Control of mixing via entropy tracking.
We study mixing of isothermal fluids by controlling the global hydrodynamic entropy <s> . In particular, based on the statistical coupling between the evolution of <s> and the global viscous dissipation <ϵ> , we analyze stirring protocols such that <s>∼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).
Hoeijmakers
Maarten
M
Department of Mechanical Engineering, Eindhoven University of Technology, 5600 MB Eindhoven, The Netherlands.
Fontenele Araujo
Francisco
F
van Heijst
Gertjan
G
Nijmeijer
Henk
H
Trieling
Ruben
R