1,619 research outputs found
Complete Chaotic Mixing in an Electro-osmotic Flow by Destabilization of Key Periodic Pathlines
The ability to generate complete, or almost complete, chaotic mixing is of
great interest in numerous applications, particularly for microfluidics. For
this purpose, we propose a strategy that allows us to quickly target the
parameter values at which complete mixing occurs. The technique is applied to a
time periodic, two-dimensional electro-osmotic flow with spatially and
temporally varying Helmoltz-Smoluchowski slip boundary conditions. The strategy
consists of following the linear stability of some key periodic pathlines in
parameter space (i.e., amplitude and frequency of the forcing), particularly
through the bifurcation points at which such pathlines become unstable.Comment: 14 pages, 11 figure
Transport and diffusion in the embedding map
We study the transport properties of passive inertial particles in a
incompressible flows. Here the particle dynamics is represented by the
dissipative embedding map of area-preserving standard map which models
the incompressible flow. The system is a model for impurity dynamics in a fluid
and is characterized by two parameters, the inertia parameter , and the
dissipation parameter . We obtain the statistical characterisers of
transport for this system in these dynamical regimes. These are, the recurrence
time statistics, the diffusion constant, and the distribution of jump lengths.
The recurrence time distribution shows a power law tail in the dynamical
regimes where there is preferential concentration of particles in sticky
regions of the phase space, and an exponential decay in mixing regimes. The
diffusion constant shows behaviour of three types - normal, subdiffusive and
superdiffusive, depending on the parameter regimes. Phase diagrams of the
system are constructed to differentiate different types of diffusion behaviour,
as well as the behaviour of the absolute drift. We correlate the dynamical
regimes seen for the system at different parameter values with the transport
properties observed at these regimes, and in the behaviour of the transients.
This system also shows the existence of a crisis and unstable dimension
variability at certain parameter values. The signature of the unstable
dimension variability is seen in the statistical characterisers of transport.
We discuss the implications of our results for realistic systems.Comment: 28 pages, 14 figures, To Appear in Phys. Rev. E; Vol. 79 (2009
Advection of vector fields by chaotic flows
We have introduced a new transfer operator for chaotic flows whose leading
eigenvalue yields the dynamo rate of the fast kinematic dynamo and applied
cycle expansion of the Fredholm determinant of the new operator to evaluation
of its spectrum. The theory hs been tested on a normal form model of the vector
advecting dynamical flow. If the model is a simple map with constant time
between two iterations, the dynamo rate is the same as the escape rate of
scalar quantties. However, a spread in Poincar\'e section return times lifts
the degeneracy of the vector and scalar advection rates, and leads to dynamo
rates that dominate over the scalar advection rates. For sufficiently large
time spreads we have even found repellers for which the magnetic field grows
exponentially, even though the scalar densities are decaying exponentially.Comment: 12 pages, Latex. Ask for figures from [email protected]
On the effectiveness of mixing in violent relaxation
Relaxation processes in collisionless dynamics lead to peculiar behavior in
systems with long-range interactions such as self-gravitating systems,
non-neutral plasmas and wave-particle systems. These systems, adequately
described by the Vlasov equation, present quasi-stationary states (QSS), i.e.
long lasting intermediate stages of the dynamics that occur after a short
significant evolution called "violent relaxation". The nature of the
relaxation, in the absence of collisions, is not yet fully understood. We
demonstrate in this article the occurrence of stretching and folding behavior
in numerical simulations of the Vlasov equation, providing a plausible
relaxation mechanism that brings the system from its initial condition into the
QSS regime. Area-preserving discrete-time maps with a mean-field coupling term
are found to display a similar behaviour in phase space as the Vlasov system.Comment: 10 pages, 11 figure
Targeted mixing in an array of alternating vortices
Transport and mixing properties of passive particles advected by an array of
vortices are investigated. Starting from the integrable case, it is shown that
a special class of perturbations allows one to preserve separatrices which act
as effective transport barriers, while triggering chaotic advection. In this
setting, mixing within the two dynamical barriers is enhanced while long range
transport is prevented. A numerical analysis of mixing properties depending on
parameter values is performed; regions for which optimal mixing is achieved are
proposed. Robustness of the targeted mixing properties regarding errors in the
applied perturbation are considered, as well as slip/no-slip boundary
conditions for the flow
Moving walls accelerate mixing
Mixing in viscous fluids is challenging, but chaotic advection in principle
allows efficient mixing. In the best possible scenario,the decay rate of the
concentration profile of a passive scalar should be exponential in time. In
practice, several authors have found that the no-slip boundary condition at the
walls of a vessel can slow down mixing considerably, turning an exponential
decay into a power law. This slowdown affects the whole mixing region, and not
just the vicinity of the wall. The reason is that when the chaotic mixing
region extends to the wall, a separatrix connects to it. The approach to the
wall along that separatrix is polynomial in time and dominates the long-time
decay. However, if the walls are moved or rotated, closed orbits appear,
separated from the central mixing region by a hyperbolic fixed point with a
homoclinic orbit. The long-time approach to the fixed point is exponential, so
an overall exponential decay is recovered, albeit with a thin unmixed region
near the wall.Comment: 17 pages, 13 figures. PDFLaTeX with RevTeX 4-1 styl
Phases saturation control on mixing driven reactions in 3D porous media
Transported chemical reactions in unsaturated porous media are relevant
across a range of environmental and industrial applications. Continuum scale
dispersive models are often based on equivalent parameters derived from analogy
with saturated conditions, and cannot appropriately account for processes such
as incomplete mixing. It is also unclear how the third dimension controls
mixing and reactions in unsaturated conditions. We obtain 3 experimental
images of the phases distribution and of transported chemical reaction by
Magnetic Resonance Imaging (MRI) using an immiscible non-wetting liquid as a
second phase and a fast irreversible bimolecular reaction. Keeping the P\'eclet
number (Pe) constant, we study the impact of phases saturation on the dynamics
of mixing and the reaction front. By measuring the local concentration of the
reaction product, we quantify temporally resolved effective reaction rate
(). We describe the temporal evolution of using the lamellar theory of
mixing, which explains faster than Fickian () rate of product
formation by accounting for the deformation of mixing interface between the two
reacting fluids. For a given Pe, although stretching and folding of the
reactive front are enhanced as saturation decreases, enhancing the product
formation, this is larger as saturation increases, i.e., volume controlled.
After breakthrough, the extinction of the reaction takes longer as saturation
decreases because of the larger non-mixed volume behind the front. These
results are the basis for a general model to better predict reactive transport
in unsaturated porous media not achievable by the current continuum paradigm
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