224 research outputs found
Schematic models for dynamic yielding of sheared colloidal glasses
The nonlinear rheological properties of dense suspensions are discussed
within simplified models, suggested by a recent first principles approach to
the model of Brownian particles in a constant-velocity-gradient solvent flow.
Shear thinning of colloidal fluids and dynamical yielding of colloidal glasses
arise from a competition between a slowing down of structural relaxation,
because of particle interactions, and enhanced decorrelation of fluctuations,
caused by the shear advection of density fluctuations. A mode coupling approach
is developed to explore the shear-induced suppression of particle caging and
the resulting speed-up of the structural relaxation.Comment: 33 pages, 10 figures; accepted for publication in Faraday Disc. 123
(2002); small numerical correction
Aging in attraction-driven colloidal glasses
Aging in an attraction-driven colloidal glass is studied by computer
simulations. The system is equilibrated without attraction and instantaneously
``quenched'', at constant colloid volume fraction, to one of two states beyond
the glass transition; one is close to the transition, and the other one deep in
the glass. The evolution of structural properties shows that bonds form in the
system, increasing the local density, creating density deficits (holes)
elsewhere. This process slows down with the time elapsed since the quench. As a
consequence of bond formation, there is a slowing down of the dynamics, as
measured by the mean squared displacement and the density, bond, and
environment correlation functions. The density correlations can be
time-rescaled to collapse their long time (structural) decay. The time scale
for structural relaxation shows for both quenches a super-linear dependence on
waiting time; it grows faster than the bond lifetime, showing the collective
origin of the transition. At long waiting times and high attraction strength,
we observe {\rem completely} arrested dynamics for more than three decades in
time, although individual bonds are not permanent on this time scale. The
localization length decreases as the state moves deeper in the glass; the
non-ergodicity parameter oscillates in phase with the structure factor. Our
main results are obtained for systems with a barrier in the pair potential that
inhibits phase separation. However, when this barrier is removed for the case
of a deep quench, we find changes in the static structure but almost none in
the dynamics. Hence our results for the aging behavior remain relevant to
experiments in which the glass transition competes with phase separation.Comment: 12 pages, 15 figure
Moment free energies for polydisperse systems
A polydisperse system contains particles with at least one attribute
(such as particle size in colloids or chain length in polymers) which takes
values in a continuous range. It therefore has an infinite number of conserved
densities, described by a density {\em distribution} . The free
energy depends on all details of , making the analysis of phase
equilibria in such systems intractable. However, in many (especially
mean-field) models the {\em excess} free energy only depends on a finite number
of (generalized) moments of ; we call these models truncatable.
We show, for these models, how to derive approximate expressions for the {\em
total} free energy which only depend on such moment densities. Our treatment
unifies and explores in detail two recent separate proposals by the authors for
the construction of such moment free energies. We show that even though the
moment free energy only depends on a finite number of density variables, it
gives the same spinodals and critical points as the original free energy and
also correctly locates the onset of phase coexistence. Results from the moment
free energy for the coexistence of two or more phases occupying comparable
volumes are only approximate, but can be refined arbitrarily by retaining
additional moment densities. Applications to Flory-Huggins theory for
length-polydisperse homopolymers, and for chemically polydisperse copolymers,
show that the moment free energy approach is computationally robust and gives
new geometrical insights into the thermodynamics of polydispersity.Comment: RevTeX, 43 pages including figure
Mode Coupling and Dynamical Heterogeneity in Colloidal Gelation: A Simulation Study
We present simulation results addressing the dynamics of a colloidal system
with attractive interactions close to gelation. Our interaction also has a
soft, long range repulsive barrier which suppresses liquid-gas type phase
separation at long wavelengths. The new results presented here lend further
weight to an intriguing picture emerging from our previous simulation work on
the same system. Whereas mode coupling theory (MCT) offers quantitatively good
results for the decay of correlators, closer inspection of the dynamics reveals
a bimodal population of fast and slow particles with a very long exchange
timescale. This population split represents a particular form of dynamic
heterogeneity (DH). Although DH is usually associated with activated hopping
and/or facilitated dynamics in glasses, the form of DH observed here may be
more collective in character and associated with static (i.e., structural)
heterogeneity.Comment: 12 pages, 12 figure
Age-dependent transient shear banding in soft glasses
We study numerically the formation of long-lived transient shear bands during
shear startup within two models of soft glasses (a simple fluidity model and an
adapted `soft glassy rheology' model). The degree and duration of banding
depends strongly on the applied shear rate, and on sample age before shearing.
In both models the ultimate steady flow state is homogeneous at all shear
rates, consistent with the underlying constitutive curve being monotonic.
However, particularly in the SGR case, the transient bands can be extremely
long lived. The banding instability is neither `purely viscous' nor `purely
elastic' in origin, but is closely associated with stress overshoot in startup
flow.Comment: 4 pages, 3 figure
Field-Induced Breakup of Emulsion Droplets Stabilized by Colloidal Particles
We simulate the response of a particle-stabilized emulsion droplet in an
external force field, such as gravity, acting equally on all particles. We
show that the field strength required for breakup (at fixed initial area
fraction) decreases markedly with droplet size, because the forces act
cumulatively, not individually, to detach the interfacial particles. The
breakup mode involves the collective destabilization of a solidified particle
raft occupying the lower part of the droplet, leading to a critical force per
particle that scales approximately as .Comment: 4 pages, plus 3 pages of supplementary materia
Absorbing-State Transitions in Granular Materials Close to Jamming.
We consider a model for driven particulate matter in which absorbing states can be reached both by particle isolation and by particle caging. The model predicts a nonequilibrium phase diagram in which analogs of hydrodynamic and elastic reversibility emerge at low and high volume fractions respectively, partially separated by a diffusive, nonabsorbing region. We thus find a single phase boundary that spans the onset of chaos in sheared suspensions to the onset of yielding in jammed packings. This boundary has the properties of a nonequilibrium second order phase transition, leading us to write a Manna-like mean field description that captures the model predictions. Dependent on contact details, jamming marks either a direct transition between the two absorbing states, or occurs within the diffusive region.ERC, Royal Society, Pembroke Colleg
Thermodynamic Interpretation of Soft Glassy Rheology Models
Mesoscopic models play an important role in our understanding of the
deformation and flow of amorphous materials. One such description, based on the
Shear Transformation Zone (STZ) theory, has recently been re-formulated within
a non-equilibrium thermodynamics framework, and found to be consistent with it.
We show here that a similar interpretation can be made for the Soft Glassy
Rheology (SGR) model. Conceptually this means that the "noise temperature" x,
proposed phenomenologically in the SGR model to control the dynamics of a set
of slow mesoscopic degrees of freedom, can consistently be interpreted as their
actual thermodynamic temperature. (Because such modes are slow to equilibrate,
this generally does not coincide with the temperature of the fast degrees of
freedom and/or heat bath.) If one chooses to make this interpretation, the
thermodynamic framework significantly constrains extensions of the SGR approach
to models in which x is a dynamical variable. We assess in this light some such
extensions recently proposed in the context of shear banding.Comment: 8 page
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