Jamming, two-fluid behaviour and 'self-filtration' in concentrated particulate suspensions

We study the flow of model experimental hard sphere colloidal suspensions at high volume fraction $\Phi$ driven through a constriction by a pressure gradient. Above a particle-size dependent limit $\Phi_0$, direct microscopic observations demonstrate jamming and unjamming--conversion of fluid to solid and vice versa--during flow. We show that such a jamming flow produces a reduction in colloid concentration $\Phi_{x}$ downstream of the constriction. We propose that this `self-filtration' effect is the consequence of a combination of jamming of the particulate part of the system and continuing flow of the liquid part, i.e. the solvent, through the pores of the jammed solid. Thus we link the concept of jamming in colloidal and granular media with a 'two-fluid'-like picture of the flow of concentrated suspensions. Results are also discussed in the light of Osborne Reynolds' original experiments on dilation in granular materials.Comment: 4 pages, 3 figure

Equilibrium phase behavior of polydisperse hard spheres

We calculate the phase behavior of hard spheres with size polydispersity, using accurate free energy expressions for the fluid and solid phases. Cloud and shadow curves, which determine the onset of phase coexistence, are found exactly by the moment free energy method, but we also compute the complete phase diagram, taking full account of fractionation effects. In contrast to earlier, simplified treatments we find no point of equal concentration between fluid and solid or re-entrant melting at higher densities. Rather, the fluid cloud curve continues to the largest polydispersity that we study (14%); from the equilibrium phase behavior a terminal polydispersity can thus only be defined for the solid, where we find it to be around 7%. At sufficiently large polydispersity, fractionation into several solid phases can occur, consistent with previous approximate calculations; we find in addition that coexistence of several solids with a fluid phase is also possible

Multi-speckle diffusing wave spectroscopy with a single mode detection scheme

We present a detection scheme for diffusing wave spectroscopy (DWS) based on a two cell geometry that allows efficient ensemble averaging. This is achieved by putting a fast rotating diffuser in the optical path between laser and sample. We show that the recorded (multi-speckle) correlation echoes provide an ensemble averaged signal that does not require additional time averaging. We find the performance of our experimental scheme comparable or even superior to camera based multi-speckle techniques that rely on direct spatial averaging. Furthermore, combined with traditional two-cell DWS, the full intensity autocorrelation function can be measured with a single experimental setup covering more than 10 decades in correlation time.Comment: Submitted to PR

Properties of cage rearrangements observed near the colloidal glass transition

We use confocal microscopy to study the motions of particles in concentrated colloidal systems. Near the glass transition, diffusive motion is inhibited, as particles spend time trapped in transient ``cages'' formed by neighboring particles. We measure the cage sizes and lifetimes, which respectively shrink and grow as the glass transition approaches. Cage rearrangements are more prevalent in regions with lower local concentrations and higher disorder. Neighboring rearranging particles typically move in parallel directions, although a nontrivial fraction move in anti-parallel directions, usually from pairs of particles with initial separations corresponding to the local maxima and minima of the pair correlation function $g(r)$, respectively.Comment: 5 pages, 4 figures; text & figures revised in v

Phase diagram of softly repulsive systems: The Gaussian and inverse-power-law potentials

We redraw, using state-of-the-art methods for free-energy calculations, the phase diagrams of two reference models for the liquid state: the Gaussian and inverse-power-law repulsive potentials. Notwithstanding the different behavior of the two potentials for vanishing interparticle distances, their thermodynamic properties are similar in a range of densities and temperatures, being ruled by the competition between the body-centered-cubic (BCC) and face-centered-cubic (FCC) crystalline structures and the fluid phase. We confirm the existence of a reentrant BCC phase in the phase diagram of the Gaussian-core model, just above the triple point. We also trace the BCC-FCC coexistence line of the inverse-power-law model as a function of the power exponent $n$ and relate the common features in the phase diagrams of such systems to the softness degree of the interaction.Comment: 22 pages, 8 figure

Critical scaling of jammed system after quench of temperature

Critical behavior of soft repulsive particles after quench of temperature near the jamming trasition is numerically investigated. It is found that the plateau of the mean square displacement of tracer particles and the pressure satisfy critical scaling laws. The critical density for the jamming transition depends on the protocol to prepare the system, while the values of the critical exponents which are consistent with the prediction of a phenomenology are independent of the protocol.Comment: 7 pages, 9 figures, to appear in Phys. Rev.

Fluid-fluid phase separation in hard spheres with a bimodal size distribution

The effect of polydispersity on the phase behaviour of hard spheres is examined using a moment projection method. It is found that the Boublik-Mansoori-Carnahan-Starling-Leland equation of state shows a spinodal instability for a bimodal distribution if the large spheres are sufficiently polydisperse, and if there is sufficient disparity in mean size between the small and large spheres. The spinodal instability direction points to the appearance of a very dense phase of large spheres.Comment: 7 pages, 3 figures, moderately REVISED following referees' comments (original was 4 pages, 3 postscript figures

Hard Spheres: Crystallization and Glass Formation

Motivated by old experiments on colloidal suspensions, we report molecular dynamics simulations of assemblies of hard spheres, addressing crystallization and glass formation. The simulations cover wide ranges of polydispersity s (standard deviation of the particle size distribution divided by its mean) and particle concentration. No crystallization is observed for s > 0.07. For 0.02 < s < 0.07, we find that increasing the polydispersity at a given concentration slows down crystal nucleation. The main effect here is that polydispersity reduces the supersaturation since it tends to stabilise the fluid but to destabilise the crystal. At a given polydispersity (< 0.07) we find three regimes of nucleation: standard nucleation and growth at concentrations in and slightly above the coexistence region; "spinodal nucleation", where the free energy barrier to nucleation appears to be negligible, at intermediate concentrations; and, at the highest concentrations, a new mechanism, still to be fully understood, which only requires small re-arrangement of the particle positions. The cross-over between the second and third regimes occurs at a concentration, around 58% by volume, where the colloid experiments show a marked change in the nature of the crystals formed and the particle dynamics indicate an "ideal" glass transition

Density functional theory for the freezing of soft-core fluids

We present a simple density functional theory for the solid phases of systems of particles interacting via soft-core potentials. In particular, we apply the theory to particles interacting via repulsive point Yukawa and Gaussian pair potentials. We find qualitative agreement with the established phase diagrams for these systems. The theory is able to account for the bcc-fcc solid transitions of both systems and the re-entrant melting that the Gaussian system exhibits.Comment: 7 pages, 4 figure

Crystal Nucleation of Colloidal Suspensions under Shear

We use Brownian Dynamics simulations in combination with the umbrella sampling technique to study the effect of shear flow on homogeneous crystal nucleation. We find that a homogeneous shear rate leads to a significant suppression of the crystal nucleation rate and to an increase of the size of the critical nucleus. A simple, phenomenological extension of classical nucleation theory accounts for these observations. The orientation of the crystal nucleus is tilted with respect to the shear direction.Comment: 4 pages, 3 figures, Submitted to Phys. Rev. Let