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Investigating the Three-dimensional Flow Separation Induced by a Model Vocal Fold Polyp

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Chemical pattern formation induced by a shear flow in a two-layer model.

Desiderio A Vasquez¹, Jeff Meyer, Hans Suedhoff

¹Departamento de Ciencias, Sección Física, Pontificia Universidad Católica del Perú, Apartado 1761, Lima, Peru.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics

|October 15, 2008

Summary

Shear flow can create chemical patterns in reaction-diffusion-advection systems, even when standard conditions for Turing patterns are not met. This study analyzes pattern formation and instability in layered flow systems.

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Area of Science:

Chemical kinetics
Fluid dynamics
Pattern formation

Background:

Turing patterns typically require higher inhibitor diffusivity than activator diffusivity.
Homogeneous steady states in reaction-diffusion-advection systems can become unstable under shear flow.
Instability in these systems can lead to the formation of complex chemical patterns.

Purpose of the Study:

To investigate chemical pattern formation in reaction-diffusion-advection systems influenced by shear flow.
To analyze the instability of homogeneous states in layered systems with relative motion.
To understand the role of shear flow in Turing pattern formation.

Main Methods:

Linear stability analysis to determine the onset of instability.
Numerical solution of nonlinear reaction-diffusion-advection equations.
Analysis of pattern formation using Taylor dispersion theory.

Main Results:

Identified instability onset as a function of relative layer speed.
Observed stationary, oscillatory, and drifting chemical patterns.
Discovered bistability regions enabling localized structure formation.

Conclusions:

Shear flow can induce chemical pattern formation beyond standard Turing conditions.
Layered flow systems exhibit diverse pattern dynamics including localized structures.
Taylor dispersion provides a framework for understanding shear-induced instabilities.