Abstract
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 $A + B \rightarrow C$ . 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.
Highlights
Solute transport and chemical reactions in channel flows are of great interest in numerous engineering applications and natural processes, including microfluidics, biomedical 916 A45-1S
We investigate the relationship between the fluid stretching and the mixing-limited reaction process in channel flows in pre-asymptotic regimes by combining numerical simulations using a Lagrangian reactive particle tracking algorithm (Perez, Hidalgo & Dentz 2019a) and an analysis based on the diffusive strip method (Duplat & Villermaux 2008; Meunier & Villermaux 2010; Le Borgne et al 2013, 2015; Perez et al 2019b)
We have established the quantitative link between fluid stretching and reactivity in channel flows, which enables the prediction of chemical reactivity from fluid stretching information only
Summary
Solute transport and chemical reactions in channel flows are of great interest in numerous engineering applications and natural processes, including microfluidics, biomedical 916 A45-1S. Dentz and P.K. Kang devices and fractured rock hydrogeology (Kotomin & Kuzovkov 1996; Dijk & Berkowitz 1998; Detwiler, Rajaram & Glass 2000; Losey et al 2002; deMello 2006; Meakin & Tartakovsky 2009; Kwon et al 2019; Lee & Kang 2020; Yoon & Kang 2021). The reactive displacement of two miscible fluids in channel flows is a fundamental process that determines, for example, the performance of microfluidics devices and the remediation of contaminated fractured rock aquifers. In many of these applications, predicting the spatio-temporal evolution of chemical reactivity is critical. We demonstrate that such prediction is possible through the concept of optimal fluid stretching, a concept that we propose in this study
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