Dense colloidal suspensions under time-dependent shear

We consider the nonlinear rheology of dense colloidal suspensions under a time-dependent simple shear flow. Starting from the Smoluchowski equation for interacting Brownian particles advected by shearing (ignoring fluctuations in fluid velocity) we develop a formalism which enables the calculation of time-dependent, far-from-equilibrium averages. Taking shear-stress as an example we derive exactly a generalized Green-Kubo relation, and an equation of motion for the transient density correlator, involving a three-time memory function. Mode coupling approximations give a closed constitutive equation yielding the time-dependent stress for arbitrary shear rate history. We solve this equation numerically for the special case of a hard sphere glass subject to step-strain.Comment: 4 page

Sensitivity of arrest in mode-coupling glasses to low-q structure

We quantify, within mode coupling theory, how changes in the liquid structure affect that of the glass. Apart from the known sensitivity to the structure factor $S(q)$ at wavevectors around the first sharp diffraction peak $q_0$, we find a strong (and inverted) response to structure at wavevectors \emph{below} this peak: an increase in $S(q_0/2)$ {\em lowers} the degree of arrest over a wide $q$-range. This strong sensitivity to `caged cage' packing effects, on length scales of order 2d, is much weaker in attractive glasses where short-range bonding dominates the steric caging effect.Comment: 4 pages, 5 figures. v2: 3 figures replaced; text rewritte

Dilatancy, Jamming, and the Physics of Granulation

Granulation is a process whereby a dense colloidal suspension is converted into pasty granules (surrounded by air) by application of shear. Central to the stability of the granules is the capillary force arising from the interfacial tension between solvent and air. This force appears capable of maintaining a solvent granule in a jammed solid state, under conditions where the same amount of solvent and colloid could also exist as a flowable droplet. We argue that in the early stages of granulation the physics of dilatancy, which requires that a powder expand on shearing, is converted by capillary forces into the physics of arrest. Using a schematic model of colloidal arrest under stress, we speculate upon various jamming and granulation scenarios. Some preliminary experimental results on aspects of granulation in hard-sphere colloidal suspensions are also reported.Comment: Original article intended for J Phys Cond Mat special issue on Granular Materials (M Nicodemi, Ed.

Run-and-tumble particles with hydrodynamics: sedimentation, trapping and upstream swimming

We simulate by lattice Boltzmann the nonequilibrium steady states of run-and-tumble particles (inspired by a minimal model of bacteria), interacting by far-field hydrodynamics, subject to confinement. Under gravity, hydrodynamic interactions barely perturb the steady state found without them, but for particles in a harmonic trap such a state is quite changed if the run length is larger than the confinement length: a self-assembled pump is formed. Particles likewise confined in a narrow channel show a generic upstream flux in Poiseuille flow: chiral swimming is not required

Dynamics and Thermodynamics of the Glass Transition

The principal theme of this paper is that anomalously slow, super-Arrhenius relaxations in glassy materials may be activated processes involving chains of molecular displacements. As pointed out in a preceding paper with A. Lemaitre, the entropy of critically long excitation chains can enable them to grow without bound, thus activating stable thermal fluctuations in the local density or molecular coordination of the material. I argue here that the intrinsic molecular-scale disorder in a glass plays an essential role in determining the activation rate for such chains, and show that a simple disorder-related correction to the earlier theory recovers the Vogel-Fulcher law in three dimensions. A key feature of this theory is that the spatial extent of critically long excitation chains diverges at the Vogel-Fulcher temperature. I speculate that this diverging length scale implies that, as the temperature decreases, increasingly large regions of the system become frozen and do not contribute to the configurational entropy, and thus ergodicity is partially broken in the super-Arrhenius region above the Kauzmann temperature $T_K$. This partially broken ergodicity seems to explain the vanishing entropy at $T_K$ and other observed relations between dynamics and thermodynamics at the glass transition.Comment: 20 pages, no figures, some further revision

Computing the local pressure in molecular dynamics simulations

Computer simulations of inhomogeneous soft matter systems often require accurate methods for computing the local pressure. We present a simple derivation, based on the virial relation, of two equivalent expressions for the local (atomistic) pressure in a molecular dynamics simulation. One of these expressions, previously derived by other authors via a different route, involves summation over interactions between particles within the region of interest; the other involves summation over interactions across the boundary of the region of interest. We illustrate our derivation using simulations of a simple osmotic system; both expressions produce accurate results even when the region of interest over which the pressure is measured is very small.Comment: 11 pages, 4 figure

A cluster mode-coupling approach to weak gelation in attractive colloids

Mode-coupling theory (MCT) predicts arrest of colloids in terms of their volume fraction, and the range and depth of the interparticle attraction. We discuss how effective values of these parameters evolve under cluster aggregation. We argue that weak gelation in colloids can be idealized as a two-stage ergodicity breaking: first at short scales (approximated by the bare MCT) and then at larger scales (governed by MCT applied to clusters). The competition between arrest and phase separation is considered in relation to recent experiments. We predict a long-lived `semi-ergodic' phase of mobile clusters, showing logarithmic relaxation close to the gel line.Comment: 4 pages, 3 figure

Velocity profiles in shear-banding wormlike micelles

Using Dynamic Light Scattering in heterodyne mode, we measure velocity profiles in a much studied system of wormlike micelles (CPCl/NaSal) known to exhibit both shear-banding and stress plateau behavior. Our data provide evidence for the simplest shear-banding scenario, according to which the effective viscosity drop in the system is due to the nucleation and growth of a highly sheared band in the gap, whose thickness linearly increases with the imposed shear rate. We discuss various details of the velocity profiles in all the regions of the flow curve and emphasize on the complex, non-Newtonian nature of the flow in the highly sheared band.Comment: 4 pages, 5 figures, submitted to Phys. Rev. Let

Dynamic Response of Block Copolymer Wormlike Micelles to Shear Flow

The linear and non-linear dynamic response to an oscillatory shear flow of giant wormlike micelles consisting of Pb-Peo block copolymers is studied by means of Fourier transform rheology. Experiments are performed in the vicinity of the isotropic-nematic phase transition concentration, where the location of isotropic-nematic phase transition lines is determined independently. Strong shear-thinning behaviour is observed due to critical slowing down of orientational diffusion as a result of the vicinity of the isotropic- nematic spinodal. This severe shear-thinning behaviour is shown to result in gradient shear banding. Time-resolved Small angle neutron scattering experiments are used to obtain insight in the microscopic phenomena that underly the observed rheological response. An equation of motion for the order-parameter tensor and an expression of the stress tensor in terms of the order-parameter tensor are used to interpret the experimental data, both in the linear and non-linear regime. Scaling of the dynamic behaviour of the orientational order parameter and the stress is found when critical slowing down due to the vicinity of the isotropic-nematic spinodal is accounted for.Comment: Accepted by J. Phys.: Condens. Matter, CODEF II Special Issue. 20 pages, 9 figure

Dynamic Response of Block Copolymer Wormlike Micelles to Shear Flow

The linear and non-linear dynamic response to an oscillatory shear flow of giant wormlike micelles consisting of Pb-Peo block copolymers is studied by means of Fourier transform rheology. Experiments are performed in the vicinity of the isotropic-nematic phase transition concentration, where the location of isotropic-nematic phase transition lines is determined independently. Strong shear-thinning behaviour is observed due to critical slowing down of orientational diffusion as a result of the vicinity of the isotropic- nematic spinodal. This severe shear-thinning behaviour is shown to result in gradient shear banding. Time-resolved Small angle neutron scattering experiments are used to obtain insight in the microscopic phenomena that underly the observed rheological response. An equation of motion for the order-parameter tensor and an expression of the stress tensor in terms of the order-parameter tensor are used to interpret the experimental data, both in the linear and non-linear regime. Scaling of the dynamic behaviour of the orientational order parameter and the stress is found when critical slowing down due to the vicinity of the isotropic-nematic spinodal is accounted for.Comment: Accepted by J. Phys.: Condens. Matter, CODEF II Special Issue. 20 pages, 9 figure