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Mode Reduction and Upscaling of Reactive Transport Under Incomplete Mixing

Abstract : Upscaling of chemical reactions in partially-mixed fluid environments is a challenging problem due to the detailed interactions between inherently nonlinear reaction kinetics and complex spatio-temporal concentration distributions under incomplete mixing. We address this challenge via the development of an order reduction method for the advection-diffusion-reaction equation (ADRE) via projection of the reaction kinetics onto a small number N of leading eigenmodes of the advection-diffusion operator (the so-called "strange eigenmodes" of the flow) as an N-by-N nonlinear system, whilst mixing dynamics only are projected onto the remaining modes. For simple kinetics and moderate Péclet and Damkhöler numbers, this approach yields analytic solutions for the concentration mean, evolving spatio-temporal distribution and PDF in terms of the well-mixed reaction kinetics and mixing dynamics. For more complex kinetics or large Péclet or Damkhöler numbers only a small number of modes are required to accurately quantify the mixing and reaction dynamics in terms of the concentration field and PDF, facilitating greatly simplified approximation and analysis of reactive transport. Approximate solutions of this low-order nonlinear system provide quantiative predictions of the evolving concentration PDF. We demonstrate application of this method to a simple random flow and various mass-action reaction kinetics.
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Contributor : Isabelle Dubigeon <>
Submitted on : Thursday, December 15, 2016 - 9:44:06 AM
Last modification on : Tuesday, December 10, 2019 - 1:44:03 PM


  • HAL Id : insu-01416923, version 1


Daniel Lester, Aditya Bandopadhyay, Marco Dentz, Tanguy Le Borgne. Mode Reduction and Upscaling of Reactive Transport Under Incomplete Mixing . American Geophysical Union Fall Meeting 2016, American Geophysical Union, Dec 2016, San Francisco, United States. pp.H43N-06. ⟨insu-01416923⟩



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