Experimental studies of front propagation and mode-locking in an advection-reaction-diffusion system

Abstract

processes. The dynamics of these fronts are governed by the interplay between mixing in the system and the interaction between the different species. Several previous studies have examined this phenomenon in the reaction-diffusion limit in which fluid flows are not present and mixing is achieved solely via molecular diffusion [5]. But fluid systems typically are not stagnant; rather, flows in the system dramatically alter and enhance transport and mixing. Despite this fact, the more general advection-reaction-diffusion problem has only recently received attention [6][7][8][9], and there have been almost no experimental studies [10][11][12]. The importance of mixing is particularly significant in light of recent studies indicating that mixing can be chaotic, even for well-ordered, laminar fluid flows [13,14].In this letter, we present experimental studies of the propagation of chemical fronts in a cellular flow consisting of a chain of oscillating vortices [15,16]. In particular, we investigate the propagation velocities for the fronts. We compare the experimental results to a theory [17] that predicts locking of the fronts to the external forcing. Mode-locking of this nature has been found in a variety of physical systems [18,19]; this, however, is the first experimental evidence of mode-locking in an advection-reaction-diffusion system.

Nonlinear Response of Inertial Tracers in Steady Laminar Flows: Differential and Absolute Negative Mobility

“…The central role played by the coupling with the velocity field clearly emerges in the GER which is satisfied in our nonequilibrium system. The striking behaviors shown by the model should be observable in experiments with biased inertial tracers in laminar flows, realized, for instance, in setups with rotating cylinders [43], two-sided lid-driven cavities [52] or magneticallydriven vortices [44,53].…”

Experiments on pattern formation in reacting systems with chaotic advection

“…Mode-locking is defined for a propagating front as follows: when modelocked, the front advances an integer number N of wavelengths in an integer number M of drive periods. We have tested these predictions with experiments on front propagation in an oscillating vortex chain [11], [12]. The flow and apparatus are show in in Figure 3.…”

“…In this article, we review some experiments that we have conducted on pattern-formation processes in advection-reaction-diffusion systems with chaotic advection. Three sets of experiments are described: (1) Pattern formation of an oscillatory chemical reaction in a flow with chaotic mixing [10]; (2) front propagation and mode-locking for an advancing chemical reaction in an oscillating vortex chain [11], [12]; and (3) synchronization of chemical oscillators in a fluid flow via superdiffusive transport [13].…”

Targeted mixing in an array of alternating vortices

“…Laboratoire affiliéà la FRUMAM (FR 2291). Laboratoire de Recherche Conventionné du CEA (DSM-06- 35). …”

“…This flow is easily accessible to experimentalists for instance using magnetohydrodynamics techniques similar to Rayleigh-Bénard convection with a control over the flow [21,22,23]. As such, understanding its influence on the advection of passive or active quantities is considered a necessary first step in order to uncover the different mechanisms governing transport in general or reactiondiffusion processes such as front propagation in turbulent flows [34,35,36,37,38]. The stream function which models an experiment in a channel with slip boundary conditions writes:…”