Hostname: page-component-586b7cd67f-t8hqh Total loading time: 0 Render date: 2024-11-29T14:19:39.010Z Has data issue: false hasContentIssue false
  • English
  • Français

Geoinspired soft mixers

Published online by Cambridge University Press:  21 September 2020

P. Meunier Open the ORCID record for P. Meunier [Opens in a new window]
P. Meunier*
Affiliation:
CNRS, Aix Marseille Université, Centrale Marseille, IRPHE, 13384Marseille, France
*
†Email address for correspondence: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

The flow with low shear inside a bladeless mixer is characterized experimentally. This soft mixer, inspired by the precession of the Earth, consists of a cylindrical container rotating around its axis and tilted from the vertical. For low Froude numbers, the free surface remains horizontal, thus generating a forcing on the tilted rotating fluid. As in the case of a precessing cylinder, this forcing excites global inertial modes (Kelvin modes) which become resonant when the height of fluid is equal to a multiple of a half-wavelength. Ekman pumping saturates the amplitude of the mode at a value proportional to the square root of the Reynolds number. For sufficiently large tilt angles and Reynolds numbers, the global mode destabilizes via a parametric triadic instability involving two additional Kelvin modes. The viscous threshold of the instability can be predicted analytically with no fitting parameter and is in excellent agreement with the experimental results. This instability generates a strong mixing which is as efficient as the one achieved using a classical Rushton turbine, but with a shear 20 times smaller. This simple bladeless mixer is thus an excellent candidate for large scale bioreactors where mixing is needed to enhance gas exchanges but where shear is harmful for fragile cells. Preliminary results obtained for the growth of microalgae (dinoflagellates) in such photobioreactors suggest that it could be a technological breakthrough in biotechnologies.

JFM classification

Geophysical and Geological Flows: Rotating flows Instability: Parametric instability Mixing: Turbulent mixing
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 903 , 25 November 2020 , A15
Check for updates
Copyright
© The Author(s), 2020. Published by Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

Albrecht, T., Blackburn, H., Lopez, J., Manasseh, R. & Meunier, P. 2015 Triadic resonances in precessing rapidly rotating cylinder flows. J. Fluid Mech. 778, R1.CrossRefGoogle Scholar
Albrecht, T., Blackburn, H. M., Lopez, J. M., Manasseh, R. & Meunier, P. 2018 On triadic resonance as an instability mechanism in precessing cylinder flow. J. Fluid Mech. 841, R3.CrossRefGoogle Scholar
Batchelor, G. 1959 Small-scale variation of convected quantities like temperature in turbulent fluid. Part 1. General discussion and the case of small conductivity. J. Fluid Mech. 5 (1), 113–133.CrossRefGoogle Scholar
Boisson, J., Cébron, D., Moisy, F. & Cortet, P.-P. 2012 Earth rotation prevents exact solid-body rotation of fluids in the laboratory. Europhys. Lett. 98 (5), 59002.CrossRefGoogle Scholar
Cherry, R. & Papoutsakis, E. 1986 Hydrodynamic effects on cells in agitated tissue culture reactors. Bioprocess Engng 1 (1), 29–41.CrossRefGoogle Scholar
Craik, A. D. D. & Leibovich, S. 1976 A rational model for Langmuir circulations. J. Fluid Mech. 73 (3), 401–426.CrossRefGoogle Scholar
Dauxois, T., Joubaud, S., Odier, P. & Venaille, A. 2018 Instabilities of internal gravity wave beams. Annu. Rev. Fluid Mech. 50, 131–156.CrossRefGoogle Scholar
Doran, P. M. 1999 Design of mixing systems for plant cell suspensions in stirred reactors. Biotechnol. Prog. 15 (3), 319–335.CrossRefGoogle ScholarPubMed
Francois, N., Xia, H., Punzmann, H. & Shats, M. 2013 Inverse energy cascade and emergence of large coherent vortices in turbulence driven by Faraday waves. Phys. Rev. Lett. 110 (19), 194501.CrossRefGoogle ScholarPubMed
Gans, R. F. 1970 On the precession of a resonant cylinder. J. Fluid Mech. 476, 865–872.CrossRefGoogle Scholar
Garcia-Ochoa, F. & Gomez, E. 2009 Bioreactor scale-up and oxygen transfer rate in microbial processes: an overview. Biotechnol. Adv. 27 (2), 153–176.CrossRefGoogle ScholarPubMed
Gauthier, G., Gondret, P. & Rabaud, M. 1998 Motions of anisotropic particles: application to visualization of three-dimensional flows. Phys. Fluids 10 (9), 2147–2154.CrossRefGoogle Scholar
Greenspan, H. P. 1969 On the non-linear interaction of inertial modes. J. Fluid Mech. 36 (2), 257–264.CrossRefGoogle Scholar
Guet, S. & Ooms, G. 2006 Fluid mechanical aspects of the gas-lift technique. Annu. Rev. Fluid Mech. 38, 225–249.CrossRefGoogle Scholar
Kelvin, L. 1880 Vibrations of a columnar vortex. Phil. Mag. 10, 155–168.Google Scholar
Kerswell, R. 1996 Upper bounds on the energy dissipation in turbulent precession. J. Fluid Mech. 321, 335–370.CrossRefGoogle Scholar
Kerswell, R. R. 1999 Secondary instabilities in rapidly rotating fluids: inertial wave breakdown. J. Fluid Mech. 382, 283–306.CrossRefGoogle Scholar
Lagrange, R., Eloy, C., Nadal, F. & Meunier, P. 2008 Instability of a fluid inside a precessing cylinder. Phys. Fluids 20 (8), 081701.CrossRefGoogle Scholar
Lagrange, R., Meunier, P., Nadal, F. & Eloy, C. 2011 Precessional instability of a fluid cylinder. J. Fluid Mech. 666, 104–145.CrossRefGoogle Scholar
Le Bars, M., Cébron, D., Le Gal, P. 2015 Flows driven by libration, precession, and tides. Annu. Rev. Fluid Mech. 47, 163–193.CrossRefGoogle Scholar
Lin, Y., Noir, J. & Jackson, A. 2014 Experimental study of fluid flows in a precessing cylindrical annulus. Phys. Fluids 26 (4), 046604.CrossRefGoogle Scholar
Lopez, J. M. & Marques, F. 2018 Rapidly rotating precessing cylinder flows: forced triadic resonances. J. Fluid Mech. 839, 239–270.CrossRefGoogle Scholar
Malkus, W. 1968 Precession of the Earth as the cause of geomagnetism: experiments lend support to the proposal that precessional torques drive the Earth's dynamo. Science 160 (3825), 259–264.CrossRefGoogle ScholarPubMed
Manasseh, R. 1992 Breakdown regimes of inertia waves in a precessing cylinder. J. Fluid Mech. 243, 261–296.CrossRefGoogle Scholar
Manasseh, R. 1994 Distorsions of inertia waves in a precessing cylinder forced near its fundamental mode resonance. J. Fluid Mech. 265, 345–370.CrossRefGoogle Scholar
Manasseh, R. 1996 Nonlinear behaviour of contained inertia waves. J. Fluid Mech. 315, 151–173.CrossRefGoogle Scholar
Mason, R. & Kerswell, R. 2002 Chaotic dynamics in a strained rotating flow: a precessing plane fluid layer. J. Fluid Mech. 471, 71–106.CrossRefGoogle Scholar
McEwan, A. 1970 Inertial oscillations in a rotating fluid cylinder. J. Fluid Mech. 40 (3), 603–640.CrossRefGoogle Scholar
Meunier, P., Eloy, C., Lagrange, R. & Nadal, F. 2008 A rotating fluid cylinder subject to weak precession. J. Fluid Mech. 599, 405–440.CrossRefGoogle Scholar
Meunier, P. & Leweke, T. 2003 Analysis and minimization of errors due to high gradients in particule image velocimetry. Exp. Fluids 35 (5), 408–421.CrossRefGoogle Scholar
Meunier, P. & Manasseh, R. 2017 Soft mixer. Patent WO 2017/149034 A1.Google Scholar
Miles, J. & Henderson, D. 1990 Parametrically forced surface waves. Annu. Rev. Fluid Mech. 22 (1), 143–165.CrossRefGoogle Scholar
Nagata, S. 1975 Mixing: Principles and Applications. Halsted Press.Google Scholar
Staquet, C. & Sommeria, J. 2002 Internal gravity waves: from instabilities to turbulence. Annu. Rev. Fluid Mech. 34 (1), 559–593.CrossRefGoogle Scholar
Thomas, J. & Yamada, R. 2019 Geophysical turbulence dominated by inertia–gravity waves. J. Fluid Mech. 875, 71–100.CrossRefGoogle Scholar
Thompson, R. 1970 Diurnal tides and shear instabilities in a rotating cylinder. J. Fluid Mech. 40, 737–751.CrossRefGoogle Scholar
Tilgner, A. 2007 Kinematic dynamos with precession driven flow in a sphere. Geophys. Astrophys. Fluid Dyn. 101 (1), 1–9.CrossRefGoogle Scholar
Van't Riet, K. & Smith, J. 1975 The trailing vortex system produced by Rushton turbine agitators. Chem. Engng Sci. 30 (9), 1093–1105.CrossRefGoogle Scholar
Villermaux, E. 2019 Mixing and stirring. Annu. Rev. Fluid Mech. 51, 245–273.CrossRefGoogle Scholar
Wu, J., Graham, L. & Noui Mehidi, N. 2006 Estimation of agitator flow shear rate. AIChE J. 52 (7), 2323–2332.CrossRefGoogle Scholar
Yarom, E. & Sharon, E. 2014 Experimental observation of steady inertial wave turbulence in deep rotating flows. Nat. Phys. 10 (7), 510.CrossRefGoogle Scholar

Meunier supplementary movie 1

Temporal evolution of the axial vorticity in the mid-height cross-section obtained by PIV. Re=4300, = 1◦.
Download Meunier supplementary movie 1(Video)
Video 4.7 MB

Meunier supplementary movie 2

Temporal evolution of the axial vorticity in the quarter-height cross-section obtained by PIV. Re=4300, = 1◦.
Download Meunier supplementary movie 2(Video)
Video 5 MB