Dispersion in Rectangular Networks: Effective Diffusivity and Large-Deviation Rate Function

Alexandra Tzella, Jacques Vanneste

Research output: Contribution to journalArticlepeer-review

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(t1/2) 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. Monte Carlo simulations of Brownian particles confirm the large-deviation results and demonstrate their effectiveness in describing the scalar distribution when t is only moderately large.
Original languageEnglish
Article number114501
Number of pages7
JournalPhysical Review Letters
Volume117
Issue number11
Early online date7 Sep 2016
DOIs
Publication statusPublished - 9 Sep 2016

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