Standing waves in 1D reaction-diffusion-advection systems

Niklas Manz

Space Time Plot

An example of a space-time plot (bright wave moving to the right) with changing flow rates, resulting in wave speed changes. A "nearly standing wave" is visible for the leftmost wave shortly before it "dies".

Advection has a huge effect on the propagation behavior of reaction-diffusion waves when an external force introduces flow in a system, as in stationary space-periodic structures with equal diffusion coefficients (Andresén et al., Stationary space-periodic structures with equal diffusion coefficients, Phys. Rev. E, 60(1), 297-301 (1999); Kærn and Menzinger, Flow-distributed oscillations: Stationary chemical waves in a reacting flow, Phys. Rev. E, 60(4), R3471, 1999; Kærn and Menzinger, Experiments on Flow-Distributed Oscillations in the Belousov-Zhabotinsky Reaction, J. Phys. Chem. A, 106(19), 4897-4903, 2002). We plan to use a chemical model system, the excitable Belousov-Zhabotinsky reaction, to investigate the effect of advection on waves in quasi-1D systems (capillary tubes).

Because reaction-diffusion waves propagate in a medium without actual mass transport of the medium itself, it is possible to create a ‘standing wave’ with opposite medium flow and the wave's propagation direction. The effect of advection by Poiseuille flow on the propagation velocity has been investigated numerically in, for example, reference (Edwards, Propagation velocities of chemical reaction fronts advected by Poiseuille flow, Chaos, 16(4), 043106, 2006).

This project started with Mitch Gavin’s Senior I.S. in 2015-16. He built the experimental setup to be able to push the piston of a syringe at a defined constant speed which allows the outflow of the solution through a needle into a capillary. Using the continuity equation from fluid dynamics we can calculate the resulting advection velocity in the capillary. Jersson Pachar, during his 2016 NSF-REU summer project, expanded the knowledge of how to use the setup and how to choose the right combination of piston speed, syringe, and capillary. An example of a space-time plot (1D grey-value cut of a capillary (bright wave moving to the right) with subsequent images at dt in y-direction) with changing flow rates, resulting in wave speed changes is shown in the figure. A "nearly standing wave" is visible for the leftmost wave shortly before it "dies".

The BZ medium needs to be low excitable to ensure no wave nucleation ahead of the wave. A usable recipe has been tested by Jersson as well. Preliminary experimental results showed the predicted wave behavior if the advection direction was opposite to the moving front (BZ wave started from the open end of the capillary toward the needle/capillary connection). The advection effect was larger than expected but we could see a stopping and reversal of the wave’s propagation velocity. We will run more detailed experiments with this improved setup to obtain reproducible and publishable results.

We also plan to initiate waves on the opposite side (syringe/needle region) to explore the behavior of advection parallel to the wave’s propagation direction.

General publications to be checked are (Kærn and Menzinger, Flow-distributed oscillations: Stationary chemical waves in a reacting flow, Phys. Rev. E, 60(4), R3471, 1999; Kærn and Menzinger, Experiments on Flow-Distributed Oscillations in the Belousov-Zhabotinsky Reaction, J. Phys. Chem. A, 106(19), 4897-4903, 2002).

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