Diffusion and rheology in a model of glassy materials

We study self-diffusion within a simple hopping model for glassy materials. (The model is Bouchaud's model of glasses [J.-P. Bouchaud, J. Physique I 2, 1705 (1992)], as extended to describe rheological properties [P. Sollich, F. Lequeux, P. Hebraud and M.E. Cates, Phys. Rev. Lett. 78, 2020 (1997)].) We investigate the breakdown, near the glass transition, of the (generalized) Stokes-Einstein relation between self-diffusion of a tracer particle and the (frequency-dependent) viscosity of the system as a whole. This stems from the presence of a broad distribution of relaxation times of which different moments control diffusion and rheology. We also investigate the effect of flow (oscillatory shear) on self-diffusion and show that this causes a finite diffusivity in the temperature regime below the glass transition (where this was previously zero). At higher temperatures the diffusivity is enhanced by a power law frequency dependence that also characterises the rheological response. The relevance of these findings to soft glassy materials (foams, emulsions etc.) as well as to conventional glass-forming liquids is discussed.Comment: 39 page (double spaced), 2 figure

Thermal fluctuations in the lattice Boltzmann method for non-ideal fluids

We introduce thermal fluctuations in the lattice Boltzmann method for non-ideal fluids. A fluctuation-dissipation theorem is derived within the Langevin framework and applied to a specific lattice Boltzmann model that approximates the linearized fluctuating Navier-Stokes equations for fluids based on square-gradient free energy functionals. The obtained thermal noise is shown to ensure equilibration of all degrees of freedom in a simulation to high accuracy. Furthermore, we demonstrate that satisfactory results for most practical applications of fluctuating hydrodynamics can already be achieved using thermal noise derived in the long wavelength-limit.Comment: 15 pages, 5 figure

Role of Metastable States in Phase Ordering Dynamics

We show that the rate of separation of two phases of different densities (e.g. gas and solid) can be radically altered by the presence of a metastable intermediate phase (e.g. liquid). Within a Cahn-Hilliard theory we study the growth in one dimension of a solid droplet from a supersaturated gas. A moving interface between solid and gas phases (say) can, for sufficient (transient) supersaturation, unbind into two interfaces separated by a slab of metastable liquid phase. We investigate the criteria for unbinding, and show that it may strongly impede the growth of the solid phase.Comment: 4 pages, Latex, Revtex, epsf. Updated two reference

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.

Colloidal Jamming at Interfaces: a Route to Fluid-bicontinuous Gels

Colloidal particles or nanoparticles, with equal affinity for two fluids, are known to adsorb irreversibly to the fluid-fluid interface. We present large-scale computer simulations of the demixing of a binary solvent containing such particles. The newly formed interface sequesters the colloidal particles; as the interface coarsens, the particles are forced into close contact by interfacial tension. Coarsening is dramatically curtailed, and the jammed colloidal layer seemingly enters a glassy state, creating a multiply connected, solid-like film in three dimensions. The resulting gel contains percolating domains of both fluids, with possible uses as, for example, a microreaction medium

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

Nonequilibrium steady states in sheared binary fluids

We simulate by lattice Boltzmann the steady shearing of a binary fluid mixture undergoing phase separation with full hydrodynamics in two dimensions. Contrary to some theoretical scenarios, a dynamical steady state is attained with finite domain lengths $L_{x,y}$ in the directions ($x,y)$ of velocity and velocity gradient. Apparent scaling exponents are estimated as $L_{x}\sim\dot{\gamma}^{-2/3}$ and $L_{y}\sim\dot{\gamma}^{-3/4}$. We discuss the relative roles of diffusivity and hydrodynamics in attaining steady state.Comment: 4 pages, 3 figure

Instability and spatiotemporal rheochaos in a shear-thickening fluid model

We model a shear-thickening fluid that combines a tendency to form inhomogeneous, shear-banded flows with a slow relaxational dynamics for fluid microstructure. The interplay between these factors gives rich dynamics, with periodic regimes (oscillating bands, travelling bands, and more complex oscillations) and spatiotemporal rheochaos. These phenomena, arising from constitutive nonlinearity not inertia, can occur even when the steady-state flow curve is monotonic. Our model also shows rheochaos in a low-dimensional truncation where sharply defined shear bands cannot form