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Quantifying Mixing using Magnetic Resonance Imaging

Quantifying Mixing using Magnetic Resonance Imaging

Published on: January 25, 2012

Targeted mixing in an array of alternating vortices.

R Bachelard¹, T Benzekri, C Chandre

¹Centre de Physique Théorique, CNRS Aix-Marseille Universités, campus de Luminy, Case 907, F-13288 Marseille cedex 9, France.

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

|November 13, 2007

Summary

This study explores particle transport in vortex arrays, finding that controlled perturbations create barriers enhancing mixing within regions while preventing long-range particle movement. Optimal mixing conditions are identified for practical applications.

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Area of Science:

Fluid dynamics
Nonlinear dynamics
Statistical mechanics

Background:

Understanding particle transport in fluid flows is crucial for various scientific and engineering disciplines.
Vortex arrays are common in nature and technology, influencing mixing and transport phenomena.
Chaotic advection arises from time-dependent or spatially complex flows, leading to enhanced mixing.

Purpose of the Study:

To investigate the transport and mixing properties of passive particles in an array of vortices.
To explore how perturbations can create dynamical barriers for controlled particle transport.
To identify conditions for enhanced mixing within barriers and suppressed long-range transport.

Main Methods:

Analysis of an integrable vortex system.
Introduction of specific perturbations to induce chaotic advection.
Numerical simulations to analyze mixing properties and their dependence on parameters.
Investigation of robustness to perturbation errors and boundary conditions.

Main Results:

Perturbations can preserve separatrices, acting as effective transport barriers.
Chaotic advection is triggered within these barriers, enhancing mixing.
Long-range transport is effectively prevented by the dynamical barriers.
Optimal mixing regimes were identified through numerical analysis.
The mixing properties show robustness to errors and different boundary conditions.

Conclusions:

Controlled perturbations in vortex arrays can create effective transport barriers.
This method enhances mixing within confined regions while suppressing large-scale transport.
The findings offer insights into designing systems for targeted mixing and transport control.