Hostname: page-component-77c89778f8-rkxrd Total loading time: 0 Render date: 2024-07-18T15:38:53.709Z Has data issue: false hasContentIssue false
  • English
  • Français

Experiments on mixing in continuous chaotic flows

Published online by Cambridge University Press:  26 April 2006

H. A. Kusch  and
J. M. Ottino
H. A. Kusch
Affiliation:
Chevron Oil Field Research Company, La Habra, CA 90633, USA
J. M. Ottino
Affiliation:
Department of Chemical Engineering, Northwestern University, Evanston, IL 60208, USA
Get access Rights & Permissions [Opens in a new window]

Abstract

We present the design and operation of a flow apparatus for investigations of mixing in time-periodic and spatially periodic chaotic flows. Uses are illustrated in terms of two devices operating in the Stokes regime: the partitioned-pipe mixer, a spatially periodic system consisting of sequences of flows in semicircular ducts, and the eccentric helical annular mixer, a time-periodic velocity field between eccentric cylinders with a superposed Poiseuille flow; other mixing flows can be implemented with relative ease. Fundamental differences between spatially periodic and time-periodic duct flows are readily apparent. Steady spatially periodic systems show segregated KAM-tubes coexisting with chaotic advection; such tubes are remarkably stable under a variety of experimental conditions. Time-periodic duct flows lead to complex streakline structures; since regular regions in the cross-sectional flow move through space, a streakline can find itself injected in a regular domain for some time then be trapped in a chaotic region, and so on, leading to ‘intermittent’ behaviour.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 236 , March 1992 , pp. 319 - 348
Copyright
© 1992 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

Aref, H. 1984 Stirring by chaotic advection. J. Fluid Mech. 143, 1–21.Google Scholar
Aref, H. 1991 Chaotic advection of fluid particles. Phil. Trans. R. Soc. Lond. A 333, 273–281.Google Scholar
Bajer, K. & Moffat, H. K. 1990 On a class of steady confined Stokes flows with chaotic streamlines. J. Fluid Mech 212, 337–363.Google Scholar
Chaiken, J., Chevray, R., Tabor, M. & Tan, Q. M. 1986 Experimental study of Lagrangian turbulence in Stokes flow. Proc. R. Soc. Lond. A 408, 165–174.Google Scholar
Chien, W.-L., Rising, H. & Ottino, J. M. 1986 Laminar mixing and chaotic mixing in several cavity flows. J. Fluid Mech. 170, 355–377.Google Scholar
Dombre, T., Frisch, U., Greene, J. M., Hénon, M., Mehr, A. & Soward, A. M. 1986 Chaotic streamlines in the ABC flows. J. Fluid Mech. 167, 353–391.Google Scholar
Fenstermacher, P. R., Swinney, H. L. & Gollub, J. P. 1979 Dynamical instabilities and the transition to chaotic Taylor vortex flow. J. Fluid Mech. 94, 103–128.Google Scholar
Franjione, J. G. & Ottino, J. M. 1987 Feasibility of numerical tracking of material lines and surfaces in chaotic flows. Phys. Fluids 30, 3641–3643.Google Scholar
Franjione, J. G. & Ottino, J. M. 1991 Stretching in duct flows. Phys. Fluids A 3, 2819–2821.Google Scholar
Franjione, J. G. & Ottino, J. M. 1992 Symmetry concepts for the geometric analysis of mixing flows. Phil. Trans. R. Soc. Lond. A (to appear).Google Scholar
Hénon, M. 1966 Sur la topologie des lignes de courant dans un cas particulier. C. R. Acad. Sci. Paris A 262, 312–314.Google Scholar
Jones, S. W., Thomas, O. M. & Aref, A. 1989 Chaotic advection by laminar flow in a twisted pipe. J. Fluid Mech. 209, 335–357.Google Scholar
Khakhar, D. V. 1986 Fluid mechanics of laminar mixing: dispersion and chaotic flows. Ph.D. thesis, University of Massachusetts, Amherst.
Khakhar, D. V., Franjione, J. G. & Ottino, J. M. 1987 A case study of chaotic mixing in deterministic flows, the partitioned pipe mixer. Chem. Engng Sci. 42, 2909–2926.Google Scholar
Kusch, H. A. 1991 Experiments on continuous chaotic mixing of viscous liquids. Ph.D. thesis. University of Massachusetts, Amherst.
Leong, C.-W. & Ottino, J. M. 1989 Experiments on mixing due to chaotic advection in a cavity, J. Fluid Mech. 209, 463–499.Google Scholar
Middleman, S. 1977 Fundamentals of Polymer Processing. McGraw-Hill.
Noll, W. 1962 Motions with constant stretch history. Arch. Rat. Mech. Anal. 11, 97–105.Google Scholar
Ottino, J. M. 1989 The Kinematics of Mixing: Stretching, Chaos, and Transport. Cambridge University Press.
Ottino, J. M., Leong, C. W., Rising, H. & Swanson, P. D. 1988 Morphological structures produced by mixing in chaotic flows. Nature 333, 419–425.Google Scholar
Pearson, J. R. A. 1981 Wider horizons for fluid mechanics. J. Fluid Mech. 106, 229–244.Google Scholar
Snyder, W. T. & Goldstein, G. A. 1965 An analysis of fully developed laminar flow in an eccentric annulus. AIChE J. 11, 462–467.Google Scholar
Solomon, T. H. & Gollub, J. P. 1988 Chaotic particle transport in time-dependent Rayleigh—Bénard convection. Phys. Rev. A 38, 6280–6286.Google Scholar
Stone, H. A., Nadim, A. & Strogatz, S. H. 1991 Chaotic streaklines inside drops immersed in steady linear flows. J. Fluid Mech. 232, 629–646.Google Scholar
Swanson, P. D. & Ottino, J. M. 1990 A comparative computational and experimental study of chaotic mixing of viscous fluids. J. Fluid Mech. 213, 227–249.Google Scholar
Swinney, H. L. & Gollub, J. P. 1985 Hydrodynamic Instabilities and the Transition to Turbulence. Topics in Applied Physics, vol. 45, 2nd edn. Springer.
Wannier, G. H. 1950 A contribution to the hydrodynamics of lubrication. Q. Appl. Maths VIII, 1–32.Google Scholar
Young, W. R. & Jones, S. 1991 Shear dispersion. Phys. Fluids A 3, 1087–1101.Google Scholar