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Effect of fluid flow on 1D reaction-diffusion waves

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Niklas Manz

This research project started as a Senior IS thesis in 2016 and continued with two NSF-REU summer research experiences.

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 use the excitable Belousov-Zhabotinsky reaction, to investigate the effect of advection on waves in quasi-1D systems (glass capillary tubes with inner diameter below 0.6 mm).

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).

Using the continuity equation from fluid dynamics we can calculate the resulting fluid velocity (advection) in the capillary if we know the inner diameters of the syringe and the capillary and the speed of the piston.

The figure gives an example of a space-time plot with a wave moving to the right and fluid flow to the left (1D gray-value cut of the center of a capillary with subsequent images at Δt in y-direction) and a nearly standing wave at about 10 mm.

Time-space plot (time going up) of wave propagating in a capillary to the right with changing fluid flowrates in the opposite direction, resulting in wave speed changes and a 'nearly stationary wave' between t = 600 s and t = 1000 s.

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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