2,587 research outputs found
Non-Equilibrium relation between mobility and diffusivity of interacting Brownian particles under shear
We investigate the relation between mobility and diffusivity for Brownian
particles under steady shear near the glass transition, using mode coupling
approximations. For the two directions perpendicular to the shear direction,
the particle motion is diffusive at long times and the mobility reaches a
finite constant. Nevertheless, the Einstein relation holds only for the
short-time in-cage motion and is violated for long times. In order to get the
relation between diffusivity and mobility, we perform the limit of small
wavevector for the relations derived previously [Phys. Rev. Lett. 102 (2009),
135701], without further approximation. We find good agreement to simulation
results. Furthermore, we split the extra term in the mobility in an exact way
into three terms. Two of them are expressed in terms of mean squared
displacements. The third is given in terms of the (less handy) force-force
correlation function.Comment: 14 pages, 4 figures, accepted for Prog. Theor. Phys. Suppl., issue
for the workshop "Frontiers in Nonequilibrium Physics", Kyoto, 200
Nonlinear rheology of dense colloidal dispersions: a phenomenological model and its connection to mode coupling theory
Rheological properties, especially 'shear-thinning', of dense colloidal
dispersions are discussed on three different levels. A generalized
phenomonological Maxwell model gives a broad framework connecting glassy
dynamics to the linear and non-linear rheology of dense amorphous particle
solutions. First principles mode coupling theory calculations for the time or
frequency dependent shear modulus give quantitative results for dispersions of
hard colloidal spheres in the linear regime. Schematic models extending mode
coupling theory to the non-linear regime recover the phenomenology of the
generalized Maxwell model, and predict universal features of flow curves,
stress versus shear-rate.Comment: 7 pages, 6 figures; to be published in the proceedings of the 18th
ECIS Conference, Almeria, Spain Sept. 19-24, 2004; special issue of 'Colloids
and Surfaces A: Physicochemical and Engineering Aspects
Nonlinear rheological properties of dense colloidal dispersions close to a glass transition under steady shear
The nonlinear rheological properties of dense colloidal suspensions under
steady shear are discussed within a first principles approach. It starts from
the Smoluchowski equation of interacting Brownian particles in a given shear
flow, derives generalized Green-Kubo relations, which contain the transients
dynamics formally exactly, and closes the equations using mode coupling
approximations. 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. The
integration through transients approach takes account of the dynamic
competition, translational invariance enters the concept of wavevector
advection, and the mode coupling approximation enables to quantitatively
explore the shear-induced suppression of particle caging and the resulting
speed-up of the structural relaxation. Extended comparisons with shear stress
data in the linear response and in the nonlinear regime measured in model
thermo-sensitive core-shell latices are discussed. Additionally, the single
particle motion under shear observed by confocal microscopy and in computer
simulations is reviewed and analysed theoretically.Comment: Review submited to special volume 'High Solid Dispersions' ed. M.
Cloitre, Vol. xx of 'Advances and Polymer Science' (Springer, Berlin, 2009);
some figures slightly cu
Elastic properties of colloidal solids with disorder
Recent progress in approaches to determine the elastic constants of solids
starting from the microscopic particle interactions is reviewed. On the
theoretical side, density functional theory approaches are discussed and
compared to more classical ones using the actual pair potentials. On the
experimental side, video microscopy has been introduced to measure the elastic
constants in colloidal solids. For glasses and disordered systems, the
theoretical basis is given for this novel technique, and some challenges and
recent advances are reviewed.Comment: Lecture notes of a seminar at the International School on Physics
'Enrico Fermi': Physics of Complex Colloids, Varenna, Italy, July 3-13 2012;
to be included in the Proceedings of Course CLXXXIV; version 2 with small
addition
Structural Relaxations in a Simple Model Molten Salt
The structural relaxations of a dense, binary mixture of charged hard spheres
are studied using the Mode Coupling Theory (MCT). Qualitative differences to
non--ionic systems are shown to result from the long--range Coulomb interaction
and charge ordering in dense molten salts. The presented non--equilibrium
results are determined by the equilibrium structure, which is input using the
well studied Mean Spherical Approximation.Comment: 6 pages, 4 Postscript figures, uses epsfig.sty, rotate.sty, here.st
Shear-thinning in dense colloidal suspensions and its effect on elastic instabilities: from the microscopic equations of motion to an approximation of the macroscopic rheology
In the vicinity of their glass transition, dense colloidal suspensions
acquire elastic properties over experimental timescales. We investigate the
possibility of a visco-elastic flow instability in curved geometry for such
materials. To this end, we first present a general strategy extending a
first-principles approach based on projections onto slow variables (so far
restricted to strictly homogeneous flow) in order to handle inhomogeneities. In
particular, we separate the advection of the microstructure by the flow, at the
origin of a fluctuation advection term, from the intrinsic dynamics. On account
of the complexity of the involved equations, we then opt for a drastic
simplification of the theory, in order to establish its potential to describe
instabilities. These very strong approximations lead to a constitutive equation
of the White-Metzner class, whose parameters are fitted with experimental
measurements of the macroscopic rheology of a glass-forming colloidal
dispersion. The model properly accounts for the shear-thinning properties of
the dispersions, but, owing to the approximations, the description is not fully
quantitative. Finally, we perform a linear stability analysis of the flow in
the experimentally relevant cylindrical (Taylor-Couette) geometry and provide
evidence that shear-thinning strongly stabilises the flow, which can explain
why visco-elastic instabilities are not observed in dense colloidal
suspensions
Nonlinear microrheology of dense colloidal suspensions: a mode-coupling theory
A mode-coupling theory for the motion of a strongly forced probe particle in
a dense colloidal suspension is presented. Starting point is the Smoluchowski
equation for bath and a single probe particle. The probe performs Brownian
motion under the influence of a strong constant and uniform external force
\Fex. It is immersed in a dense homogeneous bath of (different) particles
also performing Brownian motion. Fluid and glass states are considered; solvent
flow effects are neglected. Based on a formally exact generalized Green-Kubo
relation, mode coupling approximations are performed and an integration through
transients approach applied. A first-principles theory for the nonlinear
velocity-force relations of the probe particle in a dense fluid and for the
(de-) localized probe in a glass is obtained.
It extends the mode coupling theory of the glass transition to strongly
forced tracer motion and describes active microrheology experiments. A force
threshold is identified which needs to be overcome to pull the probe particle
free in a glass. For the model of hard sphere particles, the microscopic
equations for the threshold force and the probability density of the localized
probe are solved numerically. Neglecting the spatial structure of the theory, a
schematic model is derived which contains two types of bifurcation, the glass
transition and the force-induced delocalization, and which allows for
analytical and numerical solutions. We discuss its phase diagram, forcing
effects on the time-dependent correlation functions, and the friction
increment. The model was successfully applied to simulations and experiments on
colloidal hard sphere systems [I. Gazuz et. al., Phys. Rev. Lett. 102, 248302
(2009)], while we provide detailed information on its derivation and general
properties.Comment: 24 pages, 14 figure
Viscoelasticity and shear flow of concentrated, non-crystallizing colloidal suspensions: Comparison with Mode-Coupling Theory
We present a comprehensive rheological study of a suspension of
thermosensitive particles dispersed in water. The volume fraction of these
particles can be adjusted by the temperature of the system in a continuous
fashion. Due to the finite polydispersity of the particles (standard deviation:
17%), crystallization is suppressed and no fluid-crystal transition intervenes.
Hence, the moduli and in the linear viscoelastic regime as well as
the flow curves (shear stress as the function of the
shear rate ) could be measured in the fluid region up to the
vicinity of the glass transition. Moreover, flow curves could be obtained over
a range of shear rates of 8 orders of magnitude while and could be
measured spanning over 9 orders of magnitude. Special emphasis has been laid on
precise measurements down to the smallest shear rates/frequencies. It is
demonstrated that mode-coupling theory generalized in the integration through
transients framework provides a full description of the flow curves as well as
the viscoelastic behavior of concentrated suspensions with a single set of
well-defined parameters
Polymer-Mode-Coupling Theory of Finite-Size-Fluctuation Effects in Entangled Solutions, Melts and Gels. I. General Formulation and Predictions
The transport coefficients of dense polymeric fluids are approximately
calculated from the microscopic intermolecular forces. The following finite
molecular weight effects are discussed within the Polymer-Mode-Coupling theory
(PMC) and compared to the corresponding reptation/ tube ideas: constraint
release mechanism, spatial inhomogeneity of the entanglement constraints, and
tracer polymer shape fluctuations. The entanglement corrections to the single
polymer Rouse dynamics are shown to depend on molecular weight via the ratio
N/N_e, where the entanglement degree of polymerization, N_e, can be measured
from the plateau shear modulus. Two microscopically defined non-universal
parameters, an entanglement strength 1/alpha and a length scale ratio, delta=
xi_rho/b, where xi_rho and b are the density screening and entanglement length
respectively, are shown to determine the reduction of the entanglement effects
relative to the reptation- -like asymptotes of PMC theory. Large finite size
effects are predicted for reduced degrees of polymerization up to N/N_e\le10^3.
Effective power law variations for intermediate N/N_e of the viscosity, eta\sim
N^x, and the diffusion constant, D\sim N^{-y}, can be explained with exponents
significantly exceeding the asymptotic, reptation-like values, x\ge 3 and
y\ge2, respectively. Extensions of the theory to treat tracer dielectric
relaxation, and polymer transport in gels and other amorphous systems, are also
presented.Comment: Latex, figures and styles files included; Macromolecules, in press
(1997
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