Gels under stress: The origins of delayed collapse

Early stage of erythrocyte sedimentation rate test: Fracture of a high-volume-fraction gel

Erythrocyte sedimentation rate (ESR) is a clinical parameter used as a nonspecific marker for inflammation, and recent studies have shown that it is linked to the collapse of the gel formed by red blood cells (RBCs) at physiological hematocrits (i.e. RBC volume fraction). Previous research has suggested that the observation of a slower initial dynamics is related to the formation of fractures in the gel. Moreover, RBC gels present specific properties due to the anisotropic shape and flexibility of the RBCs. Namely, the onset of the collapse is reached earlier and the settling velocity of the gel increases with increasing attraction between the RBCs, while the gel of spherical particles shows the opposite trend. Here, we report experimental observations of the gel structure during the onset of the collapse. We suggest an equation modeling this initial process as fracturing of the gel. We demonstrate that this equation provides a model for the motion of the interface between blood plasma and the RBC gel, along the whole time span. We also observe that the increase in the attraction between the RBCs modifies the density of fractures in the gel, which explains why the gel displays an earlier onset when the aggregation energy between the RBCs increases. Our work uncovers the detailed physical mechanism underlying the ESR and provides insights into the fracture dynamics of an RBC gel. These results can improve the accuracy of clinical measurements.

Stress-independent delay time in yielding of dilute colloidal gels

We investigate the yielding under shear for dilute poly(N-isopropyl acrylamide-co-fumaric acid) (PNIPAM-FAc) colloidal gels obtained above the volume phase transition temperature. In this temperature range, the microgel suspensions form colloidal gels due to hydrophobic interparticle interactions under appropriate pH and ionic strength conditions. Step-strain tests revealed that yielding occurs when the applied strain exceeds a specific threshold, requiring a finite, stress-independent delay time (tD). This is distinct from previous findings on delayed yielding in other colloidal gels, where tD decreases with increasing stress. In the start-up shear tests, yield strain (γy) at a higher strain rate () increases with escalating , while γy at lower  remains constant. This characteristic γy- relationship is successfully explained by a simple model using the stress-independent tD value without an adjustable fitting parameter. The distinctive yielding behavior, underscored by a stress-independent tD, is expected to originate from strain-induced macroscopic phase separation into a dense colloidal gel and water, observable separately from rheological measurements.

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.

A microstructural investigation of an industrial attractive gel at pressure and temperature

Oil-continuous drilling fluids used in the oil and gas industry are formulated to be pseudoplastic with a relatively weak yield stress. These fluids are required to maintain their properties over wide temperature and pressure ranges yet there are few methods that can sensitively study the inherent structure and mechanical properties in the fluids under such conditions. Here we study a model oil-continuous drilling fluid formulation as a function of both temperature (up to 153 °C) and pressure (up to 1330 bar) with Diffusive Wave Spectroscopy (DWS). The system comprises a colloidal gel network of clay particles and trapped emulsion droplets. As a function of temperature the system undergoes local structural changes reflected in the DWS dynamics which are also consistent with macroscopic rheological measurements. On cycling to high pressure the system exhibits similar structural and dynamic changes with a strong hysteresis. Although multiple scattering in multicomponent non-ergodic samples does not directly yield self diffusion probe dynamics, the use of microrheology analysis here appears to be in good agreement with direct rheological measurements of the sample linear viscoelasticity at ambient pressure. Thus DWS microrheology succesfully probes irreversible changes in the structure and the mechanical response of the drilling fluid formulation under a high pressure cycle.

Erythrocyte Sedimentation: Collapse of a High-Volume-Fraction Soft-Particle Gel

The erythrocyte sedimentation rate is one of the oldest medical diagnostic methods whose physical mechanisms remain debatable today. Using both light microscopy and mesoscale cell-level simulations, we show that erythrocytes form a soft-particle gel. Furthermore, the high volume fraction of erythrocytes, their deformability, and weak attraction lead to unusual properties of this gel. A theoretical model for the gravitational collapse is developed, whose predictions are in agreement with detailed macroscopic measurements of the interface velocity.

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.

Gel breakdown in a formulated product via accumulated strain

Almost any formulated product is sufficiently complex that definitive elucidation of all interactions and microstructural evolutions is difficult at best and more likely intractable. Drilling fluids are no exception. Nevertheless, detailed experiment and comparison with simpler systems studied in the literature enable rational pictures to be deduced. We study the breakdown of a gelled formulated product, a drilling fluid, under the action of repeated deformation, i.e. weakly nonlinear oscillation. Our data may be rationalised by postulating that the fluid behaves as an arrested phase separating material whose natural slow structural evolution, aging and coarsening, is accelerated by the imposed sinusoidal strain consistent with previous work on well characterised systems. During the observed evolution the elastic modulus exhibits a maximum which appears correlated with a maximal connected heterogeneity of structure.

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.

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.

Gels with sense: supramolecular materials that respond to heat, light and sound

Advances in the field of supramolecular chemistry have made it possible, in many situations, to reliably engineer soft materials to address a specific technological problem. Particularly exciting are "smart" gels that undergo reversible physical changes on exposure to remote, non-invasive environmental stimuli. This review explores the development of gels which are transformed by heat, light and ultrasound, as well as other mechanical inputs, applied voltages and magnetic fields. Focusing on small-molecule gelators, but with reference to organic polymers and metal-organic systems, we examine how the structures of gelator assemblies influence the physical and chemical mechanisms leading to thermo-, photo- and mechano-switchable behaviour. In addition, we evaluate how the unique and versatile properties of smart materials may be exploited in a wide range of applications, including catalysis, crystal growth, ion sensing, drug delivery, data storage and biomaterial replacement.

Exploring the dynamics of phase separation in colloid-polymer mixtures with long range attraction

We have studied the kinetics of phase separation and gel formation in a low-dispersity colloid - non-adsorbing polymer system with long range attraction using small-angle light scattering. This system exhibits two-phase and three-phase coexistence of gas, liquid and crystal phases when the strength of attraction is between 2 and 4kBT and gel phases when the strength of attraction is increased. For those samples that undergo macroscopic phase separation, whether to gas-crystal, gas-liquid or gas-liquid-crystal coexistence, we observe dynamic scaling of the structure factor and growth of a characteristic length scale that behaves as expected for phase separation in fluids. In samples that gel, the power law associated with the growth of the dominant length scale is not equal to 1/3, but appears to depend mainly on the strength of attraction, decreasing from 1/3 for samples near the coexistence region to 1/27 at 8kBT, over a wide range of colloid and polymer concentrations.

Syneresis and delayed detachment in agar plates

Biogels made of crosslinked polymers such as proteins or polysaccharides behave as porous soft solids and store large amounts of solvent. These gels undergo spontaneous aging, called syneresis, which consists of the shrinkage of the gel matrix and the progressive expulsion of solvent. As a result, a biogel originally casted in a container often loses contact with the container sidewalls, and the detachment time is difficult to anticipate a priori, since it may occur over variable time spans (from hours to days). Here we report on syneresis phenomena in agar plates, which consist of Petri dishes filled with a gel mainly composed of agar. Direct observations and speckle pattern correlation analysis allow us to rationalize the delayed detachment of the gel from the sidewall of the Petri dish. The detachment time t* is surprisingly not controlled by the mass loss as one would intuitively expect. Instead, t* is strongly correlated to the gel minimum thickness emin measured along the sidewall of the plate, and increases as a robust function of emin, independently of the prior mass-loss history. Time-resolved correlation spectroscopy atypically applied to such weakly diffusive media gives access to the local thinning rate of the gel. This technique also allows us to detect the gel micro-displacements that are triggered by water evaporation prior to the detachment, and even to anticipate the latter from a few hours. Our work provides observables to predict the detachment time of agar gels in dishes, and highlights the relevance of speckle pattern correlation analysis for the quantitative investigation of the syneresis dynamics in biopolymer gels.