The impact of stretching-enhanced mixing and coalescence on reactivity in mixing-limited reactive flows

Abstract

We analyze the dynamics of solute mixing and reaction in a mixing-limited reactive flow by considering the transport of a tracer in a linear shear flow and in a Rankine vortex. The action of a shear flow, in general, achieves stretching of fluid elements due to the heterogeneous nature of the flow. A vortex flow exhibits not only stretching but also folding of fluid elements in a way that brings adjacent fluid elements closer at every turn. A strong stretching along the tangential direction is accompanied by a concomitant thinning in the radial direction leading to a strong diffusive flux, which may cause the material from neighboring regions of the mixing interface to aggregate. Through a Lagrangian concentration evolution technique, the diffusive strip method, we obtain the concentration field and pinpoint the signature of coalescence of two neighboring concentration regions by analyzing the concentration distribution profiles. The role of substrate deformation on the reaction kinetics of a classical heterogeneous chemical reaction is also studied where we derive analytical expressions for the coupling between the rate of product formation and the Péclet number in different time limits. Finally, the impact of coalescence on reaction rates is studied for a Rankine vortex, a result that holds important implications for simple bimolecular reactions. This analysis is useful to understand scalar dispersion in vortical flow structures and the consequences of stretching-enhanced diffusion in mixing-limited reactive flows.