Optimal stretching in the reacting wake of a bluff body

Abstract

We experimentally study spreading of the Belousov-Zhabotinsky reaction behind a bluff body in a laminar flow. Locations of reacted regions (i.e., regions with high product concentration) correlate with a moderate range of Lagrangian stretching and that range is close to the range of optimal stretching previously observed in topologically different flows [T. D. Nevins and D. H. Kelley, Phys. Rev. Lett. 117, 164502 (2016)]. The previous work found optimal stretching in a closed, vortex dominated flow, but this article uses an open flow and only a small area of appreciable vorticity. We hypothesize that optimal stretching is common in advection-reaction-diffusion systems with an excitation threshold, including excitable and bistable systems, and that the optimal range depends on reaction chemistry and not on flow shape or characteristic speed. Our results may also give insight into plankton blooms behind islands in ocean currents.

Optimal fluid stretching for mixing-limited reactions in rough channel flows

“…the formation of biofilm, dissolution and precipitation patterns), and shed new light on the notion of optimal stretching observed also in other flows (Nevins & Kelley 2016; Wang et al. 2017). For example, the stretching-induced mixing enhancement shown in this study is closely related to the reactant blowout observed in Nevins & Kelley (2016).…”

“…Hence, fluid stretching promotes mixing and enhances reaction rates. Interestingly, two recent experimental studies have reported that there are optimal ranges of fluid stretching for maximum reactivity if the reaction systems are with an excitation threshold such as the Belousov-Zhabotinsky reaction (Nevins & Kelley 2016;Wang et al 2017). The authors found reaction blowout at high stretching rates, and this blowout is explained qualitatively by the dilution of the reactant due to the fluid stretching.…”

Front tracking velocimetry in advection-reaction-diffusion systems

“…The third device is a water channel that produces a wake behind a bluff body, previously described in detail. 21 The bluff body is an equilateral triangle with a side length of 45 mm, positioned symmetrically about the channel center with one vertex pointing upstream. The channel flow is dominated by shear (not vorticity) except in the wake behind the bluff body.…”

“…Second, other barriers to front propagation may also be possible, and front tracking could locate them. For example, recent studies 20,21 have found that excitable reactions are promoted mostly in regions where the Lagrangian stretching falls in an optimal range. Outside this range, fronts propagate slowly, or are driven to extinction by a process analogous to blowing out a flame.…”

“…[16][17][18] In some cases, gentle flow enhances reaction and violent flow inhibits reaction. [19][20][21] By considering a concentration level curve which separates reacted and unreacted regions-a reaction front-the dynamics of ARD, which depend on a partial differential equation (PDE), can be approximated with a simpler dynamics that depends only on ordinary differential equations (ODEs). Burning invariant manifolds (BIMs) and burning Lagrangian Coherent Structures (bLCS), developed from such an approximation, predict when and where a front will advance.…”