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