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

Flattened and Wrinkled Encapsulated Droplets: Shape Morphing Induced by Gravity and Evaporation

We report surprising morphological changes of suspension droplets (containing class II hydrophobin protein HFBI from Trichoderma reesei in water) as they evaporate with a contact line pinned on a rigid solid substrate. Both pendant and sessile droplets display the formation of an encapsulating elastic film as the bulk concentration of solute reaches a critical value during evaporation, but the morphology of the droplet varies significantly: for sessile droplets, the elastic film ultimately crumples in a nearly flattened area close to the apex while in pendant droplets, circumferential wrinkling occurs close to the contact line. These different morphologies are understood through a gravito-elastocapillary model that predicts the droplet morphology and the onset of shape changes, as well as showing that the influence of the direction of gravity remains crucial even for very small droplets (where the effect of gravity can normally be neglected). The results pave the way to control droplet shape in several engineering and biomedical applications.

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.

Inducing a bound state between active particles

We show that two active particles can form a bound state by coupling to a driven nonequilibrium environment. We specifically investigate the case of two mutually noninteracting run-and-tumble probes moving on a ring, each in short-range interaction with driven colloids. Under conditions of timescale separation, these active probes become trapped in bound states. In fact, the bound state appears at high enough persistence (low effective temperature). From the perspective of a comoving frame, where colloids are in thermal equilibrium and the probes are active and driven, an appealing analogy appears with Cooper pairing, as electrons can be viewed as run-and-tumble particles in a pilot-wave picture.

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.

Phase behavior of binary and polydisperse suspensions of compressible microgels controlled by selective particle deswelling

We investigate the phase behavior of suspensions of poly(N-isopropylacrylamide) (pNIPAM) microgels with either bimodal or polydisperse size distribution. We observe a shift of the fluid-crystal transition to higher concentrations depending on the polydispersity or the fraction of large particles in suspension. Crystallization is observed up to polydispersities as high as 18.5%, and up to a number fraction of large particles of 29% in bidisperse suspensions. The crystal structure is random hexagonal close-packed as in monodisperse pNIPAM microgel suspensions. We explain our experimental results by considering the effect of bound counterions. Above a critical particle concentration, these cause deswelling of the largest microgels, which are the softest, changing the size distribution of the suspension and enabling crystal formation in conditions where incompressible particles would not crystallize.

Impact of single-particle compressibility on the fluid-solid phase transition for ionic microgel suspensions

We study ionic microgel suspensions composed of swollen particles for various single-particle stiffnesses. We measure the osmotic pressure π of these suspensions and show that it is dominated by the contribution of free ions in solution. As this ionic osmotic pressure depends on the volume fraction of the suspension ϕ, we can determine ϕ from π, even at volume fractions so high that the microgel particles are compressed. We find that the width of the fluid-solid phase coexistence, measured using ϕ, is larger than its hard-sphere value for the stiffer microgels that we study and progressively decreases for softer microgels. For sufficiently soft microgels, the suspensions are fluidlike, irrespective of volume fraction. By calculating the dependence on ϕ of the mean volume of a microgel particle, we show that the behavior of the phase-coexistence width correlates with whether or not the microgel particles are compressed at the volume fractions corresponding to fluid-solid phase coexistence.

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.

Critical onset of layering in sedimenting suspensions of nanoparticles

We quantitatively study the critical onset of layering in suspensions of nanoparticles in a solvent, where an initially homogeneous suspension, subject to an effective gravity a in a centrifuge, spontaneously forms well-defined layers of constant particle density, so that the density changes in a staircaselike manner along the axis of gravity. This phenomenon is well known; yet, it has never been quantitatively studied under reproducible conditions: therefore, its physical mechanism remained controversial and the role of thermal diffusion in this phenomenon was never explored. We demonstrate that the number of layers forming in the sample exhibits a critical scaling as a function of a; a critical dependence on sample height and transverse temperature gradient is established as well. We reproduce our experiments by theoretical calculations, which attribute the layering to a diffusion-limited convective instability, fully elucidating the physical mechanism of layering.

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.

Sedimentation dynamics and equilibrium profiles in multicomponent mixtures of colloidal particles

In this paper we give a general theoretical framework that describes the sedimentation of multicomponent mixtures of particles with sizes ranging from molecules to macroscopic bodies. Both equilibrium sedimentation profiles and the dynamic process of settling, or its converse, creaming, are modeled. Equilibrium profiles are found to be in perfect agreement with experiments. Our model reconciles two apparently contradicting points of view about buoyancy, thereby resolving a long-lived paradox about the correct choice of the buoyant density. On the one hand, the buoyancy force follows necessarily from the suspension density, as it relates to the hydrostatic pressure gradient. On the other hand, sedimentation profiles of colloidal suspensions can be calculated directly using the fluid density as apparent buoyant density in colloidal systems in sedimentation-diffusion equilibrium (SDE) as a result of balancing gravitational and thermodynamic forces. Surprisingly, this balance also holds in multicomponent mixtures. This analysis resolves the ongoing debate of the correct choice of buoyant density (fluid or suspension): both approaches can be used in their own domain. We present calculations of equilibrium sedimentation profiles and dynamic sedimentation that show the consequences of these insights. In bidisperse mixtures of colloids, particles with a lower mass density than the homogeneous suspension will first cream and then settle, whereas particles with a suspension-matched mass density form transient, bimodal particle distributions during sedimentation, which disappear when equilibrium is reached. In all these cases, the centers of the distributions of the particles with the lowest mass density of the two, regardless of their actual mass, will be located in equilibrium above the so-called isopycnic point, a natural consequence of their hard-sphere interactions. We include these interactions using the Boublik-Mansoori-Carnahan-Starling-Leland (BMCSL) equation of state. Finally, we demonstrate that our model is not limited to hard spheres, by extending it to charged spherical particles, and to dumbbells, trimers and short chains of connected beads.