Effects of vertical confinement on gelation and sedimentation of colloids

Necking and failure of a particulate gel strand: signatures of yielding on different length scales

"Sticky" spheres with a short-ranged attraction are a basic model of a wide range of materials from the atomic to the granular length scale. Among the complex phenomena exhibited by sticky spheres is the formation of far-from-equilibrium dynamically arrested networks which comprise "strands" of densely packed particles. The aging and failure of such gels under load is a remarkably challenging problem, given the simplicity of the model, as it involves multiple length- and time-scales, making a single approach ineffective. Here we tackle this challenge by addressing the failure of a single strand with a combination of methods. We study the mechanical response of a single strand of a model gel-former to deformation, both numerically and analytically. Under elongation, the strand breaks by a necking instability. We analyse this behaviour at three different length scales: a rheological continuum model of the whole strand; a microscopic analysis of the particle structure and dynamics; and the local stress tensor. Combining these different approaches gives a coherent picture of the necking and failure. The strand has an amorphous local structure and has large residual stresses from its initialisation. We find that neck formation is associated with increased plastic flow, a reduction in the stability of the local structure, and a reduction in the residual stresses; this indicates that the system loses its solid character and starts to behave more like a viscous fluid. These results will inform the development of more detailed models that incorporate the heterogeneous network structure of particulate gels.

Structuring colloidal gels via micro-bubble oscillations

Locally (re)structuring colloidal gels - micron-sized particles forming a connected network with arrested dynamics - can enable precise tuning of the micromechanical and -rheological properties of the system. A recent experimental study [B. Saint-Michel, G. Petekidis, and V. Garbin, Soft Matter, 2022, 18, 2092] showed that local ordering can be rapidly induced by acoustically modulating an embedded microbubble. Here, we perform Brownian dynamics simulations to understand the mechanical effect of an oscillating microbubble on the next-to-bubble structure of the embedding colloidal gel. Our simulations reveal hexagonal-close-packed structures over a range that is comparable to the amplitude of the oscillations. However, we were unable to reproduce the unexpectedly long-ranged modification of the gel structure - dozens of amplitudes - observed in experiment. This suggests including long-ranged effects, such as fluid flow, should be considered in future computational work.

Hydrodynamic stability criterion for colloidal gelation under gravity

Attractive colloids diffuse and aggregate to form gels, solidlike particle networks suspended in a fluid. Gravity is known to strongly impact the stability of gels once they are formed. However, its effect on the process of gel formation has seldom been studied. Here, we simulate the effect of gravity on gelation using both Brownian dynamics and a lattice-Boltzmann algorithm that accounts for hydrodynamic interactions. We work in a confined geometry to capture macroscopic, buoyancy-induced flows driven by the density mismatch between fluid and colloids. These flows give rise to a stability criterion for network formation, based on an effective accelerated sedimentation of nascent clusters at low volume fractions that disrupts gelation. Above a critical volume fraction, mechanical strength in the forming gel network dominates the dynamics: the interface between the colloid-rich and colloid-poor region moves downward at an ever-decreasing rate. Finally, we analyze the asymptotic state, the colloidal gel-like sediment, which we find not to be appreciably impacted by the vigorous flows that can occur during the settling of the colloids. Our findings represent the first steps toward understanding how flow during formation affects the life span of colloidal gels.

Controlling Kinetic Pathways in Demixing Microgel-Micelle Mixtures

We investigate the temperature-dependent phase behavior of mixtures of poly(N-isopropylacrylamide) (pNIPAM) microgel colloids and a triblock copolymer (PEO-PPO-PEO) surfactant. Usually, gelation in these systems results from an increase in temperature. Here we investigate the role of the heating rate, and surprisingly, we find that this causes the mechanism of aggregation to change from one which is driven by depletion of the microgels by the micelles at low temperatures to the association of the two species at high temperatures. We thus reveal two competing mechanisms for attractions between the microgel particles which can be controlled by changing the heating rate. We use this heating-rate-dependent response of the system to access multiple structures for the same system composition. Samples were found to demix into phases rich and poor in microgel particles at temperatures below 33 °C, under conditions where the microgels particles are partially swollen. Under rapid heating full demixing is bypassed, and gel networks are formed instead. The temperature history of the sample, therefore, allows for kinetic selection between different final structures, which may be metastable.

Quantitative imaging and modeling of colloidal gelation in the coagulant dipping process

Many common elastomeric products, including nitrile gloves, are manufactured by coagulant dipping. This process involves the destabilization and gelation of a latex dispersion by an ionic coagulant. Despite widespread application, the physical chemistry governing coagulant dipping is poorly understood. It is unclear which properties of an electrolyte determine its efficacy as a coagulant and which phenomena control the growth of the gel. Here, a novel experimental protocol is developed to directly observe coagulant gelation by light microscopy. Gel growth is imaged and quantified for a variety of coagulants and compared to macroscopic dipping experiments mimicking the industrial process. When the coagulant is abundant, gels grow with a t1/2 time dependence, suggesting that this phenomenon is diffusion-dominated. When there is a finite amount of coagulant, gels grow to a limiting thickness. Both these situations are modeled as one-dimensional diffusion problems, reproducing the qualitative features of the experiments including which electrolytes cause rapid growth of thick gels. We propose that the gel thickness is limited by the amount of coagulant available, and the growth is, therefore, unbounded when the coagulant is abundant. The rate of the gel growth is controlled by a combination of a diffusion coefficient and the ratio of the critical coagulation concentration to the amount of coagulant present, which in many situations is set by the coagulant solubility. Other phenomena, including diffusiophoresis, may make a more minor contribution to the rate of gel growth.

Direct Imaging of Contacts and Forces in Colloidal Gels

Colloidal dispersions are prized as model systems to understand basic properties of materials, and are central to a wide range of industries from cosmetics to foods to agrichemicals. Among the key developments in using colloids to address challenges in condensed matter is to resolve the particle coordinates in 3D, allowing a level of analysis usually only possible in computer simulation. However in amorphous materials, relating mechanical properties, and failure in particular to microscopic structure remains problematic. Here we address this challenge by studying the contacts and the forces between particles, as well as their positions. To do so, we use a colloidal model system (an emulsion) in which the interparticle forces and local stress can be linked to the microscopic structure. We demonstrate the potential of our method to reveal insights into the failure mechanisms of soft amorphous solids by determining local stress in a colloidal gel. In particular, we identify "force chains" of load--bearing droplets, and local stress anisotropy, and investigate their connection with locally rigid packings of the droplets.

Erythrocyte sedimentation: Effect of aggregation energy on gel structure during collapse

The erythrocyte (or red blood cell) sedimentation rate (ESR) is commonly interpreted as a measure of cell aggregation and as a biomarker of inflammation. It is well known that an increase of fibrinogen concentration, an aggregation-inducing protein for erythrocytes, leads to an increase of the sedimentation rate of erythrocytes, which is generally explained through the formation and faster settling of large disjoint aggregates. However, many aspects of erythrocyte sedimentation conform well with the collapse of a particle gel rather than with the sedimentation of disjoint aggregates. Using experiments and cell-level numerical simulations, we systematically investigate the dependence of ESR on fibrinogen concentration and its relation to the microstructure of the gel-like erythrocyte suspension. We show that for physiological aggregation interactions, an increase in the attraction strength between cells results in a cell network with larger void spaces. This geometrical change in the network structure occurs due to anisotropic shape and deformability of erythrocytes and leads to an increased gel permeability and faster sedimentation. Our results provide a comprehensive relation between the ESR and the cell-level structure of erythrocyte suspensions and support the gel hypothesis in the interpretation of blood sedimentation.

Real space analysis of colloidal gels: triumphs, challenges and future directions

Colloidal gels constitute an important class of materials found in many contexts and with a wide range of applications. Yet as matter far from equilibrium, gels exhibit a variety of time-dependent behaviours, which can be perplexing, such as an increase in strength prior to catastrophic failure. Remarkably, such complex phenomena are faithfully captured by an extremely simple model-'sticky spheres'. Here we review progress in our understanding of colloidal gels made through the use of real space analysis and particle resolved studies. We consider the challenges of obtaining a suitable experimental system where the refractive index and density of the colloidal particles is matched to that of the solvent. We review work to obtain a particle-level mechanism for rigidity in gels and the evolution of our understanding of time-dependent behaviour, from early-time aggregation to ageing, before considering the response of colloidal gels to deformation and then move on to more complex systems of anisotropic particles and mixtures. Finally we note some more exotic materials with similar properties.

Acanthocyte Sedimentation Rate as a Diagnostic Biomarker for Neuroacanthocytosis Syndromes: Experimental Evidence and Physical Justification

(1) Background: Chorea-acanthocytosis and McLeod syndrome are the core diseases among the group of rare neurodegenerative disorders called neuroacanthocytosis syndromes (NASs). NAS patients have a variable number of irregularly spiky erythrocytes, so-called acanthocytes. Their detection is a crucial but error-prone parameter in the diagnosis of NASs, often leading to misdiagnoses. (2) Methods: We measured the standard Westergren erythrocyte sedimentation rate (ESR) of various blood samples from NAS patients and healthy controls. Furthermore, we manipulated the ESR by swapping the erythrocytes and plasma of different individuals, as well as replacing plasma with dextran. These measurements were complemented by clinical laboratory data and single-cell adhesion force measurements. Additionally, we followed theoretical modeling approaches. (3) Results: We show that the acanthocyte sedimentation rate (ASR) with a two-hour read-out is significantly prolonged in chorea-acanthocytosis and McLeod syndrome without overlap compared to the ESR of the controls. Mechanistically, through modern colloidal physics, we show that acanthocyte aggregation and plasma fibrinogen levels slow down the sedimentation. Moreover, the inverse of ASR correlates with the number of acanthocytes (R2=0.61, p=0.004). (4) Conclusions: The ASR/ESR is a clear, robust and easily obtainable diagnostic marker. Independently of NASs, we also regard this study as a hallmark of the physical view of erythrocyte sedimentation by describing anticoagulated blood in stasis as a percolating gel, allowing the application of colloidal physics theory.

How Do Surface Properties of Nanoparticles Influence Their Diffusion in the Extracellular Matrix? A Model Study in Matrigel Using Polymer-Grafted Nanoparticles

Diffusion of nanomedicines inside the extracellular matrix (ECM) has been identified as a key factor to achieve homogeneous distribution and therefore therapeutic efficacy. Here, we sought to determine the impact of nanoparticles' (NPs) surface properties on their ability to diffuse in the ECM. As model nano-objects, we used a library of gold nanoparticles grafted with a versatile polymethacrylate corona, which enabled the surface properties to be modified. To accurately recreate the features of the native ECM, diffusion studies were carried out in a tumor-derived gel (Matrigel). We developed two methods to evaluate the diffusion ability of NPs inside this model gel: an easy-to-implement one based on optical monitoring and another one using small-angle X-ray scattering (SAXS) measurements. Both enabled the determination of the diffusion coefficients of NPs and comparison of the influence of their various surface properties, while the SAXS technique also allowed to monitor the NPs' structure as they diffused inside the gel. Positive charges and hydrophobicity were found to particularly hinder diffusion, and the different results suggested on the whole the presence of NPs-matrix interactions, therefore underlying the importance of the ECM model. The accuracy of the tumor-derived gels used in this study was evidenced by in vivo experiments involving intratumoral injections of NPs on mice, which showed that diffusion patterns in the peripheral tumor tissues were quite similar to the ones obtained within the chosen ECM model.

Dynamic behaviors of sedimenting colloidal gel materials: hydrodynamic interactions

It is a highly nonlinear poromechanics phenomenon that colloidal gel materials that are exposed to a gravitational stress greater than their yield stress undergo elastic compression.

Structural covariance in the hard sphere fluid

We study the joint variability of structural information in a hard sphere fluid biased to avoid crystallisation and form five-fold symmetric geometric motifs. We show that the structural covariance matrix approach, originally proposed for on-lattice liquids [P. Ronceray and P. Harrowell, J. Stat. Mech.: Theory Exp. 2016(8), 084002], can be meaningfully employed to understand structural relationships between different motifs and can predict, within the linear-response regime, structural changes related to motifs distinct from that used to bias the system.