265 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, $p(t)$, 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

### 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 $10^{-5}$, we
find that around a critical saturation of non-wetting fluid the non-wetting
clusters of size $s$ have a power-law distribution $n_s \sim s^{-\tau}$ with
the exponent $\tau = 1.92 \pm 0.04$ 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

### 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

### 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

### 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 $L$ crosses over from
$L^{-2}$ behavior in diffusive limit to $L^{-1}$ behavior in the convective
regime, where the crossover length $L^*$ 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

### Pore scale mixing and macroscopic solute dispersion regimes in polymer flows inside 2D model networks

A change of solute dispersion regime with the flow velocity has been studied both at the macroscopic and pore scales in a transparent array of capillary channels using an optical technique allowing for simultaneous local and global concentration mappings. Two solutions of different polymer concentrations (500 and 1000 ppm) have been used at different P\'eclet numbers. At the macroscopic scale, the displacement front displays a diffusive spreading: for $Pe \leq 10$, the dispersivity $l\_d$ is constant with $Pe$ and increases with the polymer concentration; for $Pe > 10$, $l\_d$ increases as $Pe^{1.35}$ and is similar for the two concentrations. At the local scale, a time lag between the saturations of channels parallel and perpendicular to the mean flow has been observed and studied as a function of the flow rate. These local measurements suggest that the change of dispersion regime is related to variations of the degree of mixing at the junctions. For $Pe \leq 10$, complete mixing leads to pure geometrical dispersion enhanced for shear thinning fluids; for $Pe >10$ weaker mixing results in higher correlation lengths along flow paths parallel to the mean flow and in a combination of geometrical and Taylor dispersion

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