Abstract
The evolution of a competitive–consecutive chemical reaction is computed numerically in a two-dimensional chaotic fluid flow with initially segregated reactants. Results from numerical simulations are used to evaluate a variety of reduced models commonly adopted to model the full advection–reaction–diffusion problem. Particular emphasis is placed upon fast reactions, where the yield varies most significantly with Péclet number (the ratio of diffusive to advective time scales). When effects of the fluid mechanical mixing are strongest, we find that the yield of the reaction is underestimated by a one-dimensional lamellar model that ignores the effects of fluid mixing, but overestimated by two other lamellar models that include fluid mixing.
Highlights
The evolution of chemical reactions between initially segregated reactants is strongly influenced by the scale of segregation [1,2]
We examine the influence of fluid mixing upon a competitive– consecutive reaction, A + B → R, B + R → S [1], that takes place in a two-dimensional, laminar, chaotic fluid flow. We report numerical simulations of the simultaneous advection, reaction and diffusion of the various chemical species
We have carried out accurate simulations of a two-stage competitive–consecutive chemical reaction in the liquid phase, chaotically mixed from an initially segregated initial state
Summary
The evolution of chemical reactions between initially segregated reactants is strongly influenced by the scale of segregation [1,2]. When the reactions take place in a liquid phase that is stirred continuously, their progress correspondingly depends strongly upon the details of the fluid mechanical mixing [1,2,3,4,5,6,7,8,9]. ( in applications mixing is often generated through turbulent flow, laminar flow is more appropriate for highly viscous fluids or for delicate polymers or suspensions, for instance [9].) We report numerical simulations of the simultaneous advection, reaction and diffusion of the various chemical species. Even in two space dimensions, remain a significant computational challenge, because the chaotic flow generates structures whose spatial scales decrease exponentially with time, thereby rapidly reaching any fixed spatial resolution used in the numerics, or forcing adaptive grid refinements which correspondingly involve prohibitive computational expense.
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