385 research outputs found
Universal and Non-Universal First-Passage Properties of Planar Multipole Flows
The dynamics of passive Brownian tracer particles in steady two-dimensional
potential flows between sources and sinks is investigated. The first-passage
probability, , exhibits power-law decay with a velocity-dependent
exponent in radial flow and an order-dependent exponent in multipolar flows.
For the latter, there also occur diffusive ``echo'' shoulders and exponential
decays associated with stagnation points in the flow. For spatially extended
dipole sinks, the spatial distribution of the collected tracer is independent
of the overall magnitude of the flow field.Comment: 7 pages, LaTe
Gas Transport in Porous Media: Simulations and Experiments on Partially Densified Aerogels
The experimental density dependence of gas (argon and nitrogen) permeability
of partially densified silica aerogels in the Knudsen regime is quantitatively
accounted for by a computer model. The model simulates both the structure of
the sintered material and the random ballistic motion of a point particle
inside its voids. The same model is also able to account for the densit y
dependence of the specific pore surface as measured from nitrogen adsorption
experiments.Comment: RevTex, 11 pages + 5 postscript figures appended using "uufiles".
Published in Europhys. Lett. 29, p. 567 (1995
Cluster evolution in steady-state two-phase flow in porous media
We report numerical studies of the cluster development of two-phase flow in a
steady-state environment of porous media. This is done by including biperiodic
boundary conditions in a two-dimensional flow simulator. Initial transients of
wetting and non-wetting phases that evolve before steady-state has occurred,
undergo a cross-over where every initial patterns are broken up. For flow
dominated by capillary effects with capillary numbers in order of , we
find that around a critical saturation of non-wetting fluid the non-wetting
clusters of size have a power-law distribution with
the exponent for large clusters. This is a lower value
than the result for ordinary percolation. We also present scaling relation and
time evolution of the structure and global pressure.Comment: 12 pages, 11 figures. Minor corrections. Accepted for publication in
Phys. Rev.
Screening effects in flow through rough channels
A surprising similarity is found between the distribution of hydrodynamic
stress on the wall of an irregular channel and the distribution of flux from a
purely Laplacian field on the same geometry. This finding is a direct outcome
from numerical simulations of the Navier-Stokes equations for flow at low
Reynolds numbers in two-dimensional channels with rough walls presenting either
deterministic or random self-similar geometries. For high Reynolds numbers,
when inertial effects become relevant, the distribution of wall stresses on
deterministic and random fractal rough channels becomes substantially dependent
on the microscopic details of the walls geometry. In addition, we find that,
while the permeability of the random channel follows the usual decrease with
Reynolds, our results indicate an unexpected permeability increase for the
deterministic case, i.e., ``the rougher the better''. We show that this complex
behavior is closely related with the presence and relative intensity of
recirculation zones in the reentrant regions of the rough channel.Comment: 4 pages, 5 figure
Anomalous Scaling and Solitary Waves in Systems with Non-Linear Diffusion
We study a non-linear convective-diffusive equation, local in space and time,
which has its background in the dynamics of the thickness of a wetting film.
The presence of a non-linear diffusion predicts the existence of fronts as well
as shock fronts. Despite the absence of memory effects, solutions in the case
of pure non-linear diffusion exhibit an anomalous sub-diffusive scaling. Due to
a balance between non-linear diffusion and convection we, in particular, show
that solitary waves appear. For large times they merge into a single solitary
wave exhibiting a topological stability. Even though our results concern a
specific equation, numerical simulations supports the view that anomalous
diffusion and the solitary waves disclosed will be general features in such
non-linear convective-diffusive dynamics.Comment: Corrected typos, added 3 references and 2 figure
Invasion Percolation Between two Sites
We investigate the process of invasion percolation between two sites
(injection and extraction sites) separated by a distance r in two-dimensional
lattices of size L. Our results for the non-trapping invasion percolation model
indicate that the statistics of the mass of invaded clusters is significantly
dependent on the local occupation probability (pressure) Pe at the extraction
site. For Pe=0, we show that the mass distribution of invaded clusters P(M)
follows a power-law P(M) ~ M^{-\alpha} for intermediate values of the mass M,
with an exponent \alpha=1.39. When the local pressure is set to Pe=Pc, where Pc
corresponds to the site percolation threshold of the lattice topology, the
distribution P(M) still displays a scaling region, but with an exponent
\alpha=1.02. This last behavior is consistent with previous results for the
cluster statistics in standard percolation. In spite of these discrepancies,
the results of our simulations indicate that the fractal dimension of the
invaded cluster does not depends significantly on the local pressure Pe and it
is consistent with the fractal dimension values reported for standard invasion
percolation. Finally, we perform extensive numerical simulations to determine
the effect of the lattice borders on the statistics of the invaded clusters and
also to characterize the self-organized critical behavior of the invasion
percolation process.Comment: 7 pages, 11 figures, submited for PR
Demagnetization factor for a powder of randomly packed spherical particles
The demagnetization factors for randomly packed spherical particle powders
with different porosities, sample aspect ratios and monodisperse, normal and
log-normal particle size distributions have been calculated using a numerical
model. For a relative permeability of 2, comparable to room temperature Gd, the
calculated demagnetization factor is close to the theoretical value. The
normalized standard deviation of the magnetization in the powder was 6.0%-6.7%.
The demagnetization factor decreased significantly, while the standard
deviation of the magnetization increased, for increasing relative permeability.Comment: 4 pages, 4 figure
Non-Newtonian fluid flow through three-dimensional disordered porous media
We investigate the flow of various non-Newtonian fluids through
three-dimensional disordered porous media by direct numerical simulation of
momentum transport and continuity equations. Remarkably, our results for
power-law (PL) fluids indicate that the flow, when quantified in terms of a
properly modified permeability-like index and Reynolds number, can be
successfully described by a single (universal) curve over a broad range of
Reynolds conditions and power-law exponents. We also study the flow behavior of
Bingham fluids described in terms of the Herschel-Bulkley model. In this case,
our simulations reveal that the interplay of ({\it i}) the disordered geometry
of the pore space, ({\it ii}) the fluid rheological properties, and ({\it iii})
the inertial effects on the flow is responsible for a substantial enhancement
of the macroscopic hydraulic conductance of the system at intermediate Reynolds
conditions. This anomalous condition of ``enhanced transport'' represents a
novel feature for flow in porous materials.Comment: 5 pages, 5 figures. This article appears also in Physical Review
Letters 103 194502 (2009
First Passage Time in a Two-Layer System
As a first step in the first passage problem for passive tracer in stratified
porous media, we consider the case of a two-dimensional system consisting of
two layers with different convection velocities. Using a lattice generating
function formalism and a variety of analytic and numerical techniques, we
calculate the asymptotic behavior of the first passage time probability
distribution. We show analytically that the asymptotic distribution is a simple
exponential in time for any choice of the velocities. The decay constant is
given in terms of the largest eigenvalue of an operator related to a half-space
Green's function. For the anti-symmetric case of opposite velocities in the
layers, we show that the decay constant for system length crosses over from
behavior in diffusive limit to behavior in the convective
regime, where the crossover length is given in terms of the velocities.
We also have formulated a general self-consistency relation, from which we have
developed a recursive approach which is useful for studying the short time
behavior.Comment: LaTeX, 28 pages, 7 figures not include
Dispersion enhancement and damping by buoyancy driven flows in 2D networks of capillaries
The influence of a small relative density difference on the displacement of
two miscible liquids is studied experimentally in transparent 2D networks of
micro channels. Both stable displacements in which the denser fluid enters at
the bottom of the cell and displaces the lighter one and unstable displacements
in which the lighter fluid is injected at the bottom and displaces the denser
one are realized. Except at the lowest mean flow velocity U, the average
of the relative concentration satisfies a convection-dispersion
equation. The dispersion coefficient is studied as function of the relative
magnitude of fluid velocity and of the velocity of buoyancy driven fluid
motion. A model is suggested and its applicability to previous results obtained
in 3D media is discussed
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