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Concentration fluctuations in non-isothermal reaction-diffusion systems. II. The nonlinear case

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Bedeaux, D. and Ortiz de Zárate Leira, José María and Pagonabarraga, I. and Sengers, J. V. and Kjelstrup, S. (2011) Concentration fluctuations in non-isothermal reaction-diffusion systems. II. The nonlinear case. Journal of Chemical Physics, 135 (12). ISSN 0021-9606

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Official URL: http://dx.doi.org/10.1063/1.3640010


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Abstract

In this paper, we consider a simple reaction-diffusion system, namely, a binary fluid mixture with an association-dissociation reaction between two species. We study fluctuations at hydrodynamic spatiotemporal scales when this mixture is driven out of equilibrium by the presence of a temperature gradient, while still being far away from any chemical instability. This study extends the analysis in our first paper on the subject [J. M. Ortiz de Zarate, J. V. Sengers, D. Bedeaux, and S. Kjelstrup, J. Chem. Phys. 127, 034501 (2007)], where we considered fluctuations in a non-isothermal reaction-diffusion system but still close to equilibrium. The present extension is based on mesoscopic non-equilibrium thermodynamics that we recently developed [D. Bedeaux, I. Pagonabarraga, J. M. Ortiz de Zarate, J. V. Sengers, and S. Kjelstrup, Phys. Chem. Chem. Phys. 12, 12780 (2010)] to derive the law of mass action and fluctuation-dissipation theorems for the random contributions to the dissipative fluxes in the nonlinear macroscopic description. Just as for non-equilibrium fluctuations close to equilibrium, we again find an enhancement of the intensity of the concentration fluctuations in the presence of a temperature gradient. The non-equilibrium concentration fluctuations are in both cases spatially long ranged, with an intensity depending on the wave number q. The intensity exhibits a crossover from a proportional to q(-4) to a proportional to q(-2) behavior depending on whether the corresponding wavelength is smaller or larger than the penetration depth of the reacting mixture. This opens a possibility to distinguish between diffusion-or activation-controlled regimes of the reaction experimentally. The important conclusion overall is that non-equilibrium fluctuations in non-isothermal reaction-diffusion systems are always long ranged.


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© 2011 American Institute of Physics. J.V.S. and J.O.Z. acknowledge support from The Research Council of Norway, under Grant No. 167336/V30 "Transport on a nano-scale; at surfaces and contact lines." J.O.Z. acknowledges financial support from the Spanish Ministry of Science and Innovation (MICINN) through Grant No. FIS2008-03801. I. P. acknowledges financial support from MICINN through Grant No. FIS2008-04386, and from DURSI under Project No. SGR2009-634. I. P. and J.O.Z. further acknowledge joint support from MICINN under Grant No. FIS2008-04403-E.

Uncontrolled Keywords:Fluorescence correlation spectroscopy; Molecular-dynamics simulations; Chemical-reactions; Light-scattering; Temperature-gradient; Nonequilibrium fluctuations; Stochastic simulation; Rayleigh-scattering; Local equilibrium; Kinetics
Subjects:Sciences > Physics > Thermodynamics
ID Code:27281
Deposited On:17 Nov 2014 13:26
Last Modified:26 Feb 2015 15:45

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