Related Experiment Video
Updated: Jun 29, 2026

Quantifying Mixing using Magnetic Resonance Imaging
Published on: January 25, 2012
Resonant mixing in perturbed action-action-angle flow
Dmitri L Vainchtein1, John Widloski, Roman O Grigoriev
1School of Physics, Georgia Institute of Technology, Atlanta, Georgia 30332, USA.
Abstract:
This paper presents a quantitative theory of mixing via chaotic advection in near-integrable time-dependent volume-preserving flows for the case when the base (unperturbed) flow possesses two invariants (or actions). Using a model cellular flow introduced by Solomon and Mezic as an example, we construct a quantitative theory of mixing caused by the resonance-induced diffusion of an adiabatic invariant of the flow. We compute the fraction of the mixed volume as a function of the frequency of the perturbation and show that this function is strikingly nonmonotonic, with multiple peaks. In particular, essentially complete mixing inside a flow cell is achieved on experimentally accessible time scales for certain special frequencies.
Related Concept Videos
Sound Waves: Resonance
Double Resonance Techniques: Overview
Spin decoupling is usually achieved by...
Concept of Resonance and its Characteristics
Standing Waves in a Cavity
Irrotational Flow
Turbulent Flow

