Drying paint: from micro-scale dynamics to mechanical instabilities

Small variations in particle-level interactions lead to large structural heterogeneities in colloidal gels

Colloidal gels typically exhibit mechanical properties akin to a viscoelastic solid, influenced by their underlying particulate network. Hence, the structural and morphological characteristics of the colloidal network have a significant effect on the rigidity of the gel. In this study, we show how seemingly small variations in the particle-level interactions throughout the system result in larger scale structural heterogeneities. While the microscale particle level descriptors of the colloidal network remain largely unaffected by heterogeneous interactions, larger scale properties of a colloidal gel change appreciably. The overall cluster-level mesostructure of a colloidal gel is found to be sensitive to the small variations in the interaction potential at the particle level.

Dynamics of drying colloidal suspensions, measured by optical coherence tomography

Colloidal suspensions are the basis of a wide variety of coatings, prepared as liquids and then dried into solid films. The processes at play during film formation, however, are difficult to observe directly. Here, we demonstrate that optical coherence tomography (OCT) can provide fast, non-contact, precise profiling of the dynamics within a drying suspension. Using a scanning Michelson interferometer with a broadband laser source, OCT creates cross-sectional images of the optical stratigraphy of a sample. With this method, we observed the drying of colloidal silica in Hele-Shaw cells with 10 μm transverse and 1.8 μm depth resolution, over a 1 cm scan line and a 15 s sampling period. The resulting images were calibrated to show how the concentration of colloidal particles varied with position and drying time. This gives access to important transport properties, for example, of how collective diffusion depends on particle concentration. Looking at early-time behaviours, we also show how a drying front initially develops, and how the induction time before the appearance of a solid film depends on the balance of diffusion and evaporation-driven motion. Pairing these results with optical microscopy and particle tracking techniques, we find that film formation can be significantly delayed by any density-driven circulation occurring near the drying front.

Directional drying of a colloidal dispersion: quantitative description with water potential measurements using water clusters in a poly(dimethylsiloxane) microfluidic chip

We have developed a poly(dimethylsiloxane) (PDMS) microfluidic chip to study the directional drying of a colloidal dispersion confined in a channel. Our measurements on a dispersion of silica nanoparticles once again revealed the phenomenology commonly observed for such systems: the formation of a porous solid with linear growth in the channel at short times, slowing down at longer times as the evaporation rate decreases. The growth of the solid is also accompanied by mechanical stresses that are released by the delamination of the solid from the channel walls and the formation of cracks. In addition to these observations, we report original measurements using hydrophilic filler in the PDMS formulation used (Sylgard-184). When the PDMS matrix is in contact with water, water molecules pool around these hydrophilic sites, resulting in the formation of microscopic water clusters whose size depends on the water potential ψ. In our work, we have used these water clusters to estimate the water potential profile in the channel as the porous solid grows. Using a transport model that also takes into account solid delamination in the channel, we then linked these water potential measurements to the hydraulic permeability of the porous solid. These measurements finally enabled us to show that the slowdown in the evaporation rate is due to the invasion of the porous solid by air/water nanomenisci at a critical capillary pressure ψcap.

Controlled viscous fingering in volatile fluid towards spontaneous evolution of ordered 3D patterns

Mimicking nature using artificial technologies has always been a quest/fascination of scientists and researchers of all eras. This paper characterizes viscous fingering instability-based, lithography-less, spontaneous, and scalable process towards fabrication of 3D patterns like nature-inspired honeycomb structures with ultra-high aspect ratio walls. Rich experimental characterization data on volatile polymer solution evolution in a uniport lifted Hele-Shaw cell (ULHSC) is represented on a non-dimensional phase plot. The plot with five orders of magnitude variation of non-dimensional numbers on each axis demarcates the regions of several newly observed phenomena: 'No retention', 'Bridge breaking', and 'Wall formation' with 'stable' and 'unstable' interface evolution. A new non-dimensional ratio of the velocity of evaporating static interface versus lifting velocity is proposed for the same. This phase plot along with physical insights into the phenomena observed, pave pathways for extending the method to multiport LHSC (MLHSC) to demonstrate multiwell honeycomb structures. The work thus establishes a solid foundation with valuable insights for scalable manufacturing of devices useful for application in biomedical and other domains.

Confined directional drying of a colloidal dispersion: kinetic modeling

We derive a model to describe the dynamics of confined directional drying of a colloidal dispersion. In such experiments, a dispersion of rigid colloids is confined in a capillary tube or a Hele-Shaw cell. Solvent evaporation from the open end accumulates the particles at the tip up to the formation of a porous packing that invades the cell at a rate . Our model based on a classical description of fluid mechanics and capillary phenomena, predicts different regimes for the growth of the consolidated packing, l versus t. At early times, the evaporation rate is constant and the growth is linear, l ∝ t. At longer times, the evaporation rate decreases and the consolidated packing grows as . This slowdown is either related to the recession of the drying interface within the packing thus adding a resistance to evaporation (capillary-limited regime), or to the Kelvin effect which decreases the partial pressure of water at the drying interface (flow-limited regime). We illustrate these results with numerical relations describing hard spheres, showing that these regimes are a priori experimentally observable. Beyond this description of the confined directional drying of colloidal dispersions, our results also highlight the importance of relative humidity control in such experiments.

Unidirectional drying of a suspension of diffusiophoretic colloids under gravity

Recent experiments (K. Inoue and S. Inasawa, RSC Adv., 2020, 10, 15763-15768) and simulations (J.-B. Salmon and F. Doumenc, Phys. Rev. Fluids, 2020, 5, 024201) demonstrated the significant impact of gravity on unidirectional drying of a colloidal suspension. However, under gravity, the role of colloid transport induced by an electrolyte concentration gradient, a mechanism known as diffusiophoresis, is unexplored to date. In this work, we employ direct numerical simulations and develop a macrotransport theory to analyze the advective-diffusive transport of an electrolyte-colloid suspension in a unidirectional drying cell under the influence of gravity and diffusiophoresis. We report three key findings. First, drying a suspension of solute-attracted diffusiophoretic colloids causes the strongest phase separation and generates the thinnest colloidal layer compared to non-diffusiophoretic or solute-repelled colloids. Second, when colloids are strongly solute-repelled, diffusiophoresis prevents the formation of colloid concentration gradient and hence gravity has a negligible effect on colloidal layer formation. Third, our macrotransport theory predicts new scalings for the growth of the colloidal layer. The scalings match with direct numerical simulations and indicate that the colloidal layer produced by solute-repelled diffusiophoretic colloids could be an order of magnitude thicker compared to non-diffusiophoretic or solute-attracted colloids. Our results enable tailoring the separation of colloid-electrolyte suspensions by tuning the interactions between the solvent, electrolyte, and colloids under Earth's or microgravity, which is central to ground-based and in-space applications.

Interplay of Consolidation Fronts and Cracks in Drying Colloidal Coatings and Its Application in Controlling Crack Pattern Formation

Cracks are frequently observed in drying colloidal coatings. Although a rich collection of crack patterns has been reported, the systematic study on how cracks grow into the final morphology during the drying process remains elusive. In this work, we use directional drying channels with wedge-shaped edges of different angles to study the interplay of advancing consolidation fronts and propagating cracks. We found that although the shape of the advancing consolidation fronts is altered by the drying edge, the growth direction of the following cracks remains perpendicular to the consolidation fronts during the whole drying process, resulting in cracks with a large curvature. We rationalize the evolution of consolidation fronts with the distribution of capillary pressure revealed by a Laplace model. Further, the growth direction of cracks can be explained by the fracture mechanics mechanism that the main orientation of internal tensile stresses developed during the consolidation determines the crack growth direction. Utilizing this understanding, wavy crack patterns are generated in rectangular drying channels with an alternating temperature field, demonstrating a feasible method of designing and controlling drying-induced crack patterns for micro-/nano-fabrication applications.

Recent progress on crack pattern formation in thin films

Fascinating pattern formation by quasi-static crack growth in thin films has received increasing interest in both interdisciplinary science and engineering applications. The paper mainly reviews recent experimental and theoretical progress on the morphogenesis and propagation of various quasi-static crack patterns in thin films. Several key factors due to changes in loading types and substrate confinement for choosing crack paths toward different patterns are summarized. Moreover, the effect of crack propagation coupled to other competing or coexisting stress-relaxation processes in thin films, such as interface debonding/delamination and buckling instability, on the formation and transition of crack patterns is discussed. Discussions on the sources and changes in the driving force that determine crack pattern evolution may provide guidelines for the reliability and failure mechanism of thin film structures by cracking and for controllable fabrication of various crack patterns in thin films.

Mild stratification in drying films of colloidal mixtures

Size stratification of bidisperse colloidal mixtures during vertical drying was investigated using the implicit solvent Langevin dynamics (LD) simulation and the explicit solvent lattice Boltzmann (LB) method. Simulations were performed for the Péclet number (Pe) over a wide range of 1-1000. In the case of a low size ratio of 2, mild stratification was observed in both simulation methods, in contrast to distinct stratification with thick "small-on-top" or "large-on-top" layers. The LD simulations exhibited a "small-on-top" stratification or mixed state. In contrast, the LB simulations exhibited a "large-on-top" or mixed state, according to the variation in Pe. The results demonstrated that the explicit solvent reduced the collective diffusion under moderate Pe conditions. This suppressed the steep concentration gradient of small particles in the packed region of particles near the air-solvent interface. Thus, distinguishable stratification patterns were obtained for the implicit and explicit solvent models.

Combinatorial topology and geometry of fracture networks

A map is proposed from the space of planar surface fracture networks to a four-parameter mathematical space, summarizing the average topological connectivity and geometrical properties of a network idealized as a convex polygonal mesh. The four parameters are identified as the average number of nodes and edges, the angular defect with respect to regular polygons, and the isoperimetric ratio. The map serves as a low-dimensional signature of the fracture network and is visually presented as a pair of three-dimensional graphs. A systematic study is made of a wide collection of real crack networks for various materials, collected from different sources. To identify the characteristics of the real materials, several well-known mathematical models of convex polygonal networks are presented and worked out. These geometric models may correspond to different physical fracturing processes. The proposed map is shown to be discriminative, and the points corresponding to materials of similar properties are found to form closely spaced groups in the parameter space. Results for the real and simulated systems are compared in an attempt to identify crack networks of unknown materials.

Microfluidic Evaporation, Pervaporation, and Osmosis: From Passive Pumping to Solute Concentration

Evaporation, pervaporation, and forward osmosis are processes leading to a mass transfer of solvent across an interface: gas/liquid for evaporation and solid/liquid (membrane) for pervaporation and osmosis. This Review provides comprehensive insight into the use of these processes at the microfluidic scales for applications ranging from passive pumping to the screening of phase diagrams and micromaterials engineering. Indeed, for a fixed interface relative to the microfluidic chip, these processes passively induce flows driven only by gradients of chemical potential. As a consequence, these passive-transport phenomena lead to an accumulation of solutes that cannot cross the interface and thus concentrate solutions in the microfluidic chip up to high concentration regimes, possibly up to solidification. The purpose of this Review is to provide a unified description of these processes and associated microfluidic applications to highlight the differences and similarities between these three passive-transport phenomena.

Microfluidic osmotic compression of a charge-stabilized colloidal dispersion: Equation of state and collective diffusion coefficient

We show, using a model coupling mass transport and liquid theory calculations for a charge-stabilized colloidal dispersion, that diffusion significantly limits measurement times of its equation of state (EOS), osmotic pressure vs composition, using the osmotic compression technique. Following this result, we present a microfluidic chip allowing one to measure the entire EOS of a charged dispersion at the nanoliter scale in a few hours. We also show that time-resolved analyses of relaxation to equilibrium in this microfluidic experiment lead to direct estimates of the collective diffusion coefficient of the dispersion in Donnan equilibrium with a salt reservoir.

Elastic plastic fracture mechanics investigation of toughness of wet colloidal particulate materials: Influence of saturation

HYPOTHESIS

Previous use of linear elastic fracture mechanics to estimate toughness of wet particulate materials underestimates the toughness because it does not account for plastic deformation as a dissipation mechanism. Plastic deformation is responsible for the majority of energy dissipated during the fracture of wet colloidal particulate materials. Plastic deformation around the crack tip increases with saturation of the particulate body. The toughness of the body increases with increasing saturation.

EXPERIMENTS

Elastic plastic fracture mechanics using the J-integral approach was used for the first time to measure the fracture toughness (J_IC) of wet micron sized alumina powder bodies as a function of saturation. The samples were prepared by slip casting. The saturation was controlled by treatment in a humidity chamber. The elastic modulus (E) and the energy dissipated by plastic flow (A_pl) were measured in uniaxial compression. The critical stress intensity factor (K_IC) was measured using a diametral compression sample with a flaw of known size. The fracture toughness (J_IC) was calculated from these measured quantities and the geometry of the specimen.

FINDINGS

Elastic plastic fracture mechanics was used for the first time to quantitively account for plastic deformation of wet particulate materials. The linear elastic fracture mechanics approach previously used accounted for less than 1% of the total energy dissipated in fracture. Toughness (J_IC) was found to increase with increasing saturation due to plastic deformation that increased with saturation level. The improved understanding of toughness as a function of saturation will aid in providing quantitative analysis of cracking in drying colloidal films and bodies.

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.

Packing Polydisperse Colloids into Crystals: When Charge-Dispersity Matters

Monte Carlo simulations, fully constrained by experimental parameters, are found to agree well with a measured phase diagram of aqueous dispersions of nanoparticles with a moderate size polydispersity over a broad range of salt concentrations, c_{s}, and volume fractions, ϕ. Upon increasing ϕ, the colloids freeze first into coexisting compact solids then into a body centered cubic phase (bcc) before they melt into a glass forming liquid. The surprising stability of the bcc solid at high ϕ and c_{s} is explained by the interaction (charge) polydispersity and vibrational entropy.

Positive and negative birefringence in packed films of binary spherical colloidal particles

We have investigated the birefringence in packed films of binary spherical colloidal particles. Particulate films were obtained by drying a mixed suspension of colloidal particles with two different diameters. We observed positive and negative birefringence depending on the diameters and volume ratios of the large and small particles. When the diameters of the large and small particles were similar, the films showed positive birefringence. However, negative birefringence or weakening of positive birefringence was observed in films with a large diameter ratio and an optimal volume fraction of large particles. The large particles were embedded in packed small particles in the negative and weakened positive birefringent films. We propose a packing structure in which a single shell layer of small particles formed around a large particle. Using this model, we estimated the required volume ratio of large particles, and it was in good agreement with the optimal volume fraction. The relation between the packing structure of the binary colloidal particles and the birefringence is discussed.

We have investigated the birefringence in packed films of binary spherical colloidal particles.

Long-range, selective, on-demand suspension interactions: Combining and triggering soluto-inertial beacons

Structures and particles that slowly release solute into solution can attract or repel other particles in suspension via diffusiophoresis, a process we termed "soluto-inertial (SI) interactions." These SI interactions involve "beacons" that establish and sustain nonequilibrium solute fluxes over long durations. Here, we demonstrate the versatility of the SI concept and introduce distinct strategies to manipulate solute gradients and, hence, suspension behavior using beacons with different physicochemical properties. First, we demonstrate on-demand particle migration using beacons that can be actuated with a trigger. We then show the synergy between multiple, distinct beacons that modify solute fluxes in a way that allows directed, yet selective, colloidal migration to specific target sites. Moreover, this multibeacon harmony enhances migration velocities, and delays the equilibration of the SI effect. The different SI techniques highlighted here suggest previously unidentified possibilities for sorting and separating colloidal mixtures, targeting particle delivery, and enhancing rates of suspension flocculation.

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.

Influence of Bénard-Marangoni instability on the morphology of drying colloidal films

The drying of colloidal suspensions is a very complex process leading to a sol-gel transition induced by solvent evaporation. The resulting film can even crack and delaminate. In this study, we investigate the drying process of a colloidal suspension with a highly volatile solvent and we show for initially millimeter-thick layers that the resulting pattern of delaminated plates considerably differs from what is usually observed for aqueous colloidal suspensions. Visualization using an IR camera reveals that hexagonal convection cells can develop during the drying of suspensions with a highly volatile solvent and may persist until the film consolidation. This leads to the formation of non-homogeneous films presenting surface corrugations. Thus, we highlight the importance of the hydrodynamics during the first phase of strong solvent evaporation and its consequences for the following drying steps. A criterion predicting whether or not Bénard-Marangoni instability effectively occurs will be discussed. Finally, we report a non-classical delamination mode generating fragments with convex surfaces, whereas buckle-driven delamination usually results in concave shapes.

Jellium and cell model for titratable colloids with continuous size distribution

A good understanding and determination of colloidal interactions is paramount to comprehend and model the thermodynamic and structural properties of colloidal suspensions. In concentrated aqueous suspensions of colloids with a titratable surface charge, this determination is, however, complicated by the density dependence of the effective pair potential due to both the many-body interactions and the charge regulation of the colloids. In addition, colloids generally present a size distribution which results in a virtually infinite combination of colloid pairs. In this paper, we develop two methods and describe the corresponding algorithms to solve this problem for arbitrary size distributions. An implementation in Nim is also provided. The methods, inspired by the seminal work of Torres et al., [J. Chem. Phys. 128, 154906 (2008)] are based on a generalization of the cell and renormalized jellium models to polydisperse suspensions of spherical colloids with a charge regulating boundary condition. The latter is described by the one-pK-Stern model. The predictions of the models are confronted to the equations of state of various commercially available silica dispersions. The renormalized Yukawa parameters (effective charges and screening lengths) are also calculated. The importance of size and charge polydispersity as well as the validity of these two models is discussed in light of the results.

Universal scaling of polygonal desiccation crack patterns

Polygonal desiccation crack patterns are commonly observed in natural systems. Despite their quotidian nature, it is unclear whether similar crack patterns which span orders of magnitude in length scales share the same underlying physics. In thin films, the characteristic length of polygonal cracks is known to monotonically increase with the film thickness; however, existing theories that consider the mechanical, thermodynamic, hydrodynamic, and statistical properties of cracking often lead to contradictory predictions. Here we experimentally investigate polygonal cracks in drying suspensions of micron-sized particles by varying film thickness, boundary adhesion, packing fraction, and solvent. Although polygonal cracks were observed in most systems above a critical film thickness, in cornstarch-water mixtures, multiscale crack patterns were observed due to two distinct desiccation mechanisms. Large-scale, primary polygons initially form due to capillary-induced film shrinkage, whereas small-scale, secondary polygons appear later due to the deswelling of the hygroscopic particles. In addition, we find that the characteristic area of the polygonal cracks, A_{p}, obeys a universal power law, A_{p}=αh^{4/3}, where h is the film thickness. By quantitatively linking α with the material properties during crack formation, we provide a robust framework for understanding multiscale polygonal crack patterns from microscopic to geologic scales.

Shear bands and the evolving microstructure in a drying colloidal film studied with scanning µ-SAXS

Shear localisation in thin bands is an important process involved in the plastic deformation of materials subject to stress. This process is often sensitive to the sample microstructure (amorphous/crystalline). Here we show using the scanning µ-SAXS technique, how these different microstructures influence the plastic deformations in a drying colloidal film. In crystalline samples, the presence of an ordering transition at the compaction front was directly identified through the development of a six-fold symmetry in the scattering pattern in 20 wt% samples. It is shown that plastic deformations in individual groups of particles during the compaction process can be tracked and measured in real time. Higher concentration suspensions were found to result in amorphous structures. The transition between crystalline and amorphous microstructures with initial particle concentration was also found to correlate with the appearance of shear bands. Through 2D spatial mapping of the local film structure, the presence of shear bands in the films was directly related to the microscale spatial variations in strain magnitude and compression direction. Our measurements also showed that shear bands lead to a reduction in the local particle volume fraction ~1–2%, indicating significant dilatancy.

Cracking effects in squashable and stretchable thin metal films on PDMS for flexible microsystems and electronics

Here, we study cracking of nanometre and sub-nanometre-thick metal lines (titanium, nickel, chromium, and gold) evaporated onto commercial polydimethylsiloxane (PDMS) substrates. Mechanical and electromechanical testing reveals potentially technologically useful effects by harnessing cracking. When the thin film metal lines are subjected to uniaxial longitudinal stretching, strain-induced cracks develop in the film. The regularity of the cracking is seen to depend on the applied longitudinal strain and film thickness-the findings suggest ordering and the possibility of creating metal mesas on flexible substrates without the necessity of lithography and etching. When the metal lines are aligned transversally to the direction of the applied strain, a Poisson effect-induced electrical 'self-healing' can be observed in the films. The Poisson effect causes process-induced cracks to short circuit, resulting in the lines being electrically conducting up to very high strains (~40%). Finally, cracking results in the observation of an enhanced transversal gauge factor which is ~50 times larger than the geometric gauge factor for continuous metal films-suggesting the possibility of high-sensitivity thin-film metal strain gauge flexible technology working up to high strains.

Microstructures and mechanics in the colloidal film drying process

We use Brownian Dynamics (BD) simulations and continuum models to study the microstructures and mechanics in the colloidal film drying process. Colloidal suspensions are compressed between a planar moving interface and a stationary substrate. In the BD simulations, we develop a new Energy Minimization Potential-Free (EMPF) algorithm to enforce the hard-sphere potential in confined systems and to accurately measure the stress profile. The interface moves either at a constant velocity U_w or via a constant imposed normal stress Σ_e. Comparing the interface motions to the particle Brownian motion defines the Péclet numbers Pe_U = U_wa/d₀ and Pe_Σ = Σ_ea³/k_BT, respectively, where d₀ = k_BT/ζ with k_BT the thermal energy scale, ζ the single-particle resistance, and a the particle radius. With a constant interface velocity, thermodynamics drives the suspension behavior when Pe_U ≪ 1, and homogeneous crystallization appears when the gap spacing between the two boundaries pushes the volume fraction above the equilibrium phase boundary. In contrast, when Pe_U ≫ 1, local epitaxial crystal growth appears adjacent to the moving interface even for large gap sizes. Interestingly, the most amorphous film microstructures are found at moderate Pe_U. The film stress profile develops sharp transitions and becomes step-like with growing Péclet number. With a constant imposed stress, the interface stops moving as the suspension pressure increases and the microstructural and mechanical behaviors are similar to the constant velocity case. Comparison with the simulations shows that the model accurately captures the stress on the moving interface, and quantitatively resolves the local stress and volume fraction distributions for low to moderate Péclet numbers. This work demonstrates the critical role of interface motion on the film microstructures and stresses.

Memory effect and anisotropy of particle arrangements in granular paste

It is known that pastes of fine powder, for example those of clay, retain memory of shaking applied early in a drying process. This memory results in the appearance of anisotropic patterns of desiccation cracks after drying. In this work, we find a similar behavior in pastes consisting of large granular particles, specifically cornstarch and Lycopodium spores. Because of the large particle size, we were able to observe particle arrangements in Lycopodium paste with micro-focus X-ray computerized tomography ( μ CT). We prepared pastes consisting of Lycopodium particles and water. Agar was added to the paste in order to allow for solidification during a drying process. In these samples, we found statistical anisotropy induced by shaking applied early in the drying process. This anisotropy possesses a feature that was predicted on the basis of results obtained in previous experimental and theoretical studies.

Fast, Robust Evaluation of the Equation of State of Suspensions of Charge-Stabilized Colloidal Spheres

Increasing demand is appearing for the fast, robust prediction of the equation of state of colloidal suspensions, notably with a view to using it as input data to calculate transport coefficients in complex flow solvers. This is also of interest in rheological studies, industrial screening tests of new formulations, and the real-time interpretation of osmotic compression experiments, for example. For charge-stabilized spherical particles, the osmotic pressure can be computed with standard liquid theories. However, this calculation can sometimes be lengthy and/or unstable under some physicochemical conditions, a drawback that precludes its use in multiscale flow simulators. As a simple, fast, and robust replacement, the literature reports estimations of the osmotic pressure that have been built by adding the Carnahan-Starling and the cell model pressures (CSCM model). The first contribution is intended to account for colloid-colloid contacts, and the second, for electrostatic effects. This approximation has not yet been thoroughly tested. In this work, the CSCM is evaluated by comparison with data from experiments on silica particles, Monte Carlo simulations, and solutions of the accurate Rogers-Young integral equation scheme with a hard-sphere Yukawa potential obtained from the extrapolated point-charge renormalization method for a wide range of volume fractions, surface charge densities, and interaction ranges. We find that the CSCM is indeed perfectly adequate in the electrostatically concentrated regime, where it can be used from vanishingly small to high surface charge because there is error cancellation between the Carnahan-Starling and cell model contributions at intermediate charge. The CSCM is thus a nice extension of the cell model to liquid-like dense suspensions, which should find application in the domains mentioned above. However, it fails for dilute suspensions with strong electrostatics. In this case, we show that, and explain why, perturbation methods and the rescaled mean spherical approximation are good alternatives in terms of precision, ease of implementation, computational cost, and robustness.