# 32nd M. Smoluchowski Symposium on Statistical Physics

18-21 September 2019
Kraków
Europe/Warsaw timezone

## Cross-diffusion in concentrated reactive systems revealed by perturbation of FKPP wave front

19 Sep 2019, 12:40
20m
Kraków

Talk

### Speaker

Mr. Gabriel Morgado (Institute of Physical Chemistry - PAN / Sorbonne Universite)

### Description

The sensitivity to perturbations of the Fisher, Kolmogorov, Petrovskii, and Piskunov (FKPP) wave front is used to find a quantity revealing the perturbation of diffusion in a concentrated solution. We consider two chemical species A and B engaged in the reaction A + B $\rightarrow$ 2A. When A and B have different diffusivities $D_A$ and $D_B$, the deterministic dynamics includes cross-diffusion terms due to the deviation from the dilution limit [1].

The behaviors of the front speed, the shift between the concentration profiles of the two species, and the width of the reactive zone are investigated, both analytically and numerically. The analytic results are deduced from a perturbation approach in the limit of small diffusion terms with respect to reaction terms. The shift between the two profiles turns out to be a well-adapted criterion presenting noticeable variations with the deviation from the dilution limit in a wide range of parameter values. In particular, the difference between the shifts obtained in a dilute system and a concentrated system increases as $D_B$ differs from $D_A$, especially in the case $D_B>D_A$ [2].

[1] L. Signon, B. Nowakowski, and A. Lemarchand, Phys. Rev. E 93, 042402 (2016).
[2] G. Morgado, B. Nowakowski, and A. Lemarchand, Phys. Rev. E 99, 022205 (2019).

### Primary authors

Mr. Gabriel Morgado (Institute of Physical Chemistry - PAN / Sorbonne Universite) Dr. Annie Lemarchand (Sorbonne Universite - CNRS) Prof. Bogdan Nowakowski (Institute of Physical Chemistry - PAN)