Hostname: page-component-5b777bbd6c-rbv74 Total loading time: 0 Render date: 2025-06-21T18:54:48.406Z Has data issue: false hasContentIssue false
  • English
  • Français

Laminar mixing and chaotic mixing in several cavity flows

Published online by Cambridge University Press:  21 April 2006

W.-L. Chien ,
H. Rising  and
J. M. Ottino
W.-L. Chien
Affiliation:
Department of Chemical Engineering, University of Massachusetts, Amherst, MA 01003, USA
H. Rising
Affiliation:
Department of Mathematics, University of Massachusetts, Amherst, MA 01003, USA
J. M. Ottino
Affiliation:
Department of Chemical Engineering, University of Massachusetts, Amherst, MA 01003, USA
Get access Rights & Permissions [Opens in a new window]

Abstract

The objective of this work is an experimental study of laminar mixing in several kinds of two-dimensional cavity flows by means of material line and blob deformation in a new experimental system consisting of two sets of roller pairs connected by belts. The apparatus can be adjusted to produce a range of aspect ratios (0.067–10), Reynolds numbers (0.1–100), and various kinds of flow fields with one or two moving boundaries. Flow visualization is conducted by marking underneath the free surface of the flow with a tracer solution of low diffusivity and of approximately the same density and viscosity as the flowing fluid. The effects of the initial location of the material blob, relative motion of the two bands, and minor changes in the geometry of the flow region are investigated experimentally.

The alternate periodic motion of two bands in a cavity flow is an example of a laminar flow which might lead to chaotic mixing. The governing parameter is the dimensionless frequency of oscillation of the walls f which, under the proper conditions, is able to produce horseshoe functions of various types. The deformation of blobs is central to the understanding of mixing and can be studied to identify horseshoe functions. It is found that the efficiency of mixing depends strongly on the value of f and that there exists an optimal value of f that produces the best mixing in a given time.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 170 , September 1986 , pp. 355 - 377
Copyright
© 1986 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.)

Article purchase

Temporarily unavailable

References

Aref H.1984 Stirring by chaotic advection. J. Fluid Mech 143, 1–21.Google Scholar
Bigg, D. & Middleman S.1974 Laminar mixing of a pair of fluids in a rectangular cavity. Ind. Engng. Chem. Fundam. 13, 184–190.Google Scholar
Burggraf O. C.1966 Analytical and numerical studies of the structure of steady separated flows. J. Fluid Mech. 24, 113–151.Google Scholar
Chella, R. & Ottino J. M.1985a Fluid mechanics of mixing in a single screw extruder. Ind. Engng. Chem. Fundam. 24, 170–180.Google Scholar
Chella, R. & Ottino J. M.1985b Stretching in some classes of fluid motions and asymptotic mixing efficiencies as a measure of flow classification. Arch. Rat Mech. Anal. 90, 15–42.Google Scholar
Doherty, M. F. & Ottino J. M.1986 Chaos in deterministic systems: strange attractors, turbulence, and applications in chemical engineering. Chem. Engng. Sci. (to appear).Google Scholar
Greenspan D.1974 Discrete Numerical Methods in Physics and Engineering. Academic.
Guckenheimer, J. & Holmes P.1983 Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields. Springer.
Harlow, F. H. & Amsden A. A.1970 The MAC methods. Los Alamos Scientific Laboratory Monograph LA-4370.Google Scholar
Khakhar D. V., Rising, H. & Ottino J. M.1986 An analysis of chaotic mixing in two model flows. J. Fluid Mech. (in press).Google Scholar
Khakhar D. V., Chella, R. & Ottino J. M.1984 Stretching, chaotic motion and breakup of elongated droplets in time dependent flows. Adv. Rheology, vol. 2, (Fluids), pp. 81–88, Proc. IX Intl. Congress of Rheology (ed. B. Mena, A. Garcia-Rejon & C. Rangel-Nafaile). Universidad Autonoma de Mexico.
Malone M. F.1979 Numerical simulation of hydrodynamics problems in polymer processing. Ph.D. thesis, University of Massachusetts, Amherst, MA.
Middleman S.1977 Fundamentals of Polymer Processing. McGraw-Hill.
Moser J.1973 Stable and Random Motions in Dynamical Systems. Princeton University Press.
Nallasamy, M. & Prasad K. K.1977 On cavity flow at high Reynolds numbers. J. Fluid Mech. 79, 391–414.Google Scholar
Ottino, J. M. & Chella R.1983 Laminar mixing of polymeric liquids: brief review and recent theoretical developments. Polym. Engng. Sci. 23, 357–379.Google Scholar
Pan, F. & Acrivos A.1967 Steady flows in rectangular cavities. J. Fluid Mech. 28, 643–655.Google Scholar
Peyret, R. & Taylor T. D.1983 Computational Methods of Fluid Flow. Springer.
Rising, H. & Ottino J. M.1986 The use of horseshoe functions in mixing studies. Physica D (in preparation).Google Scholar
Savasl Ö.1985 On flow visualization using reflective flakes. J. Fluid Mech. 152, 235–248.Google Scholar
Schreiber, R. & Keller H. B.1983a Spurious solutions in a driven cavity calculations J. Comp. Phys. 49, 165–172.Google Scholar
Schreiber, R. & Keller H. B.1983b Driven cavity flows by efficient numerical techniques. J. Comp. Phys. 49, 310–333.Google Scholar
Shearer C. J.1973 Mixing of highly viscous liquids: flow geometries for streamlines subdivision and redistribution. Chem. Engng. Sci. 28, 1091–1098.Google Scholar
Smale S.1963 Diffeomorphisms with many periodic points. In Differential and Combinational Topology (ed. S. S. Cairns), pp. 63–68. Princeton University Press.
Smale S.1967 Differentiable dynamical systems. Bull. Am. Math. Soc. 73, 747–817.Google Scholar
Taylor Sir G. I.1934 The formation of emulsions in definable fields of flow Proc. Roy. Soc. Lond. A 146, 501–523.Google Scholar
Vahl Davis, G. de & Mallison, G. D. 1976 An evaluation of upwind and central difference approximation by a study of recirculating flow. Comput. Fluids 4, 29–46.Google Scholar
Winters, K. H. & Cliffe K. A.1979 A finite element study of laminar flows in a square cavity. UKAERE Harwell Rep. R9444.Google Scholar