Reaction front dynamics under shear flow for arbitrary Damköhler numbers
Résumé
Reaction fronts where two reactive fluids displace one another play an important role in a range of applications,
including contaminant plume transport and reaction, soil and aquifer remediation, CO2 sequestration, geothermal
dipoles and the development of hotspots of reaction in mixing zones. The background flow induces enhanced
mixing, and therefore reaction, through interfacial shear. Hence the coupling of fluid flow with chemical reactions
is pivotal in understanding and quantifying effective reaction kinetics in reaction fronts. While this problem has
been addressed in the limit of fast reactions (e.g. de Simoni 2005, Le Borgne 2014), in natural systems reactions
can span a large range of Damköhler numbers since their characteristic reaction times vary over a large range of
typical values. Here the coupling of shear flow and reversible chemical reactions is studied for a reaction front with
initially separated reactants at arbitrary Damköhler numbers. Approximate analytical expressions for the global
production rate are derived based on a reactive lamella approach. We observe three distinct regimes, each of them
characterized by different scalings of the global production rate and width of the reactive zone. We describe the
dependency of these scalings and the associated characteristic transition times as a function of Damköhler and Péclet
numbers. These results are validated against 2D numerical simulations. The study is expected to shed light on
the inherently complex cases of reactive mixing with varying reaction rates under the influence of an imposed flow.
de Simoni et al. (2005) Water Resour. Res., 41, W11410
Le Borgne et al. (2014) GRL, 41(22), 7898