Highly nonlinear dynamics in a slowly sedimenting colloidal gel

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.

A double rigidity transition rules the fate of drying colloidal drops

The evaporation of drops of colloidal suspensions plays an important role in numerous contexts, such as the production of powdered dairies, the synthesis of functional supraparticles, and virus and bacteria survival in aerosols or drops on surfaces. The presence of colloidal particles in the evaporating drop eventually leads to the formation of a dense shell that may undergo a shape instability. Previous works propose that, for drops evaporating very fast, the instability occurs when the particles form a rigid porous solid, constituted of permanently aggregated particles at random close packing. To date, however, no measurements could directly test this scenario and assess whether it also applies to drops drying at lower evaporation rates, severely limiting our understanding of this phenomenon and the possibility of harnessing it in applications. Here, we combine macroscopic imaging and space- and time-resolved measurements of the microscopic dynamics of colloidal nanoparticles in drying drops sitting on a hydrophobic surface, measuring the evolution of the thickness of the shell and the spatial distribution and mobility of the nanoparticles. We find that, above a threshold evaporation rate, the drop undergoes successively two distinct shape instabilities, invagination and cracking. While permanent aggregation of nanoparticles accompanies the second instability, as hypothesized in previous works on fast-evaporating drops, we show that the first one results from a reversible glass transition of the shell, unreported so far. We rationalize our findings and discuss their implications in the framework of a unified state diagram for the drying of colloidal drops sitting on a hydrophobic surface.

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.

Surfactant induced catastrophic collapse of carbon black suspensions used in flow battery application

HYPOTHESIS

Carbon black particles act as electronically conductive additives in the slurry electrodes used in electrochemical redox flow batteries. Modifying the carbon black slurry formulation with the addition of a nonionic surfactant could impart improved particle dispersion, gravitational stability, and flowability leading to better battery performance.

EXPERIMENTS

Carbon black particles were dispersed in 1 M H₂SO₄ with volume fractions Φ = 0.01 to 0.06 and a nonionic surfactant (Triton X-100) concentration of c_surf. = 0, 0.05, and 0.1 M. Particle size was characterized using microscopy and surfactant adsorption using UV-vis spectroscopy. Sedimentation kinetics was measured using a custom camera set-up that tracks the height of the settling particle bed. Rheology experiments were conducted to measure linear viscoelasticity and shear flow behavior.

FINDINGS

The sedimentation dynamics of the slurry resembled that of a gel collapse. At short times we observed fast sedimentation associated with structural gel collapse and at long times very slow sedimentation associated with compaction of the sediment. Rheological investigations revealed that the slurry indeed behaved like colloidal gels. Addition of nonionic surfactant at α (= (c_surf./c_CB)) < 0.75 improved particle dispersion and increased gel elasticity. However, α> 0.75 led to a weaker gel that exhibits a fast 'catastrophic collapse' under gravity.

Spatially uniform dynamics in equilibrium colloidal gels

Gels of DNA nanostars, besides providing a compatible scaffold for biomedical applications, are ideal model systems for testing the physics of equilibrium colloidal gels. Here, using dynamic light scattering and photon correlation imaging (a recent technique that, by blending light scattering and imaging, provides space-resolved quantification of the dynamics), we follow the process of gel formation over 10 orders of magnitude in time in a model system of tetravalent DNA nanostars in solution, a realization of limited-valence colloids. Such a system, depending on the nanostar concentration, can form either equilibrium or phase separation gels. In stark contrast to the heterogeneity of concentration and dynamics displayed by the phase separation gel, the equilibrium gel shows absence of aging and a remarkable spatially uniform dynamics.

Consolidation of strong colloidal gels under arbitrary compressive loadings

Although highly successful, classical constitutive theories for the consolidation of strong colloidal gels are limited to one-dimensional (1D) uniaxial consolidation. Many consolidation applications are inherently multidimensional and there currently exists little understanding and no constitutive theory for how strong colloidal gels consolidate under arbitrary compressive loadings. In this study, we address this shortcoming by considering the consolidation mechanics of strong colloidal gels under arbitrary compressive loadings via 2D DEM biaxial simulations of assemblies of cohesive frictional particles. We show that although particle-scale consolidation differs significantly between uniaxial and isotropic consolidation, the maximum normal stress during consolidation is a unique function of the volumetric strain and hence the concentration of the solids phase. We use these insights to develop a generalised constitutive model for the macroscopic compressive rheology under arbitrary compressive loadings that is consistent with the classical constitutive model for uniaxial consolidation. Surprisingly, we find that this generalized constitutive model can predict multidimensional consolidation under arbitrary compressive loadings without need for further characterisation beyond uniaxial consolidation. These results provide significant insights into the consolidation of strong colloidal gels and facilitate prediction of multi-dimensional consolidation over a wide range of applications, and so represents an initial foray toward the development of a tensorial rheology of strong colloidal gels.

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.

Multiscale relaxation in aging colloidal gels: From localized plastic events to system-spanning quakes

Relaxation of internal stresses through a cascade of microscopic restructuring events is the hallmark of many materials, ranging from amorphous solids like glasses and gels to geological structures subjected to a persistent external load. By means of photon correlation imaging, a recently developed technique that blends the powers of scattering and imaging, we provide a spatially and temporally resolved survey of the restructuring and aging processes that spontaneously occur in physical gels originating from an arrested phase separation. We show that the temporal dynamics is characterized by an intermittent sequence of spatially localized "microquakes" that eventually lead to global rearrangements occurring at a rate that scales with the gel age. Notably, these dramatic upheavals of the gel structure are heralded by a progressive acceleration of the microscopic gel dynamics that originates from recognizable active spots and then spreads at a large but finite speed through the gel. Within the "slack" phase between two of these "macroquakes," the fluctuations of the degree of temporal correlation obey a non-Gaussian statistics described by a generalized logistic distribution. The evidence we obtained bear consistent analogies with the stress relaxation processes taking place in earthquake sequences and with the intermittent restructuring of plastic crystals at the microscale.

Colloidal Brazil nut effect in microswimmer mixtures induced by motility contrast

We numerically and experimentally study the segregation dynamics in a binary mixture of microswimmers which move on a two-dimensional substrate in a static periodic triangular-like light intensity field. The motility of the active particles is proportional to the imposed light intensity, and they possess a motility contrast, i.e., the prefactor depends on the species. In addition, the active particles also experience a torque aligning their motion towards the direction of the negative intensity gradient. We find a segregation of active particles near the intensity minima where typically one species is localized close to the minimum and the other one is centered around in an outer shell. For a very strong aligning torque, there is an exact mapping onto an equilibrium system in an effective external potential that is minimal at the intensity minima. This external potential is similar to (height-dependent) gravity such that one can define effective "heaviness" of the self-propelled particles. In analogy to shaken granular matter in gravity, we define a "colloidal Brazil nut effect" if the heavier particles are floating on top of the lighter ones. Using extensive Brownian dynamics simulations, we identify system parameters for the active colloidal Brazil nut effect to occur and explain it based on a generalized Archimedes' principle within the effective equilibrium model: heavy particles are levitated in a dense fluid of lighter particles if their effective mass density is lower than that of the surrounding fluid. We also perform real-space experiments on light-activated self-propelled colloidal mixtures which confirm the theoretical predictions.

Gravitational collapse of colloidal gels: non-equilibrium phase separation driven by osmotic pressure

Delayed gravitational collapse of colloidal gels is characterized by initially slow compaction that gives way to rapid bulk collapse, posing interesting questions about the underlying mechanistic origins. Here we study gel collapse utilizing large-scale dynamic simulation of a freely draining gel of physically bonded particles subjected to gravitational forcing. The hallmark regimes of collapse are recovered: slow compaction, transition to rapid collapse, and long-time densification. Microstructural changes are monitored by tracking particle positions, coordination number, and bond dynamics, along with volume fraction, osmotic pressure, and potential energy. Together these reveal the surprising result that collapse can occur with a fully intact network, where the tipping point arises when particle migration dissolves strands in a capillary-type instability. While it is possible for collapse to rupture a gel network into clusters that then sediment, and hydrodynamic interactions can make interesting contributions, neither is necessary. Rather, we find that the "delay" arises from gravity-enhanced coarsening, which triggers the re-emergence of phase separation. The mechanism of this transition is a leap toward lower potential energy of the gel, driven by bulk negative osmotic pressure that condenses the particle phase: the gel collapses in on itself under negative osmotic pressure allowing the gel, to tunnel through the equilibrium phase diagram to a higher volume fraction "state". Remarkably, collapse stops when condensation stops, when gravitational advection produces a positive osmotic pressure, re-arresting the gel.

Compressive yield stress of depletion gels from stationary centrifugation profiles

We have investigated the stationary sedimentation profiles of colloidal gels obtained by an arrested phase-separation process driven by depletion forces, which have been compressed either by natural gravity or by a centrifugal acceleration ranging between 6g and 2300g. Our measurements show that the gel rheological properties display a drastic change when the gel particle volume fraction exceeds a value [Formula: see text], which barely depends on the strength of the interparticle attractive forces that consolidate the network. In particular, the gel compressive yield stress [Formula: see text], which increases as [Formula: see text] for [Formula: see text], displays a diverging behaviour for [Formula: see text], with an asymptotic value that is close to the random close packing value for hard spheres. The evidence we obtained suggests that [Formula: see text] basically coincides with the liquid (colloid-rich) branch of the metastable coexistence curve, rather than with the lower (and ϕ-dependent) values expected for an attractive glass line penetrating inside the coexistence region.

Use of RAFT macro-surfmers for the synthesis of transparent aqueous colloids with tunable interactions

We propose a new method to produce fluorinated nanoparticles (NPs) based on ab initio reversible addition-fragmentation chain transfer (RAFT) emulsion polymerization without the use of toxic surfactants. NP size, surface charge, and chemistry can be controlled via the adoption of different macromolecular transfer agents produced via RAFT polymerization of amphiphilic monomers. Thanks to this versatility, interparticle interactions can be easily tuned by changing solvent composition and temperature. In addition, the refractive index and density of the solvent can simultaneously match those of the NPs by adding sodium polytungstate, an organic salt widely used for density gradient centrifugation. These colloids may be used as model systems for the study of self-assembly and aggregation in aqueous media when optical methods are required.

Universality in consolidation of colloidal gels

Consolidation of colloidal dispersions under external load is a complex process involving inter-particle interactions, thermal forces and hydrodynamics. Despite its importance in diverse industrial applications, past studies involving experiments, scaling approaches and simulations are yet to provide a comprehensive understanding of how the microstructure determines the mechanical response in three dimensional colloidal gels. Here, we develop a model that accounts for the microstructural details and predicts the mechanical response under slow, uniaxial compression of a strongly aggregated three dimensional colloidal gel. The particle network assumes a fractal structure that is independent of the strength of inter-particle interactions. While the yield strain changes negligibly during the entire process, the yield stress increases by several orders of magnitude. The predicted yield stress and strain are in close agreement with those observed in simulations and experiments with diverse colloidal systems, suggesting a universality in the consolidation process.

Gravitational collapse of depletion-induced colloidal gels

We study the ageing and ultimate gravitational collapse of colloidal gels in which the interparticle attraction is induced by non-adsorbing polymers via the depletion effect. The gels are formed through arrested spinodal decomposition, whereby the dense phase arrests into an attractive glass. We map the experimental state diagram onto a theoretical one obtained from computer simulations and theoretical calculations. Discrepancies between the experimental and simulated gel regions in the state diagram can be explained by the particle size and density dependence of the boundary below which the gel is not strong enough to resist gravitational stress. Visual observations show that gravitational collapse of the gels falls into two distinct regimes as the colloid and polymer concentrations are varied, with gels at low colloid concentrations showing the onset of rapid collapse after a delay time. Magnetic resonance imaging (MRI) was used to provide quantitative, spatio-temporally resolved measurements of the solid volume fraction in these rapidly collapsing gels. We find that during the delay time, a dense region builds up at the top of the sample. The rapid collapse is initiated when the gel structure is no longer able to support this dense layer.

Dynamics of colloid accumulation under flow over porous obstacles

The accumulation of colloidal particles to build dense structures from dilute suspensions may follow distinct routes. The mechanical, structural and geometrical properties of these structures depend on local hydrodynamics and colloidal interactions. Using model suspensions flowing into microfabricated porous obstacles, we investigate this interplay by tuning both the flow pattern and the ionic strength. We observe the formation of a large diversity of shapes, and demonstrate that growing structures in turn influence the local velocity pattern, favouring particle deposition either locally or over a wide front. We also show that these structures are labile, stabilised by the flow pushing on them, in low ionic strength conditions, or cohesive, in a gel-like state, at higher ionic strength. The interplay between aggregate cohesion and erosion thus selects preferential growth modes and therefore dictates the final shape of the structure.

Avalanche-like fluidization of a non-Brownian particle gel

We report on the fluidization dynamics of an attractive gel composed of non-Brownian particles made of fused silica colloids. Extensive rheology coupled to ultrasonic velocimetry allows us to characterize the global stress response together with the local dynamics of the gel during shear startup experiments. In practice, after being rejuvenated by a preshear, the gel is left to age for a time tw before being subjected to a constant shear rate [small gamma, Greek, dot above]. We investigate in detail the effects of both tw and [small gamma, Greek, dot above] on the fluidization dynamics and build a detailed state diagram of the gel response to shear startup flows. The gel may display either transient shear banding towards complete fluidization or steady-state shear banding. In the former case, we unravel that the progressive fluidization occurs by successive steps that appear as peaks on the global stress relaxation signal. Flow imaging reveals that the shear band grows until complete fluidization of the material by sudden avalanche-like events which are distributed heterogeneously along the vorticity direction and correlated to large peaks in the slip velocity at the moving wall. These features are robust over a wide range of tw and [small gamma, Greek, dot above] values, although the very details of the fluidization scenario vary with [small gamma, Greek, dot above]. Finally, the critical shear rate [small gamma, Greek, dot above]* that separates steady-state shear-banding from steady-state homogeneous flow depends on the width of the shear cell and exhibits a nonlinear dependence with tw. Our work brings about valuable experimental data on transient flows of attractive dispersions, highlighting the subtle interplay between shear, wall slip and aging whose modeling constitutes a major challenge that has not been met yet.

External and internal gelation of pectin solutions: microscopic dynamics versus macroscopic rheology

Pectin is a natural biopolymer that forms, in the presence of divalent cations, ionic-bound gels typifying a large class of biological gels stabilized by non-covalent cross-links. We investigate and compare the kinetics of formation and aging of pectin gels obtained either through external gelation via perfusion of free Ca(2+) ions, or by internal gelation due to the supply of the same ions from the dissolution of CaCO3 nanoparticles. The microscopic dynamics obtained with photon correlation imaging, a novel optical technique that allows obtaining the microscopic dynamics of the sample while retaining the spatial resolution of imaging techniques, is contrasted with macroscopic rheological measurements at constant strain. Pectin gelation is found to display peculiar two-stage kinetics, highlighted by non-monotonic growth in time of both microscopic correlations and gel mechanical strength. These results are compared to those found for alginate, another biopolymer extensively used in food formulation.

Time-evolution scenarios for short-range depletion gels subjected to the gravitational stress

By exploiting photon correlation imaging and ghost particle velocimetry, two novel optical correlation techniques particularly suited to the investigation of the microscopic dynamics of spatially heterogeneous samples, we investigate the settling and restructuring dynamics of colloidal gels generated by short-ranged depletion interactions. Three distinct regions can be clearly set apart within the liquid-liquid coexistence region of the phase diagram where gel formation is observed. When depletion forces are barely sufficient to drive the system within the metastable region, an initial disordered gel hosts the rapid nucleation of crystallites, which stress the gel structure until it fully collapses, leading to the formation of a macroscopic colloidal crystal. For stronger attractive forces, two distinct scenarios are observed, depending on the particle volume fraction ϕ0 of the original suspension. At low ϕ0, the gel breaks after a short delay time into separate clusters, which rapidly settle until they compact in a denser disordered phase. The latter eventually undergoes a slow compression, which is accounted for by a poroelastic model where the microscopic gel dynamics is fully ruled by its macroscopic deformation. Yet, it is the intermediate stage between cluster settling and final compaction which displays very peculiar features, evidenced by anomalous settling profiles which are not shared, to our knowledge, by any other sedimentation processes investigated so far. For larger values of ϕ0, gel breaking is conversely suppressed, the structure undergoes a continuous compression that cannot be explained by a poroelastic model, and the microscopic dynamics is characterized by logarithmic correlation functions resembling those found for attractive glasses.

Settled and unsettled issues in particle settling

Colloid sedimentation has played a seminal role in the development of statistical physics thanks to the celebrated experiments by Perrin, which provided a concrete demonstration of molecular reality and gave strong support to Einstein's theory of Brownian motion. This review, which mostly focuses on settling at low Peclét number, where Brownian fluctuations are dominant, aims to show that a lot more can be learnt both from the sedimentation equilibrium and from the particle settling dynamics of a wide class of systems, ranging from simple colloids to mesogenic suspensions, from soft solids to active particles and living organisms. At the same time, the occurrence of unexpected and surprising effects brings about challenging questions in statistical and fluid mechanics that make sedimentation an exciting field of research.

Simultaneous measurement of the microscopic dynamics and the mesoscopic displacement field in soft systems by speckle imaging

The constituents of soft matter systems such as colloidal suspensions, emulsions, polymers, and biological tissues undergo microscopic random motion, due to thermal energy. They may also experience drift motion correlated over mesoscopic or macroscopic length scales, e.g. in response to an internal or applied stress or during flow. We present a new method for measuring simultaneously both the microscopic motion and the mesoscopic or macroscopic drift. The method is based on the analysis of spatio-temporal cross-correlation functions of speckle patterns taken in an imaging configuration. The method is tested on a translating Brownian suspension and a sheared colloidal glass.

Floating nematic phase in colloidal platelet-sphere mixtures

The phase behaviour of colloidal dispersions is interesting for fundamental reasons and for technological applications such as photonic crystals and electronic paper. Sedimentation, which in everyday life is relevant from blood analysis to the shelf life of paint, is a means to determine phase boundaries by observing distinct layers in samples that are in sedimentation-diffusion equilibrium. However, disentangling the effects due to interparticle interactions, which generate the bulk phase diagram, from those due to gravity is a complex task. Here we show that a line in the space of chemical potentials µ(i), where i labels the species, represents a sedimented sample and that each crossing of this sedimentation path with a binodal generates an interface under gravity. Complex phase stacks can result, such as the sandwich of a floating nematic layer between top and bottom isotropic phases that we observed in a mixture of silica spheres and gibbsite platelets.

The unbearable heaviness of colloids: facts, surprises, and puzzles in sedimentation

Sedimentation has played a key role in the development of colloid science. In fact, it is because of the celebrated experiments by Perrin, yielding a concrete demonstration of molecular reality and giving strong support to Einstein's theory of Brownian motion, that colloids enter the realm of basic physics. Subsequent investigations have shown that a lot more can be learnt both from sedimentation equilibrium and from particle settling dynamics. These advances, together with new experimental approaches, will be reviewed in this paper. Yet, we shall also show that inquiring about gravity settling is far from being a closed matter: for instance, the concept of buoyancy for a settling colloidal mixture is far from being obvious. Moreover, sedimentation holds novel surprises, such as colloidal inflations and settling disasters, showing that a simple external field like gravity may induce mind-boggling, and theoretically challenging effects.

Equilibrium concentration profiles and sedimentation kinetics of colloidal gels under gravitational stress

We study the sedimentation of colloidal gels by using a combination of light scattering, polarimetry and video imaging. The asymptotic concentration profiles (z,t → ∞) exhibit remarkable scaling properties: profiles for gels prepared at different initial volume fractions and particle interactions can be superimposed onto a single master curve by using suitable reduced variables. We show theoretically that this behavior stems from a power law dependence of the compressive elastic modulus versus , which we directly test experimentally. The sedimentation kinetics comprises an initial latency stage, followed by a rapid collapse where the gel height h decreases at constant velocity and a final compaction stage characterized by a stretched exponential relaxation of h toward a plateau. Analogies and differences with previous works are briefly discussed.

Sudden collapse of a colloidal gel

Metastable gels formed by weakly attractive colloidal particles display a distinctive two-stage time-dependent settling behavior under their own weight. Initially, a space-spanning network is formed that, for a characteristic time, which we define as the lag time τ(d), resists compaction. This solidlike behavior persists only for a limited time. Gels whose age t(w) is greater than τ(d) yield and suddenly collapse. We use a combination of confocal microscopy, rheology, and time-lapse video imaging to investigate both the process of sudden collapse and its microscopic origin in a refractive-index matched emulsion-polymer system. We show that the height h of the gel in the early stages of collapse is well described by the surprisingly simple expression, h(τ)=h(0)-Aτ(3/2), with h(0) the initial height and τ=t(w)-τ(d) the time counted from the instant where the gel first yields. We propose that this unexpected result arises because the colloidal network progressively builds up internal stress as a consequence of localized rearrangement events, which leads ultimately to collapse as thermal equilibrium is reestablished.