to solid-circle pattern during an evaporation process. The results are in qualitative agreement with existing experiments, and the other predictions on how the evapo…
A method of simulating the drying process of a soft matter solution with an implicit solvent model by moving the liquid-vapor interface is applied to various solution films and droplets. For a solution of a polymer and nanoparticles, we observe "polymer-on-top" stratification, similar to that found previously with an explicit solvent model. Furthermore, "polymer-on-top" is found even when the nanoparticle size is smaller than the radius of gyration of the polymer chains. For a suspension droplet of a bidisperse mixture of nanoparticles, we show that core-shell clusters of nanoparticles can be …
Sessile droplets of aqueous poly(ethylene oxide) solution, with average molecular weight of 100 kDa, are monitored during evaporative drying at ambient conditions over a range of initial concentrations $c_0$. For all droplets with $c_0 \geq 3%$, central conical structures, which can be hollow and nearly 50% taller than the initial droplet, are formed during a growth stage. Although the formation of superficially similar structures has been explained for glass-forming polymers using a skin-buckling model which predicts the droplet to have constant surface area during the growth stage (L. Paucha…
Large scale molecular dynamics simulations are used to study drying suspensions of a binary mixture of large and small particles in explicit and implicit solvents. The solvent is first modeled explicitly and then mapped to a uniform viscous medium by matching the diffusion coefficients and the pair correlation functions of the particles. `Small-on-top' stratification of the particles, with an enrichment of the smaller ones at the receding liquid-vapor interface during drying, is observed in both models under the same drying conditions. With the implicit solvent model, we are able to model much…
When colloidal suspensions dry, stresses build up and cracks often occur - a phenomenon undesirable for important industries such as paint and ceramics. We demonstrate an effective method which can completely eliminate cracking during drying: by adding emulsion droplets into colloidal suspensions, we can systematically decrease the amount of cracking, and eliminate it completely above a critical droplet concentration. Since the emulsion droplets eventually also evaporate, our technique achieves an effective function while making little changes to the component of final product, and may therefo…
In drying liquid films of polymer-colloid mixtures, the stratification in which polymers are placed on top of larger colloids is studied. It is often presumed that the formation of segregated polymer-colloid layers is solely due to the proportion in size at fast evaporation as in binary colloid mixtures. By comparing experiments with a theoretical model, we found that the transition in viscosity near the drying interface was another important parameter for controlling the formation of stratified layers in polymer-colloid mixtures. At high evaporation rates, increased polymer concentrations nea…
When a droplet containing a non-volatile component is dried on a substrate, it leaves a ringlike deposit on the substrate. We propose a theory which predicts the deposit distribution based on a model of fluid flow and contact line motion of the droplet. It is shown that the deposition pattern changes continuously from coffee-ring to volcano-like and to mountain-like depending on the mobility of the contact line and the evaporation rate. Analytical expression is given for the peak position of the distribution of deposit left on the substrate.
We investigate the 3D structure and drying dynamics of complex mixtures of emulsion droplets and colloidal particles, using confocal microscopy. Air invades and rapidly collapses large emulsion droplets, forcing their contents into the surrounding porous particle pack at a rate proportional to the square of the droplet radius. By contrast, small droplets do not collapse, but remain intact and are merely deformed. A simple model coupling the Laplace pressure to Darcy's law correctly estimates both the threshold radius separating these two behaviors, and the rate of large-droplet evacuation. Fin…
We isolate a nano-colloidal droplet of surrogate mucosalivary fluid to gain fundamental insights into the infectivity of air borne nuclei during the Covid-19 pandemic. Evaporation experiments are performed with salt-water solutions seeded with a viral load of inactive nanoparticles in an acoustic levitator. We seek to emulate the drying, flow and precipitation dynamics of such air borne mucosalivary droplets. Observations with the surrogate fluid are validated by similar experiments with actual samples from a healthy subject. A unique feature emerges with regards to the final crystallite dimen…
Pattern formation in drying protein droplets continues to attract considerable research attention because it can be linked to specific protein-protein interactions. An extensive study of the drying evolution and the final crack patterns are presented, highlighting the concentration dependence (from 1 to 13 wt%) on two globular proteins, lysozyme (Lys) and bovine serum albumin (BSA), in de-ionized water. The drying evolution starts with a constant contact radius mode and shifts to a mixed mode where both fluid front and contact angle changes. The contact angle monotonically decreases, whereas, …
We report results of a detailed experimental investigation into the drying of sessile droplets of aqueous poly(ethylene oxide) (PEO) polymer solutions under various experimental conditions. Samples are prepared with a range of initial concentrations c_0 and are filtered to remove traces of undissolved PEO clusters. In typical experiments, droplets with initial volumes between 5\muL and 50\muL are left to evaporate while temperature and relative humidity are monitored. Droplets either form a disk-like solid "puddle" or a tall conical "pillar". The droplet mass is monitored using a microbalance …
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 the deposition. In this paper, 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 behaviour and a dot-like deposit is left aft…
A quantitative understanding of the evaporative drying kinetics and nucleation rates of aqueous based aerosol droplets is important for a wide range of applications, from atmospheric aerosols to industrial processes such as spray drying. Here, we introduce a numerical model for interpreting measurements of the evaporation rate and phase change of drying free droplets made using a single particle approach. We explore the evaporation of aqueous sodium chloride and sodium nitrate solution droplets. Although the chloride salt is observed to reproducibly crystallise at all drying rates, the nitrate…
Understanding the relationship between colloidal building block shape and self-assembled material structure is important for the development of novel materials by self-assembly. In this regard, colloidal superballs are unique building blocks because their shape can smoothly transition between spherical and cubic. Assembly of colloidal superballs under spherical confinement results in macroscopic clusters with ordered internal structure. By utilizing Small Angle X-Ray Scattering (SAXS), we probe the internal structure of colloidal superball dispersion droplets during confinement. We observe and…
Spreading of respiratory diseases, such as COVID-19, from contaminated surfaces is dependent on the drying time of the deposited droplets containing the virus. The evaporation rate depends on environmental conditions, such as ambient temperature and relative humidity and physical properties (e.g., droplet volume, contact angle and composition). The respiratory droplets contain salt (NaCl), protein (mucin), and surfactant (dipalmitoylphosphatidylcholine) in addition to water, which are expected to influence the evaporation in a big way. A diffusion-based theoretical model for estimating the dry…
The method of formation of nanoparticle aggregates such as high-coverage spherical shells of microspheres or 3-D micro crystals grown in the geometry unaffected by a substrate is described. In the reported experiment, the evaporation of single levitated water droplet containing 200 nm diameter polystyrene spheres was studied. Successive stages of the drying process were discussed by analyzing the intensity of light elastically scattered by the evaporating droplet. The numerically simulated self-assembly coincides nicely with the observed morphologies resulting from transformation of a droplet …
Large scale molecular dynamics simulations for bidisperse nanoparticle suspensions with an explicit solvent are used to investigate the effects of evaporation rates and volume fractions on the nanoparticle distribution during drying. Our results show that ``small-on-top'' stratification can occur when ${\rm Pe}_sϕ_s \gtrsim c$ with $c\sim 1$, where ${\rm Pe}_s$ is the Péclet number and $ϕ_s$ is the volume fraction of the smaller particles. This threshold of ${\rm Pe}_sϕ_s$ for ``small-on-top'' is larger by a factor of $\simα^2$ than the prediction of the model treating solvent as an implicit v…
We predict and analyze the drying time of respiratory droplets from a COVID-19 infected subject, which is a crucial time to infect another subject. The drying of the droplet is predicted by diffusion-limited evaporation model for a sessile droplet placed on a partially-wetted surface with a pinned contact line. The variation of droplet volume, contact angle, ambient temperature, and humidity are considered. We analyze the chances of the survival of the viruses present in the droplet, based on the lifetime of the droplets in several conditions, and find that the chances of survival of the virus…
We report a study on the kinetics of drying of a droplet of aqueous gelatin containing sodium chloride. The process of drying recorded on video, clearly shows different regimes of growth leading to a variety of crystalline patterns. Large faceted crystals of $\sim$mm size form in the early stages of evaporation, followed by highly branched multi-fractal patterns with micron sized features. We simulate the growth using a simple algorithm incorporating aggregation and evaporation, which reproduces the cross-over between the two growth regimes. As evaporation proceeds, voids form in the gel film.…
Coalescence-induced alignment of anisotropic particles in drying sessile droplets
Forschungszentrum Jülich（于利希研究中心）；Helmholtz Institute Erlangen-Nürnberg for Renewable Energy (IET-2)（亥姆霍兹埃尔朗根-纽伦堡可再生能源研究所（IET-2））；Friedrich-Alexander-Universität Erlangen-Nürnberg（埃尔朗根-纽伦堡弗里德里希·亚历山大大学）
We simulated an experiment in which a thin colloidal sessile droplet is allowed to dry out on a horizontal hydrophilic surface when a mask just above the droplet predominantly allows evaporation from the droplet free surface directly beneath the holes in the mask [Harris D J, Hu H, Conrad J C and Lewis J A 2007 \textit{Phys. Rev. Lett.} \textbf{98} 148301]. We considered one particular case when centre-to-centre spacing between the holes is much less than the drop diameter. In our model, advection, diffusion, and sedimentation were taken into account. FlexPDE was utilized to solve an advection…
This short review is devoted to the simple process of drying a multi-component droplet consisting of a complex fluid containing a salt. These processes provide a fascinating subject for study. The explanation of the rich variety of patterns formed is not only an academic challenge, but a problem of practical importance, as applications are growing in medical diagnosis and improvement of coating/printing technology. The fundamental scientific problem is the study of the mechanism of micro- and nanoparticle self-organization in open systems. The specific fundamental problem to be solved, related…
How particles are deposited at the edge of evaporating droplets, i.e. the {\em coffee ring} effect, plays a crucial role in phenomena as diverse as thin-film deposition, self-assembly, and biofilm formation. Recently, microorganisms have been shown to passively exploit and alter these deposition dynamics to increase their survival chances under harshening conditions. Here, we show that, as the droplet evaporation rate slows down, bacterial mobility starts playing a major role in determining the growth dynamics of the edge of drying droplets. Such motility-induced dynamics can influence several…
The vertical drying of a two dimensional colloidal film containing zero-thickness sticks (lines) was studied by means of kinetic Monte Carlo (MC) simulations. The continuous two-dimensional problem for both the positions and orientations was considered. The initial state before drying was produced using a model of random sequential adsorption with isotropic orientations of the sticks. During the evaporation, an upper interface falls with a linear velocity in the vertical direction and the sticks undergo translational and rotational Brownian motions. The MC simulations were run at different ini…
Dynamic density functional theory (DDFT) is a promising approach for predicting the structural evolution of a drying suspension containing one or more types of colloidal particles. The assumed free-energy functional is a key component of DDFT that dictates the thermodynamics of the model and, in turn, the density flux due to a concentration gradient. In this work, we compare several commonly used free-energy functionals for drying hard-sphere suspensions including local-density approximations based on the ideal-gas, virial, and Boublík-Mansoori-Carnahan-Starling-Leland (BMCSL) equations of sta…
We report a study of the structure of droplets of colloidal gels containing dissolved sodium chloride. The components segregate and form intricate patterns. The salt crystalizes in fractal and multi-fractal dendritic forms which are determined by the material which forms the colloidal gel. Here potato starch, gelatine and carboxymethyl cellulose have been used. The substrate also plays a role in some cases. Photographs and micrographs at different level of magnification are shown.
The free-energy barrier of filling a spherical cavity having an inner wall of various wettabiities is studied. The morphology and free energy of a lens-shaped droplet are determined from the minimum of the free energy. The effect of line tension on the free energy is also studied. Then, the equilibrium contact angle of the droplet is determined from the generalized Young's equation. By increasing the droplet volume within the spherical cavity, the droplet morphology changes from spherical with an equilibrium contact angle of $180^{\circ}$ to a lens with a convex meniscus, where the morphologic…
Using lubrication theory, drying processes of sessile colloidal droplets on a solid substrate are studied. A simple model is proposed to describe temporal dynamics both the shape of the drop and the volume fraction of the colloidal particles inside the drop. The concentration dependence of the viscosity is taken into account. It is shown that the final shapes of the drops depend on both the initial volume fraction of the colloidal particles and the capillary number. The results of our simulations are in a reasonable agreement with the published experimental data. The computations for the drops…
Evaporation-Driven Nanowire Self-Assembly in an Elongated Droplet
Helmholtz Institute Erlangen-Nürnberg for Renewable Energy (IET-2), Forschungszentrum Jülich（于利希研究中心埃尔朗根-纽伦堡亥姆霍兹可再生能源研究所）；Friedrich-Alexander-Universität Erlangen-Nürnberg（埃尔朗根-纽伦堡弗里德里希·亚历山大大学）
