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Chemical instability induced by a shear flow.

Desiderio A Vasquez¹

¹Department of Physics, Indiana University Purdue University Fort Wayne, Fort Wayne, Indiana 46805, USA.

Physical Review Letters

|September 28, 2004

Summary

Shear flow can induce a novel instability in chemical reaction-diffusion systems. Above a flow speed threshold, a homogeneous state destabilizes, forming a moving chemical pattern.

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Area of Science:

Chemical kinetics
Fluid dynamics
Pattern formation

Background:

Reaction-diffusion systems exhibit complex dynamics, including pattern formation.
Shear flow can significantly alter the stability of chemical systems.
Turing's instability is a known mechanism for pattern formation in reaction-diffusion systems.

Purpose of the Study:

To predict a new type of instability in reaction-diffusion systems driven by shear flow.
To investigate the conditions under which a homogeneous steady state becomes unstable in a Poiseuille flow.
To characterize the resulting chemical patterns and their relationship to fluid velocity.

Main Methods:

Theoretical analysis of a reaction-diffusion system subjected to Poiseuille flow.
Identification of the critical flow speed threshold for instability.
Analysis of pattern characteristics, including speed and morphology.

Main Results:

A homogeneous steady state loses stability as shear flow speed increases beyond a critical threshold.
The instability manifests as a steady chemical pattern that propagates with the average fluid velocity.
This pattern formation occurs when the activator is more diffusive than the inhibitor, differing from Turing's instability.

Conclusions:

Shear flow can induce a novel instability in reaction-diffusion systems, leading to pattern formation.
The direction and speed of pattern propagation are dictated by the fluid flow.
This finding expands the understanding of pattern formation mechanisms in chemically active fluid flows.

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