1,439 research outputs found
Rheological instability in a simple shear thickening model
We study the strain response to steady imposed stress in a spatially
homogeneous, scalar model for shear thickening, in which the local rate of
yielding \Gamma(l) of mesoscopic `elastic elements' is not monotonic in the
local strain l. Despite this, the macroscopic, steady-state flow curve (stress
vs. strain rate) is monotonic. However, for a broad class of \Gamma(l), the
response to steady stress is not in fact steady flow, but spontaneous
oscillation. We discuss this finding in relation to other theoretical and
experimental flow instabilities. Within the parameter ranges we studied, the
model does not exhibit rheo-chaos.Comment: 8 pages, 3 figs. Minor corrections made. To appear in Euro. Phys.
Let
Phase Separation in Binary Fluid Mixtures with Continuously Ramped Temperature
We consider the demixing of a binary fluid mixture, under gravity, which is
steadily driven into a two phase region by slowly ramping the temperature. We
assume, as a first approximation, that the system remains spatially isothermal,
and examine the interplay of two competing nonlinearities. One of these arises
because the supersaturation is greatest far from the meniscus, creating
inversion of the density which can lead to fluid motion; although isothermal,
this is somewhat like the Benard problem (a single-phase fluid heated from
below). The other is the intrinsic diffusive instability which results either
in nucleation or in spinodal decomposition at large supersaturations.
Experimental results on a simple binary mixture show interesting oscillations
in heat capacity and optical properties for a wide range of ramp parameters. We
argue that these oscillations arise under conditions where both nonlinearities
are important
Bulk rheology and microrheology of active fluids
We simulate macroscopic shear experiments in active nematics and compare them
with microrheology simulations where a spherical probe particle is dragged
through an active fluid. In both cases we define an effective viscosity: in the
case of bulk shear simulations this is the ratio between shear stress and shear
rate, whereas in the microrheology case it involves the ratio between the
friction coefficient and the particle size. We show that this effective
viscosity, rather than being solely a property of the active fluid, is affected
by the way chosen to measure it, and strongly depends on details such as the
anchoring conditions at the probe surface and on both the system size and the
size of the probe particle.Comment: 12 pages, 10 figure
Osmotic Pressure of Solutions Containing Flexible Polymers Subject to an Annealed Molecular Weight Distribution
The osmotic pressure in equilibrium polymers (EP) in good solvent is
investigated by means of a three dimensional off-lattice Monte Carlo
simulation. Our results compare well with real space renormalisation group
theory and the osmotic compressibility K \propto \phi \upd \phi/\upd P from
recent light scattering study of systems of long worm-like micelles. We confirm
the scaling predictions for EP based on traditional physics of quenched
monodisperse polymers in the dilute and semidilute limit. Specifically, we find
and, hence, in the semidilute
regime --- in agreement with both theory and experiment. At higher
concentrations where the semidilute blobs become too small and hard-core
interactions and packing effects become dominant, a much stronger increase %
\log(P/\phi)\approx \log(\Nav^2/\phi) \propto \phi is evidenced and,
consequently, the compressibility decreases much more rapidly with than
predicted from semidilute polymer theory, but again in agreement with
experiment.Comment: 7 pages, 4 figures, LATE
Colloidal templating at a cholesteric - oil interface: Assembly guided by an array of disclination lines
We simulate colloids (radius m) trapped at the interface between
a cholesteric liquid crystal and an immiscible oil, at which the helical order
(pitch p) in the bulk conflicts with the orientation induced at the interface,
stabilizing an ordered array of disclinations. For weak anchoring strength W of
the director field at the colloidal surface, this creates a template, favoring
particle positions eitheron top of or midway between defect lines, depending on
. For small , optical microscopy experiments confirm this
picture, but for larger no templating is seen. This may stem from the
emergence at moderate W of a rugged energy landscape associated with defect
reconnections.Comment: 5 pages, 4 figure
Strain versus stress in a model granular material: a Devil's staircase
The series of equilibrium states reached by disordered packings of rigid,
frictionless discs in two dimensions, under gradually varying stress, are
studied by numerical simulations. Statistical properties of trajectories in
configuration space are found to be independent of specific assumptions ruling
granular dynamics, and determined by geometry only. A monotonic increase in
some macroscopic loading parameter causes a discrete sequence of
rearrangements. For a biaxial compression, we show that, due to the statistical
importance of such events of large magnitudes, the dependence of the resulting
strain on stress direction is a Levy flight in the thermodynamic limit.Comment: REVTeX, 4 pages, 5 included PostScript figures. New version altered
throughout text, very close to published pape
Fluctuating lattice Boltzmann
The lattice Boltzmann algorithm efficiently simulates the Navier Stokes
equation of isothermal fluid flow, but ignores thermal fluctuations of the
fluid, important in mesoscopic flows. We show how to adapt the algorithm to
include noise, satisfying a fluctuation-dissipation theorem (FDT) directly at
lattice level: this gives correct fluctuations for mass and momentum densities,
and for stresses, at all wavevectors . Unlike previous work, which recovers
FDT only as , our algorithm offers full statistical mechanical
consistency in mesoscale simulations of, e.g., fluctuating colloidal
hydrodynamics.Comment: 7 pages, 3 figures, to appear in Europhysics Letter
Hawkes process as a model of social interactions: a view on video dynamics
We study by computer simulation the "Hawkes process" that was proposed in a
recent paper by Crane and Sornette (Proc. Nat. Acad. Sci. USA 105, 15649
(2008)) as a plausible model for the dynamics of YouTube video viewing numbers.
We test the claims made there that robust identification is possible for
classes of dynamic response following activity bursts. Our simulated timeseries
for the Hawkes process indeed fall into the different categories predicted by
Crane and Sornette. However the Hawkes process gives a much narrower spread of
decay exponents than the YouTube data, suggesting limits to the universality of
the Hawkes-based analysis.Comment: Added errors to parameter estimates and further description. IOP
style, 13 pages, 5 figure
A minimal model for chaotic shear banding in shear-thickening fluids
We present a minimal model for spatiotemporal oscillation and rheochaos in
shear-thickening complex fluids at zero Reynolds number. In the model, a
tendency towards inhomogeneous flows in the form of shear bands combines with a
slow structural dynamics, modelled by delayed stress relaxation. Using
Fourier-space numerics, we study the nonequilibrium `phase diagram' of the
fluid as a function of a steady mean (spatially averaged) stress, and of the
relaxation time for structural relaxation. We find several distinct regions of
periodic behavior (oscillating bands, travelling bands, and more complex
oscillations) and also regions of spatiotemporal rheochaos. A low-dimensional
truncation of the model retains the important physical features of the full
model (including rheochaos) despite the suppression of sharply defined
interfaces between shear bands. Our model maps onto the FitzHugh-Nagumo model
for neural network dynamics, with an unusual form of long-range coupling.Comment: Revised version (in particular, new section III.E. and Appendix A
Tensorial Constitutive Models for Disordered Foams, Dense Emulsions, and other Soft Nonergodic Materials
In recent years, the paradigm of `soft glassy matter' has been used to
describe diverse nonergodic materials exhibiting strong local disorder and slow
mesoscopic rearrangement. As so far formulated, however, the resulting `soft
glassy rheology' (SGR) model treats the shear stress in isolation, effectively
`scalarizing' the stress and strain rate tensors. Here we offer generalizations
of the SGR model that combine its nontrivial aging and yield properties with a
tensorial structure that can be specifically adapted, for example, to the
description of fluid film assemblies or disordered foams.Comment: 18 pages, 4 figure
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