Dispersion in rectangular networks: effective diffusivity and large-deviation rate function

Alexandra Tzella, Jacques Vanneste

Research output: Contribution to journalLetterpeer-review

6 Citations (Scopus)
129 Downloads (Pure)


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 pages5
JournalPhysical Review Letters
Issue number11
Early online date7 Sept 2016
Publication statusPublished - 9 Sept 2016


Dive into the research topics of 'Dispersion in rectangular networks: effective diffusivity and large-deviation rate function'. Together they form a unique fingerprint.

Cite this