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. Finally, we use these systems to make novel hierarchical structures.
The ordering of particles in the drying process of a colloidal suspension is crucial in determining the properties of the resulting film. For example, microscopic inhomogeneities can lead to the formation of cracks and defects that can deteriorate the quality of the film considerably. This type of problem is inherently multiscale and here we study it numerically, using our recently developed method for the simulation of soft polymeric capsules in multicomponent fluids. We focus on the effect of the particle softness on the film microstructure during the drying phase and how it relates to the f…
Drying of bacterial suspensions is frequently encountered in a plethora of natural and engineering processes. However, the evaporation-driven mechanical instabilities of dense consolidating bacterial suspensions have not been explored heretofore. Here, we report the formation of two different crack patterns of drying suspensions of \textit{Escherichia coli} (\textit{E. coli}) with distinct motile behaviors. Circular cracks are observed for wild-type \textit{E. coli} with active swimming, whereas spiral-like cracks form for immotile bacteria. Using the elastic fracture mechanics and the poroela…
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…
Cracking of suspensions during drying is a common problem. While additives, e.g. binders and surfactants, can mitigate this problem, some applications, such as printing conductive pastes or sintering green bodies, do not lend themselves to the use of additives. Capillary suspensions provide an alternative formulation without additives. In this work, we use simultaneous stress and weight measurements to investigate the influence of formulation and drying conditions. Capillary suspensions dry more homogeneously and with lower peak stresses, leading to an increased robustness against cracking com…
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…
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…
From suspensions to porous multilayers: microstructure formation and particle packing in drying colloidal films
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（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 report an experimental study of the drying-induced peeling of a bilayer, consisting of an elastomeric disk coated with a suspension of nanoparticles. We show that although capillary forces associated with the scale of the droplet can not compete with the adhesion of the elastomer on a surface, nevertheless large tensile stresses develop in the coating, which results in a moment bending the bilayer. We attribute this stress to the nano-menisci in the pores of the colloidal material and we propose a model that describes successfully the early stage curvature of the bilayer. Thus, we show that…
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…
Hypothesis: Lateral accumulation and film defects during drying of hard particle coatings is a common problem, typically solved using polymeric additives and surface active ingredients, which require further processing of the dried film. Capillary suspensions with their tunable physical properties, devoid of polymers, offer new pathways in producing uniform and defect free particulate coatings. Experiments: We investigated the effect of small amounts of secondary liquid on the coating's drying behavior. Stress build-up and weight loss in a temperature and humidity controlled drying chamber wer…
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）
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…
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…
We study the stress developed during the drying of a colloidal drop of silica nanoparticles. In particular, we use the wrinkling instability of a thin floating sheet to measure the net stress applied by the deposit on the substrate and we focus on the effect of the particle polydispersity. In the case of a bidisperse suspension, we show that a small number of large particles substantially decreases the expected stress, which we interpret as the formation of lower hydrodynamic resistance paths in the porous material. As colloidal suspensions are usually polydisperse, we show for different avera…
The process of colloidal drying gives way to particle self-assembly in numerous elds including photonics or biotechnology. Yet, the mechanisms and conditions driving the nal particle arrangement in dry colloidal layers remain elusive. Here, we examine how the drying rate selects the nanostructure of thick dried layers in four dierent suspensions of silica nanospheres. Depending on particle size and dispersity, either an amorphous arrangement, a crystalline arrangement, or a rate-dependent amorphous-to-crystalline transition occurs at the drying surface. Amorphous arrangements are observed in t…
From paints to food products, solvent evaporation is ubiquitous and critically impacts product rheological properties. It affects Newtonian fluids by concentrating any non-volatile components and viscoelastic materials, which hardens up. In both of these cases, solvent evaporation leads to a change in the sample volume, which makes any rheological measurements particularly challenging with traditional shear geometries. Here we show that the rheological properties of a sample experiencing `slow' evaporation can be monitored in a time-resolved fashion by using a zero normal-force controlled prot…
We present a Monte Carlo (MC) grid-based model for the drying of drops of a nanoparticle suspension upon a heterogeneous surface. The model consists of a generalised lattice-gas in which the interaction parameters in the Hamiltonian can be varied to model different properties of the materials involved. We show how to choose correctly the interactions, to minimise the effects of the underlying grid so that hemispherical droplets form. We also include the effects of surface roughness to examine the effects of contact-line pinning on the dynamics. When there is a `lid' above the system, which pre…
We studied the morphology of linear particle deposits obtained by inkjet-printing of silica nanoparticle suspension in drying condition where contact line depinning occurs. We show that this evaporation mode can be obtained by adjusting the particle concentration in different solvents. For isolated drops, deposited manually or by inkjet printing, drying induces the formation of two concentric rings in which particles self-assemble into a monolayer. For fused drops, our main result is that stable rivulets could be formed by drop overlap leading, after drying, to the formation of three parallel …
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 …
Drying of particle suspensions is an ubiquitous phenomenon with many natural and practical applications. In particular, in unidirectional drying, the evaporation of the solvent induces flows which accumulate particles at the liquid/air interface. The progressive build-up of a dense region of particles can be used, in particular, in the processing of advanced materials and architectures while the development of heterogeneities and defects in such systems is critical to their function. A lot of attention has thus been paid to correlate the flow and particles dynamics to the ordering of particles…
When a suspension dries, the suspending fluid evaporates, leaving behind a dry film composed of the suspended particles. During the final stages of drying, the height of the fluid film on the substrate drops below the particle size, inducing local interface deformations that lead to strong capillary interactions among the particles. Although capillary interactions between rigid particles are well studied, much is still to be understood about the behaviour of soft particles and the role of their softness during the final stages of film drying. Here, we use our recently-introduced numerical meth…
The vertical drying of a colloidal film containing rod-like particles was studied by means of kinetic Monte Carlo (MC) simulation. The problem was approached using a two-dimensional square lattice and the rods were represented as linear $k$-mers (i.e., particles occupying $k$ adjacent sites). The initial state before drying was produced using a model of random sequential adsorption (RSA) with isotropic orientations of the $k$-mers (orientation of the $k$-mers along horizontal $x$ and vertical $y$ directions are equiprobable). In the RSA model, overlapping of the $k$-mers is forbidden. During t…
We develop a lattice gas model for the drying of droplets of a nanoparticle suspension on a planar surface, using dynamical density functional theory (DDFT) to describe the time evolution of the solvent and nanoparticle density profiles. The DDFT assumes a diffusive dynamics but does not include the advective hydrodynamics of the solvent, so the model is relevant to highly viscous or near to equilibrium systems. Nonetheless, we see an equivalent of the coffee-ring stain effect, but in the present model it occurs for thermodynamic rather the fluid-mechanical reasons. The model incorporates the …
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…
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…
It is shown that porous spherical particles can be obtained via the freezing of silica nanoparticle aqueous suspensions emulsified in a continuous oil phase. After two freeze-thaw cycles, nanoparticles turn aggregated into flocculated objects with microstructure that depends upon emulsion volume fraction and droplet size. For low volume fractions, regular microspheres are produced while for large ones, irregular beads with several tens of micrometer radius are formed. Electronic microscopy, mercury porosimetry and nitrogen adsorption are used to get insights into these porous particles typical…
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 ra…
Under inhomogeneous flow, dense suspensions exhibit complex behaviour that violates the conventional homogenous rheology. Specifically, one finds flowing regions with a macroscopic friction coefficient below the yielding criterion, and volume fraction above the jamming criterion. We demonstrate the underlying physics by incorporating shear rate fluctuations into a recently proposed tensor model for the microstructure and stress, and applying the model to an inhomogeneous flow problem. The model predictions agree qualitatively with particle-based simulations.
Recent experiments report that slowly-sheared noncolloidal particle suspensions can exhibit unexpected rate($ω$)-dependent complex viscosities in oscillatory shear, despite a constant relative viscosity in steady shear. Using a minimal hydrodynamic model, we show that a weak interparticle attraction reproduces this behavior. At volume fractions $ϕ=20\sim50$%, the complex viscosities in both experiments and simulations display power-law reductions in shear, with a $ϕ$-dependent exponent maximum at $ϕ=40$%, resulting from the interplay between hydrodynamic, collision and adhesive interactions. F…
We report rheological measurements of a noncolloidal particle suspension in a Newtonian solvent at 40% solid volume fraction. An anomalous, frequency-dependent complex viscosity is found under oscillatory shear (OS) flow, whereas a constant dynamic viscosity is found under the same shear rates in steady shear (SS) flow. We show that this contradiction arises from the underlying microstructural difference between OS and SS, mediated by weak interparticle forces. Discrete element simulations of proxy particle suspensions confirm this hypothesis and reveal an adhesion-induced, shear thinning mech…
The present article highlights an approach to generate contrasting patterns from drying droplets in a liquid bridge configuration, different from well-known coffee rings. Reduction of the confinement distance (the gap between the solid surfaces) leads to systematized nano-particle agglomeration yielding to spokes-like patterns similar to those found on scallop shells instead of circumferential edge deposition. Alteration of the confinement length modulates the curvature that entails variations in the evaporation flux across the liquid-vapor interface. Consequently, flow inside different liquid…
The complexity of the interactions between the constituent granular and liquid phases of a suspension requires an adequate treatment of the constituents themselves. A promising way for numerical simulations of such systems is given by hybrid computational frameworks. This is naturally done, when the Lagrangian description of particle dynamics of the granular phase finds a correspondence in the fluid description. In this work we employ extensions of the Lattice-Boltzmann Method for non-Newtonian rheology, free surfaces, and moving boundaries. The models allows for a full coupling of the phases,…
When a droplet is generated, the ligament connecting the drop to the nozzle thins down and eventually pinches off. Adding solid particles to the liquid phase leads to a more complex dynamic, notably by increasing the shear viscosity. Moreover, it introduces an additional length scale to the system, the diameter of the particles, which eventually becomes comparable to the diameter of the ligament. In this paper, we experimentally investigate the thinning and pinch-off of drops of suspensions with two different sizes of particles. We characterize the thinning for different particle size ratios a…
The formation of drops of a complex fluid, for instance including dissolved polymers and/or solid particles, has practical implications in several industrial and biophysical processes. In this Letter, we experimentally investigate the generation of drops of a viscoelastic suspension, made of non-Brownian spherical particles dispersed in a dilute polymer solution. Using high-speed imaging, we characterize the different stages of the detachment. Our experiments show that the particles primarily affect the initial Newtonian necking by increasing the fluid viscosity. In the viscoelastic regime, pa…
