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Updated: Jun 8, 2026

Quantifying Mixing using Magnetic Resonance Imaging
Published on: January 25, 2012
Control of mixing via entropy tracking
Maarten Hoeijmakers1, Francisco Fontenele Araujo, Gertjan van Heijst
1Department of Mechanical Engineering, Eindhoven University of Technology, 5600 MB Eindhoven, The Netherlands.
Abstract:
We study mixing of isothermal fluids by controlling the global hydrodynamic entropy . In particular, based on the statistical coupling between the evolution of and the global viscous dissipation <ϵ> , we analyze stirring protocols such that ∼t(α)⇔<ϵ>∼t(α-1), with 0<α≤1. For a model array of vortices [Fukuta and Murakami, Phys. Rev. E 57, 449 (1998)], we show that: (i) feedback control can be achieved via input-output linearization, (ii) mixing is monotonically enhanced for increasing entropy production, and (iii) the mixing time t(m) scales as t(m)∼<ϵ>(-1/2).
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