Gravitational collapse of depletion-induced colloidal gels

Thermoreversible gels of hollow silica nanorod dispersions

Colloidal suspensions of anisotropic particles are ubiquitous in particle-based industries. Consequently, there is a need to quantify the effects of particle shape on equilibrium phases and kinetic state transitions, particularly at lower aspect ratios (L/D ≈ 1-10). We present a new, colloidal system comprised of hollow, octadecyl-coated silica rods with 40 nm diameter with controlled aspect ratio and thermoreversible short-range attractions. Rheology and dynamic light scattering measurements on suspensions of these hollow adhesive hard rods with nominal aspect ratio ≈3 suspended in tetradecane exhibit thermoreversible gelation without complicating effects of gravitational settling. Small angle neutron scattering measurements of the microstructure are analyzed to determine the effective strength of attraction in the form of Baxter sticky parameter. Quantitative agreement is found with simulation predictions of the thermoreversible gel transition as a function of volume fraction, further validating a universal state diagram and providing guidance for the effects of aspect ratio on gelation.

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.

Hydrodynamic lubrication in colloidal gels

Colloidal gels are elasto-plastic materials composed of an out-of-equilibrium, self-assembled network of micron-sized (solid) particles suspended in a fluid. Recent work has shown that far-field hydrodynamic interactions do not change gel structure, only the rate at which the network forms and ages. However, during gel formation, the interplay between short-ranged attractions leading to gelation and equally short-ranged hydrodynamic lubrication interactions remains poorly understood. Here, we therefore study gelation using a range of hydrodynamic descriptions: from single-body (Brownian Dynamics), to pairwise (Rotne-Prager-Yamakawa), to (non-)lubrication-corrected many-body (Stokesian Dynamics). We confirm the current understanding informed by simulations accurate in the far-field. Yet, we find that accounting for lubrication can strongly impact structure at low colloid volume fraction. Counterintuitively, strongly dissipative lubrication interactions also accelerate the aging of a gel, irrespective of colloid volume fraction. Both elements can be explained by lubrication forces facilitating collective dynamics and therefore phase-separation. Our findings indicate that despite the computational cost, lubricated hydrodynamic modeling with many-body far-field interactions is needed to accurately capture the evolution of the gel structure.

Colloidal gelation with non-sticky particles

Colloidal gels are widely applied in industry due to their rheological character-no flow takes place below the yield stress. Such property enables gels to maintain uniform distribution in practical formulations; otherwise, solid components may quickly sediment without the support of gel matrix. Compared with pure gels of sticky colloids, therefore, the composites of gel and non-sticky inclusions are more commonly encountered in reality. Through numerical simulations, we investigate the gelation process in such binary composites. We find that the non-sticky particles not only confine gelation in the form of an effective volume fraction, but also introduce another lengthscale that competes with the size of growing clusters in gel. The ratio of two key lengthscales in general controls the two effects. Using different gel models, we verify such a scenario within a wide range of parameter space, suggesting a potential universality in all classes of colloidal composites.

Characterization and Optimization of Fluorescent Organosilica Colloids for 3D Confocal Microscopy Prepared Under "Zero-Flow" Conditions

We optimize and characterize the preparation of 3-trimethoxysilyl propyl methacrylate (TPM) colloidal suspensions for three-dimensional confocal microscopy. We revisit a simple synthesis of TPM microspheres by nucleation of droplets from prehydrolyzed TPM oil in a "zero-flow" regime and demonstrate how precise and reproducible control of particle size may be achieved via single-step nucleation with a focus on how the reagents are mixed. We also revamp the conventional dyeing method for TPM particles to achieve uniform transfer of a fluorophore to the organosilica droplets, improving particle identification. Finally, we illustrate how a ternary mixture of tetralin, trichloroethylene, and tetrachloroethylene may be used as a suspension medium which matches the refractive index of these particles while allowing independent control of the density mismatch between particle and solvent.

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.

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.

Impact of granular inclusions on the phase behavior of colloidal gels

Colloidal gels formed from small attractive particles are commonly used in formulations to keep larger components in suspension. Despite extensive work characterising unfilled gels, little is known about how the larger inclusions alter the phase behavior and microstructure of the colloidal system. Here we use numerical simulations to examine how larger 'granular' particles can alter the gel transition phase boundaries. We find two distinct regimes depending on both the filler size and native gel structure: a 'passive' regime where the filler fits into already-present voids, giving little change in the transition, and an 'active' regime where the filler no longer fits in these voids and instead perturbs the native structure. In this second regime the phase boundary is controlled by an effective colloidal volume fraction given by the available free volume.

Complex optical transport, dynamics, and rheology of intermediately attractive emulsions

Introducing short-range attractions in Brownian systems of monodisperse colloidal spheres can substantially impact their structures and consequently their optical transport and rheological properties. Here, for size-fractionated colloidal emulsions, we show that imposing an intermediate strength of attraction, well above but not much larger than thermal energy ([Formula: see text] [Formula: see text], through micellar depletion leads to a striking notch in the measured inverse mean free path of optical transport, [Formula: see text], as a function of droplet volume fraction, [Formula: see text]. This notch, which appears between the hard-sphere glass transition, [Formula: see text], and maximal random jamming, [Formula: see text], implies the existence of a greater population of compact dense clusters of droplets, as compared to tenuous networks of droplets in strongly attractive emulsion gels. We extend a prior decorated core-shell network model for strongly attractive colloidal systems to include dense non-percolating clusters that do not contribute to shear rigidity. By constraining this extended model using the measured [Formula: see text], we improve and expand the microrheological interpretation of diffusing wave spectroscopy (DWS) experiments made on attractive colloidal systems. Our measurements and modeling demonstrate richness and complexity in optical transport and shear rheological properties of dense, disordered colloidal systems having short-range intermediate attractions between moderately attractive glasses and strongly attractive 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.

Sedimentation path theory for mass-polydisperse colloidal systems

Both polydispersity and the presence of a gravitational field are inherent to essentially any colloidal experiment. While several theoretical works have focused on the effect of polydispersity on the bulk phase behavior of a colloidal system, little is known about the effect of a gravitational field on a polydisperse colloidal suspension. We extend here the sedimentation path theory to study sedimentation-diffusion-equilibrium of a mass-polydisperse colloidal system: the particles possess different buoyant masses but they are otherwise identical. The model helps to understand the interplay between gravity and polydispersity on sedimentation experiments. Since the theory can be applied to any parent distribution of buoyant masses, it can also be used to study the sedimentation of monodisperse colloidal systems. We find that mass-polydispersity has a strong influence in colloidal systems near density matching for which the bare density of the colloidal particles equals the solvent density. To illustrate the theory, we study crystallization in sedimentation-diffusion-equilibrium of a suspension of mass-polydisperse hard spheres.

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.

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.

Imaging Erythrocyte Sedimentation in Whole Blood

The erythrocyte sedimentation rate (ESR) is one of the oldest medical diagnostic tools. However, currently there is some debate on the structure formed by the cells during the sedimentation process. While the conventional view is that erythrocytes sediment as separate aggregates, others have suggested that they form a percolating gel, similar to other colloidal suspensions. However, visualization of aggregated erythrocytes, which would settle the question, has always been challenging. Direct methods usually study erythrocytes in 2D situations or low hematocrit (∼1%). Indirect methods, such as scattering or electric measurements, provide insight on the suspension evolution, but cannot directly discriminate between open or percolating structures. Here, we achieved a direct probing of the structures formed by erythrocytes in blood at stasis. We focused on blood samples at rest with controlled hematocrit of 45%, from healthy donors, and report observations from three different optical imaging techniques: direct light transmission through thin samples, two-photon microscopy and light-sheet microscopy. The three techniques, used in geometries with thickness from 150 μm to 3 mm, highlight that erythrocytes form a continuous network with characteristic cracks, i.e., a colloidal gel. The characteristic distance between the main cracks is of the order of ∼100 μm. A complete description of the structure then requires a field of view of the order of ∼1 mm, in order to obtain a statistically relevant number of structural elements. A quantitative analysis of the erythrocyte related processes and interactions during the sedimentation need a further refinement of the experimental set-ups.

Toward a flow-dependent phase-stability criterion: Osmotic pressure in sticky flowing suspensions

Equilibrium phase instability of colloids is robustly predicted by the Vliegenthart-Lekkerkerker (VL) critical value of the second virial efficient, but no such general criterion has been established for suspensions undergoing flow. A transition from positive to negative osmotic pressure is one mechanical hallmark of a change in phase stability in suspensions and provides a natural extension of the equilibrium osmotic pressure encoded in the second virial coefficient. Here, we propose to study the non-Newtonian rheology of an attractive colloidal suspension using the active microrheology framework as a model for focusing on the pair trajectories that underlie flow stability. We formulate and solve a Smoluchowski relation to understand the interplay between attractions, hydrodynamics, Brownian motion, and flow on particle microstructure in a semi-dilute suspension and utilize the results to study the viscosity and particle-phase osmotic pressure. We find that an interplay between attractions and hydrodynamics leads to dramatic changes in the nonequilibrium microstructure, which produces a two-stage flow-thinning of viscosity and leads to pronounced flow-induced negative osmotic pressure. We summarize these findings with an osmotic pressure heat map that predicts where hydrodynamic enhancement of attractive bonds encourages flow-induced aggregation or phase separation. We identify a critical isobar-a flow-induced critical pressure consistent with phase instability and a nonequilibrium extension of the VL criterion.

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.

Diffusion, phase behavior, and gelation in a two-dimensional layer of colloids in osmotic equilibrium with a polymer reservoir

The addition of enough non-adsorbing polymers to an otherwise stable colloidal suspension gives rise to a variety of phase behaviors and kinetic arrest due to the depletion attraction induced between the colloids by the polymers. We report a study of these phenomena in a two-dimensional layer of colloids. The three-dimensional phenomenology of crystal-fluid coexistence is reproduced, but gelation takes a novel form, in which the strands in the gel structure are locally crystalline. We compare our findings with a previous simulation and theory and find substantial agreement.

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.

Phase separation and collapse in almost density matched depletion induced colloidal gels in presence and absence of air bubbles: An MRI imaging study

HYPOTHESIS

Vesicle-polymer dispersions are found in drug-delivery systems and consumer products but undergo phase separation. Previous studies of phase separation have focussed on systems with high density differences between continuous and vesicular phases. In this study, we investigate phase separation in vesicle-polymer mixtures with very small density differences, in the presence and absence of air bubbles.

EXPERIMENTS

Magnetic resonance (MR) imaging, X-ray Computed Tomography and rheological measurements are reported which characterise the properties and stability of vesicle suspensions composed of the cationic surfactant, diethylesterdimethyl ammonium chloride, mixed with non-adsorbing polymer. ¹H T₂ MR relaxation images are employed to observe phase separation, for a range of vesicle-polymer mixtures, which are analysed using Moran's I spatial autocorrelation to quantify the extent and rate of phase separation.

FINDINGS

It was found that in presence of air bubbles, phase separation follows a compression/collapse mechanism, typical of colloidal gels with large density differences between the phases. Without air bubbles, phase separation develops through the formation of tiny cracks and fractures in the samples. MRI enabled visualisation of the evolution of phase separation inside highly turbid samples. The rate of phase separation was found to generally increase with increasing polymer concentration and decrease with increasing vesicle volume fraction.

Diffusing wave microrheology of strongly attractive dense emulsions

We advance the microrheological interpretation of optical diffusing wave spectroscopy (DWS) measurements of strongly attractive emulsions at dense droplet volume fractions, ϕ. Beyond accounting for collective scattering, we show that measuring the mean free path of optical transport over a wide range of ϕ is necessary to quantify the effective size of the DWS probes, which we infer to be local dense clusters of droplets through a decorated core-shell network model. This approach yields microrheological elastic shear moduli that are in quantitative agreement with mechanical rheometry.

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.

Soft matter: rubber and networks

Rubber networks are important and form the basis for materials with properties ranging from rubber tires to super absorbents and contact lenses. The development of the entropy ideas of rubber deformation thermodynamics provides a powerful framework from which to understand and to use these materials. In addition, swelling of the rubber in the presence of small molecule liquids or solvents leads to materials that are very soft and 'gel' like in nature. The review covers the thermodynamics of polymer networks and gels from the perspective of the thermodynamics and mechanics of the strain energy density function. Important relationships are presented and experimental results show that the continuum ideas contained in the phenomenological thermodynamics are valid, but that the molecular bases for some of them remain to be fully elucidated. This is particularly so in the case of the entropic gels or swollen networks. The review is concluded with some perspectives on other networks, ranging from entropic polymer networks such as thermoplastic elastomers to physical gels in which cross-link points are formed by glassy or crystalline domains. A discussion is provided for other physical gels in which the network forms a spinodal-like decomposition, both in thermoplastic polymers that form a glassy network upon phase separation and for colloidal gels that seem to have a similar behavior.

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.

Arrested and temporarily arrested states in a protein-polymer mixture studied by USAXS and VSANS

We investigate the transition of the phase separation kinetics from a complete to an arrested liquid-liquid phase separation (LLPS) in mixtures of bovine γ-globulin with polyethylene glycol (PEG). The solutions feature LLPS with upper critical solution temperature phase behavior. At higher PEG concentrations or low temperatures, non-equilibrium, gel-like states are found. The kinetics is followed during off-critical quenches by ultra-small angle X-ray scattering (USAXS) and very-small angle neutron scattering (VSANS). For shallow quenches a kinetics consistent with classical spinodal decomposition is found, with the characteristic length (ξ) growing with time as ξ ∼ t^1/3. For deep quenches, ξ grows only very slowly with a growth exponent smaller than 0.05 during the observation time, indicating an arrested phase separation. For intermediate quench depths, a novel growth kinetics featuring a three-stage coarsening is observed, with an initial classical coarsening, a subsequent slowdown of the growth, and a later resumption of coarsening approaching again ξ ∼ t^1/3. Samples featuring the three-stage coarsening undergo a temporarily arrested state. We hypothesize that, while intermittent coarsening and collapse might contribute to the temporary nature of the arrested state, migration-coalescence of the minority liquid phase through the majority glassy phase may be the main mechanism underlying this kinetics, which is also consistent with earlier simulation results.

Characterisation of heterogeneity and spatial autocorrelation in phase separating mixtures using Moran's I

In complex colloidal systems, particle-poor regions can develop within particle-rich phases during sedimentation or creaming. These particle-poor regions are overlooked by 1D profiles, which are typically used to assess particle distributions in a sample. Alternative methods to visualise and quantify these regions are required to better understand phase separation, which is the focus of this paper. Magnetic resonance imaging has been used to monitor the development of compositional heterogeneity in a vesicle-polymer mixture undergoing creaming. T₂ relaxation time maps were used to identify the distribution of vesicles, with vesicle-poor regions exhibiting higher T₂ relaxation times than regions richer in vesicles. Phase separated structures displayed a range of different morphologies and a variety of image analysis methods, including first-order statistics, Fourier transformation, grey level co-occurrence matrices and Moran's I spatial autocorrelation, were used to characterise these structures, and quantify their heterogeneity. Of the image analysis techniques used, Moran's I was found to be the most effective at quantifying the degree and morphology of phase separation, providing a robust, quantitative measure by which comparisons can be made between a diverse range of systems undergoing phase separation. The sensitivity of Moran's I can be enhanced by the choice of weight matrices used.

Magnetic Resonance Imaging and Velocity Mapping in Chemical Engineering Applications

This review aims to illustrate the diversity of measurements that can be made using magnetic resonance techniques, which have the potential to provide insights into chemical engineering systems that cannot readily be achieved using any other method. Perhaps the most notable advantage in using magnetic resonance methods is that both chemistry and transport can be followed in three dimensions, in optically opaque systems, and without the need for tracers to be introduced into the system. Here we focus on hydrodynamics and, in particular, applications to rheology, pipe flow, and fixed-bed and gas-solid fluidized bed reactors. With increasing development of industrially relevant sample environments and undersampling data acquisition strategies that can reduce acquisition times to <1 s, magnetic resonance is finding increasing application in chemical engineering research.

Stable, Fluorescent Polymethylmethacrylate Particles for the Long-Term Observation of Slow Colloidal Dynamics

Suspensions of solid micron-scale colloidal particles in liquid solvents are a foundational model system used to explore a wide range of phase transitions, including crystallization, gelation, spinodal decomposition, and the glass transition. One of the most commonly used systems for these investigations is the fluorescent spherical particles of polymethylmethacrylate (PMMA) suspended in a mixture of nonpolar solvents that match the density and the refractive index of the particles to minimize sedimentation and scattering. However, the particles can swell in these solvents, changing their size and density, and may leak the fluorescent dye over days to weeks; this constrains the exploration of slow and kinetically limited processes, such as near-boundary phase separation or the glass transition. In this paper, we produce PMMA colloidal particles that employ polymerizable and photostable cyanine-based fluorescent monomers spanning the range of visible wavelengths and a polymeric stabilizer prepared from polydimethylsiloxane, PDMS-graft-PMMA. Using microcalorimetry, we characterize the thermodynamics of an accelerated equilibration process for these dispersions in the buoyancy- and refractive-index-matching solvents. We use confocal differential dynamic microscopy to demonstrate that they behave as hard spheres. The suspended particles are stable for months to years, maintaining fixed particle size and density, and do not leak dye. Thus, these particles enable longer term experiments than may have been possible earlier; we demonstrate this by observing spinodal decomposition in a mixture of these particles with a depletant polymer in the microgravity environment of the International Space Station. Using fluorescence microscopy, we observe coarsening over several months and measure the growth of the characteristic length scale to be a fraction of a picometer per second; this rate is among the slowest observed in a phase-separating system. Our protocols should facilitate the synthesis of a variety of particles.

Effects of vertical confinement on gelation and sedimentation of colloids

We consider the sedimentation of a colloidal gel under confinement in the direction of gravity. The confinement allows us to compare directly experiments and computer simulations, for the same system size in the vertical direction. The confinement also leads to qualitatively different behaviour compared to bulk systems: in large systems gelation suppresses sedimentation, but for small systems sedimentation is enhanced relative to non-gelling suspensions, although the rate of sedimentation is reduced when the strength of the attraction between the colloids is strong. We map interaction parameters between a model experimental system (observed in real space) and computer simulations. Remarkably, we find that when simulating the system using Brownian dynamics in which hydrodynamic interactions between the particles are neglected, we find that sedimentation occurs on the same timescale as the experiments. An analysis of local structure in the simulations showed similar behaviour to gelation in the absence of gravity.