Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 0806.2972

Diffusive transport of light in a two-dimensional disordered packing of disks: Analytical approach to transport-mean-free path

Zeinab Sadjadi·MirFaez Miri·M. Reza Shaebani·Sareh Nakhaee
View original source ↗Read source document ↗Export metadata ↓

Abstract

We study photon diffusion in a two-dimensional random packing of monodisperse disks as a simple model of granular media and wet foams. We assume that the intensity reflectance of disks is a constant. We present an analytic expression for the transport-mean-free path in terms of the velocity of light in the disks and host medium, radius and packing fraction of the disks, and the intensity reflectance. For the glass beads immersed in the air or water, we estimate transport-mean-free paths about half the experimental ones. For the air bubbles immersed in the water, transport-mean-free paths is an inverse function of liquid volume fraction of the model wet foam. This throws new light on the empirical law of Vera et. al, and promotes more realistic models.

Explore related subjects

cond-mat.softcond-mat.stat-mech

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Zeinab Sadjadi, MirFaez Miri, M. Reza Shaebani, Sareh Nakhaee. 2008-09-20. Diffusive transport of light in a two-dimensional disordered packing of disks: Analytical approach to transport-mean-free path. https://doi.org/10.1103/physreve.78.031121

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Speed up of passive tracers in mixtures with active chemical reactions

Diffusivity of passive tracers in complex mixtures is widely relevant for industrial applications and for probing biological systems. Interactions with the surrounding medium typically generate a drag force that suppresses tracer diffusion, although self-propulsion can accelerate tracers via active fluctuations. Similar effects are not understood in mixtures with particle conversion and exchange, although these are particularly relevant in biological contexts, where actively driven reactions prevail. By studying a thermodynamically consistent model of chemical reactions in mixtures, we show that reactions provide an additional relaxation pathway that suppresses interaction-induced memory, reducing the drag on tracers and restoring their diffusivity toward the value expected in the absence of solutes. Moreover, active reactions generate nonequilibrium fluctuations that can push tracer diffusivity beyond this limit, an effect we confirm with particle-based simulations. Our results identify chemical activity as a distinct route to controlling mass transport and offer a framework for interpreting microrheology experiments in chemically active mixtures.

cond-mat.soft↗
arXiv2026

Diffusion of charged rods across 3D varying section channels

We analyze the transport of rod-like particles by diffusion and drift in a three-dimensional channel with varying circular or elliptic cross section. Applying the Fick-Jacobs approximation to the transport equation of the particles' probability distribution, we derive an effective one-dimensional substitute model and the associated free energy profile. Our results show that the data for the mean first passage time of rods, once expressed as a function of the effective free energy barrier, collapse onto the same master curve as obtained for point or spherical particles. The observed universality provides a simple framework for predicting transport times of anisotropic particles in confined geometries without resolving the full multidimensional dynamics.

cond-mat.soft↗
arXiv2026

Reciprocal theorem for ion-releasing colloidal particles

We describe a generalization of the reciprocal theorem for particles suspended in electrolyte solutions and subjected to an electric field that could be either applied or emerged spontaneously. Attention is focused on catalytic colloids that release ions. The power of the generalization is to capture the effect of formation of a secondary cloud around a catalytic particle, which is equivalent to accounting for an excess charge $Q$ of a system. Our results show that the propulsion speed of catalytic particles has an extra contribution proportional to $Q$ and an external field $E_{\infty}$. The derived equation for $Q$ reveals that its sign is defined by the difference in the ion diffusivity and the magnitude is controlled by the average flux of ions from the surface. We demonstrate the application of the generalized theorem to electro- and diffusiophoresis of homogeneously releasing ions passive particles, as well as to a self-propulsion of inhomogeneous active particles (microswimmers). It is shown that whilst in some situations the extra term in the reciprocal theorem vanishes or has a little effect on the particle mobility, in many others it may dramatically change its magnitude, and even sign. In addition, the relevance of our results for microswimmer interactions is discussed briefly.

cond-mat.soft↗