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Fast chemical reaction in two-dimensional Navier-Stokes flow: Initial regime

Ait-Chaalal, Farid and Bourqui, Michel S. and Bartello, Peter (2012) Fast chemical reaction in two-dimensional Navier-Stokes flow: Initial regime. Physical Review E, 85 (4). Art. No. 046306. ISSN 1539-3755. doi:10.1103/PhysRevE.85.046306.

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This paper studies an infinitely fast bimolecular chemical reaction in a two-dimensional biperiodic Navier-Stokes flow. The reactants in stoichiometric quantities are initially segregated by infinite gradients. The focus is placed on the initial stage of the reaction characterized by a well-defined one-dimensional material contact line between the reactants. Particular attention is given to the effect of the diffusion κ of the reactants. This study is an idealized framework for isentropic mixing in the lower stratosphere and is motivated by the need to better understand the effect of resolution on stratospheric chemistry in climate-chemistry models. Adopting a Lagrangian straining theory approach, we relate theoretically the ensemble mean of the length of the contact line, of the gradients along it, and of the modulus of the time derivative of the space-average reactant concentrations (here called the chemical speed) to the joint probability density function of the finite-time Lyapunov exponent λ with two times τ and τ̃. The time 1/λ measures the stretching time scale of a Lagrangian parcel on a chaotic orbit up to a finite time t, while τ measures it in the recent past before t, and τ̃ in the early part of the trajectory. We show that the chemical speed scales like κ^(1/2) and that its time evolution is determined by rare large events in the finite-time Lyapunov exponent distribution. The case of smooth initial gradients is also discussed. The theoretical results are tested with an ensemble of direct numerical simulations (DNSs) using a pseudospectral model.

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Additional Information:© 2012 American Physical Society. Received 6 June 2011; revised manuscript received 10 December 2011; published 11 April 2012. This research was supported by the Natural Sciences and Engineering Research Council of Canada (NSERC). We thank the anonymous reviewer who contributed very significantly to improve the theoretical development of Sec. IIB.
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Natural Sciences and Engineering Research Council of Canada (NSERC)UNSPECIFIED
Issue or Number:4
Classification Code:PACS: 47.52.+j, 47.70.Fw, 05.45.-a, 92.60.hd
Record Number:CaltechAUTHORS:20120507-110252505
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:31328
Deposited By: Tony Diaz
Deposited On:08 May 2012 18:29
Last Modified:09 Nov 2021 19:51

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