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

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

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.

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

Atypical work and unemployment protection in Europe

This paper evaluates the degree of income protection the tax-benefit system provides to atypical workers in the event of unemployment. Our approach relies on simulating transitions from employment to unemployment for the entire workforce in EU member states to compare household financial circumstances before and after the transition. Our results show that coverage rates of unemployment insurance are low among atypical workers, who are also more exposed to the risk of poverty, both while in work and in unemployment. Low work intensity employees are characterized by high net replacement rates. However, this is due to the major role played by market incomes of other household members. Finally, we show that in countries where self-employed workers are not eligible for unemployment insurance benefits, extending the eligibility to this group of workers would increase their replacement rates and make them less likely to fall into poverty in the event of unemployment

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

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 $C(x,t)$ 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

Permeability of Microporous Carbon Preforms

The permeability of microporous amorphous carbon preforms with varying pore size and pore distributions has been experimentally examined. The porous structures have been characterized by mercury porosimetry and by quantitative metallography of pressure-infiltration-cast metal matrix composites based on the carbon preforms. The permeability shows a linear correlation with the fraction porosity and the square of the pore diameter

Permeability of self-affine rough fractures

The permeability of two-dimensional fractures with self-affine fractal roughness is studied via analytic arguments and numerical simulations. The limit where the roughness amplitude is small compared with average fracture aperture is analyzed by a perturbation method, while in the opposite case of narrow aperture, we use heuristic arguments based on lubrication theory. Numerical simulations, using the lattice Boltzmann method, are used to examine the complete range of aperture sizes, and confirm the analytic arguments.Comment: 11 pages, 9 figure