Particle transport and flow in irregular structures
Abstract Book of the XXIII IUPAP International Conference on Statistical Physics, Genova, Italy, (9-13 July 2007)

Filters are used in chimneys, water purification, cigarettes and many other everyday situations. The mass of the particles one wants to capture crucially determines the efficiency of the filtering. In the first part of this talk, we use analytical and numerical calculations to present a very rich scenario of scaling laws relating this efficiency to particle size and density, and the velocity and viscosity of the carrying fluid. These are combined in the dimensionless, so called Stokes number $St$. In the case of horizontal flow or neutrally buoyant particles we find a critical number $St_c$ below which no particles are trapped, i.e. the filter does not work. Above $St_c$ the capture efficiency increases like the square root of $St-St_c$. Under the action of gravity, the threshold abruptly vanishes and capture occurs at any Stokes number increasing linearly in $St$. We discovered further scaling laws in the entire penetration profile and as function of the porosity of the filter. In the second part of the talk, we reveal a surprising similarity 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, the distribution of wall stresses on deterministic and random fractal rough channels becomes substantially dependent on the microscopic details of the walls geometry. While the permeability of the random channel follows the usual decrease with Reynolds, our results indicate an unexpected permeability increase for the deterministic case.
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