Abstract
The dispersion of a diffusive scalar in a fluid flowing through a network has many applications including to biological flows, porous media, water supply, and urban pollution. Motivated by this, we develop a large-deviation theory that predicts the evolution of the concentration of a scalar released in a rectangular network in the limit of large time t≫1. This theory provides an approximation for the concentration that remains valid for large distances from the center of mass, specifically for distances up to O(t) and thus much beyond the O(t^{1/2}) range where a standard Gaussian approximation holds. A byproduct of the approach is a closed-form expression for the effective diffusivity tensor that governs this Gaussian approximation. MonteCarlo simulations of Brownian particles confirm the large-deviation results and demonstrate their effectiveness in describing the scalar distribution when t is only moderately large.
Highlights
The dispersion of a diffusive scalar in a fluid flowing through a network has many applications including to biological flows, porous media, water supply, and urban pollution
We develop a largedeviation theory that predicts the evolution of the concentration of a scalar released in a rectangular network in the limit of large time t ≫ 1
In this Letter, we investigate the dispersion of a diffusive scalar released in a fluid flowing through a rectangular network
Summary
In this Letter, we investigate the dispersion of a diffusive scalar released in a fluid flowing through a rectangular network (see Fig. 1). Dispersion in Rectangular Networks: Effective Diffusivity and Large-Deviation Rate Function
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