We study the reactive displacement of two miscible fluids in channel flows and establish a quantitative link between fluid stretching and chemical reactivity. At the mixing interface, the two fluids react according to the instantaneous irreversible bimolecular reaction. We simulate the advection-diffusion-reaction problem using a random walk based reactive particle method that is free of numerical dispersion. The relative contributions of stretching and diffusion to mixing-limited reaction is controlled by changing the Péclet number, and the channel roughness is also systematically varied. We observe optimal ranges of fluid stretching that maximize reactivity, which are captured by a Lagrangian stretching measure based on an effective time period that honours the stretching history. We show that the optimality originates from the competition between the enhanced mixing by fluid stretching and the mass depletion of the reactants. We analytically derive the spatial distribution of reaction products using a lamellar formulation and successfully predict the optimal ranges of fluid stretching, which are consistent across different levels of channel roughness. These findings provide a mechanistic understanding of how the interplay between fluid stretching, diffusion and channel roughness controls mixing-limited reactions in rough channel flows, and show how reaction hot spots can be predicted from the concept of optimal fluid stretching.
Bibliographical noteFunding Information:
S.Y. and P.K.K. acknowledge a grant from Korea Environment Industry and Technology Institute (KEITI) through Subsurface Environmental Management (SEM) Project (2020002440002), funded by the Korea Ministry of Environment (MOE). P.K.K. acknowledges MnDRIVE Advancing Industry, Conserving Our Environment at the University of Minnesota. M.D. acknowledges funding of the European Research Council (ERC) through the project MHetScale (contract number 617511), and the Spanish Research Agency (AEI) through the project HydroPore (contract number PID2019-106887GB-C31). We thank the Minnesota Supercomputing Institute (MSI) at the University of Minnesota for computational resources and support.
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- laminar reacting flows
- mixing and dispersion
- porous media