1,265 research outputs found
Interplay between a hydrodynamic instability and a phase transition: the Faraday instability in dispersions of rodlike colloids
Strong effects of the Faraday instability on suspensions of rodlike colloidal
particles are reported through measurements of the critical acceleration and of
the surface wave amplitude. We show that the transition to parametrically
excited surface waves displays discontinuous and hysteretic features. This
subcritical behaviour is attributed to the shear-thinning properties of our
colloidal suspensions thanks to a phenomenological model based on rheological
data under large amplitude oscillatory shear. Birefringence measurements
provide direct evidence that Faraday waves induce local nematic ordering of the
rodlike colloids. While local alignment simply follows the surface oscillations
for dilute, isotropic suspensions, permanent nematic patches are generated by
surface waves in samples close to the isotropic-to-nematic transition and above
the transition large domains align in the flow direction. This strong coupling
between the fluid microstructure and a hydrodynamic instability is confirmed by
numerical computations based on the microstructural response of rodlike viruses
in shear flow.Comment: 8 pages, 6 figure
Modeling transitional plane Couette flow
The Galerkin method is used to derive a realistic model of plane Couette flow
in terms of partial differential equations governing the space-time dependence
of the amplitude of a few cross-stream modes. Numerical simulations show that
it reproduces the globally sub-critical behavior typical of this flow. In
particular, the statistics of turbulent transients at decay from turbulent to
laminar flow displays striking similarities with experimental findings.Comment: 33 pages, 10 figure
Ergodicity Breaking in a Deterministic Dynamical System
The concept of weak ergodicity breaking is defined and studied in the context
of deterministic dynamics. We show that weak ergodicity breaking describes a
weakly chaotic dynamical system: a nonlinear map which generates subdiffusion
deterministically. In the non-ergodic phase non-trivial distribution of the
fraction of occupation times is obtained. The visitation fraction remains
uniform even in the non-ergodic phase. In this sense the non-ergodicity is
quantified, leading to a statistical mechanical description of the system even
though it is not ergodic.Comment: 11 pages, 4 figure
Pattern fluctuations in transitional plane Couette flow
In wide enough systems, plane Couette flow, the flow established between two
parallel plates translating in opposite directions, displays alternatively
turbulent and laminar oblique bands in a given range of Reynolds numbers R. We
show that in periodic domains that contain a few bands, for given values of R
and size, the orientation and the wavelength of this pattern can fluctuate in
time. A procedure is defined to detect well-oriented episodes and to determine
the statistics of their lifetimes. The latter turn out to be distributed
according to exponentially decreasing laws. This statistics is interpreted in
terms of an activated process described by a Langevin equation whose
deterministic part is a standard Landau model for two interacting complex
amplitudes whereas the noise arises from the turbulent background.Comment: 13 pages, 11 figures. Accepted for publication in Journal of
statistical physic
Signature of elasticity in the Faraday instability
We investigate the onset of the Faraday instability in a vertically vibrated
wormlike micelle solution. In this strongly viscoelastic fluid, the critical
acceleration and wavenumber are shown to present oscillations as a function of
driving frequency and fluid height. This effect, unseen neither in simple
fluids nor in previous experiments on polymeric fluids, is interpreted in terms
of standing elastic waves between the disturbed surface and the container
bottom. It is shown that the model of S. Kumar [Phys. Rev. E, {\bf 65}, 026305
(2002)] for a viscoelastic fluid accounts qualitatively for our experimental
observations. Explanations for quantitative discrepancies are proposed, such as
the influence of the nonlinear rheological behaviour of this complex fluid.Comment: 4 pages, 4 figure
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The air-liquid flow in a microfluidic airway tree
This paper was presented at the 2nd Micro and Nano Flows Conference (MNF2009), which was held at Brunel University, West London, UK. The conference was organised by Brunel University and supported by the Institution of Mechanical Engineers, IPEM, the Italian Union of Thermofluid dynamics, the Process Intensification Network, HEXAG - the Heat Exchange Action Group and the Institute of Mathematics and its Applications.Microfluidic techniques are employed to investigate air-liquid flows in the pulmonary airway tree. A network of microchannels with five generations is made and used as a simplified model of the pulmonary airway tree. Liquid plugs are injected into the network and pushed by air flow to divide at every bifurcation before reaching the exits. The resistance associated with the presence of one plug in a given generation is defined to establish a linear relation between the driving pressure and the total flow rate in the network. Based on this resistance, we have good predictions of the flow of two successive plugs in the network. For two-plug flows under the same driving pressure, the total flow rate depends not only on the lengths of the plugs but also the initial distance between the two. Strong long range interactions are found between daughter plugs, especially when they are flowing through the bifurcations. We also observe different flow patterns under different pushing conditions. Under a constant pressure forcing, the flow develops symmetrically while a constant flow rate push achieves an asymmetric flow.This study is funded by the ANR under the “Sante-Environnement et Sante-Travail” programme
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
Secondary Instabilities of Surface Waves on Viscous Fluids in the Faraday Instability
Secondary instabilities of Faraday waves show three regimes: (1) As seen
previously, low-viscosity (nu) fluids destabilize first into squares. At higher
driving accelerations a, squares show low-frequency modulations corresponding
to the motion of phase defects, while theory predicts a stationary transverse
amplitude modulation (TAM). (2) High-nu fluids destabilize first to stripes.
Stripes then show an oscillatory TAM whose frequency is incommensurate with the
driving frequency. At higher a, the TAM undergoes a phase instability. At still
higher a, edge dislocations form and fluid droplets are ejected. (3)
Intermediate-nu fluids show a complex coexistence of squares and stripes, as
well as stationary and oscillatory TAM instabilities of the stripes.Comment: REVTEX, with 3 separate uuencoded figures, to appear in Europhys.
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Chaotic versus stochastic behavior in active-dissipative nonlinear systems
We study the dynamical state of the one-dimensional noisy generalized Kuramoto-Sivashinsky (gKS) equation by making use of time-series techniques based on symbolic dynamics and complex networks. We focus on analyzing temporal signals of global measure in the spatiotemporal patterns as the dispersion parameter of the gKS equation and the strength of the noise are varied, observing that a rich variety of different regimes, from high-dimensional chaos to pure stochastic behavior, emerge. Permutation entropy, permutation spectrum, and network entropy allow us to fully classify the dynamical state exposed to additive noise
Grain boundary motion in layered phases
We study the motion of a grain boundary that separates two sets of mutually
perpendicular rolls in Rayleigh-B\'enard convection above onset. The problem is
treated either analytically from the corresponding amplitude equations, or
numerically by solving the Swift-Hohenberg equation. We find that if the rolls
are curved by a slow transversal modulation, a net translation of the boundary
follows. We show analytically that although this motion is a nonlinear effect,
it occurs in a time scale much shorter than that of the linear relaxation of
the curved rolls. The total distance traveled by the boundary scales as
, where is the reduced Rayleigh number. We obtain
analytical expressions for the relaxation rate of the modulation and for the
time dependent traveling velocity of the boundary, and especially their
dependence on wavenumber. The results agree well with direct numerical
solutions of the Swift-Hohenberg equation. We finally discuss the implications
of our results on the coarsening rate of an ensemble of differently oriented
domains in which grain boundary motion through curved rolls is the dominant
coarsening mechanism.Comment: 16 pages, 5 figure
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