Mixing of a generalized Newtonian fluid in a corotating discontinuous cavity flow is studied. The flow period and the rheological coefficients are used as parameters. Using geometrical construction of periodic orbits and bifurcation analysis we find mixing windows in the parameter space. A system within a mixing window is capable of producing uniform mixtures. Some bifurcation values have also been determined. A system whose parameters are in the neighborhood of these values will mostly not produce a uniform mixture. The main conclusion is that shear thinning degrades mixing in the cavity flow.
Issue Section:
Research Papers
1.
Acrivos, A., ed., 1991, Proceedings of the IUTAM Symposium of Fluid Mechanics of Stirring and Mixing, La Jolla, CA, 20–24 Aug. 1990, Physics of Fluids A, Vol. 3, pp. 1009–1469.
2.
Aref
H.
1984
, “Stirring by Chaotic Advection
,” Journal of Fluid Mechanics
, Vol. 143
, pp. 1
–21
.3.
Chien
W.-L.
Rising
H.
Ottino
J. M.
1986
, “Laminar Mixing and Chaotic Mixing in Several Cavity Flows
,” Journal of Fluid Mechanics
, Vol. 170
, pp. 355
–377
.4.
Cross
M. M.
1973
, “Rheology of Synthetic Latices: Influence of Shear Rate and Temperature
,” Journal of Colloid Interface Science
, Vol. 44
, pp. 175
–176
.5.
Franjione
J. G.
Leong
C. W.
Ottino
J. M.
1989
, “Symmetries Within Chaos: A Route to Effective Mixing
,” Physics of Fluid A
, Vol. 1
, pp. 1772
–1783
.6.
Greene
J. M.
MacKay
R. S.
Vivaldi
F.
Feigenbaum
M. J.
1981
, “Universal Behaviour in Families of Area Preserving Maps
,” Physica D
, Vol. 3
, pp. 468
–486
.7.
Guckenheimer, J., and Holmes, P., 1983, Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields, Springer-Verlag, New York, p. 119.
8.
Kiani, A., Rakos, R., and Sebastian, D. H., 1989, “Three-Dimensional Computational Analysis of Fluted Mixing Devices,” Proceedings of the ANTEC 89, pp. 62–65.
9.
Leong, C. W., 1989, “A Detailed Analysis of Chaotic Mixing of Viscous Fluids in Time-Periodic Cavity Flows,” Ph.D. thesis, University of Massachusetts, Amherst.
10.
Leong
C. W.
Ottino
J. M.
1989
, “Experiments on Mixing Due to Chaotic Advection in a Cavity
,” Journal of Fluid Mechanics
, Vol. 209
, pp. 463
–499
.11.
Leong
C. W.
Ottino
J. M.
1990
, “Increase in Regularity by Polymer Addition During Chaotic Mixing in Two-Dimensional Flows
,” Physical Reviews Letters
, Vol. 64
, pp. 874
–877
.12.
Ling
F. H.
1993
, “The Effect of Mixing Protocol on Mixing in Discontinuous Cavity Flows
,” Physics Letters A
, Vol. 177
, pp. 331
–337
.13.
Ling, F. H., and Gogos, C., 1992, “Statistical Evaluation of Uniformity of Simulated Mixtures,” Proceedings of the ANTEC 92, pp. 2476–2479.
14.
Ling
F. H.
Schmidt
G.
1992
, “Mixing Windows in Discontinuous Cavity Flows
,” Physics Letters A
, Vol. 165
, pp. 221
–230
.15.
Ling
F. H.
Schmidt
G.
1993
, “Bifurcations and Mixing Windows in Sinusoidal Cavity Flow Mixing Systems
,” International Journal of Bifurcation and Chaos
, Vol. 3
, pp. 1457
–1476
.16.
Ottino, J. M., 1989, The Kinematics of Mixing: Stretching, Chaos, and Transport, Cambridge University Press, Cambridge.
17.
Ottino
J. M.
1990
, “Mixing, Chaotic Advection, and Turbulence
,” Annual Review of Fluid Mechanics
, Vol. 22
, pp. 207
–253
.18.
Powell
A.
1966
, “The Influence of the Molecular Size Distribution within a Liquid on the Viscous Flow of the Liquid
,” Polymer
, Vol. 7
, pp. 91
–97
.19.
Sastrohartono
T.
Kwon
T. H.
1990
, “Finite Element Analysis of Mixing Phenomena in Tangential Twin-Screw Extruders for Non-Newtonian Fluids
,” International Journal of Numerical Methods in Engineering
, Vol. 30
, pp. 1369
–1383
.
This content is only available via PDF.
Copyright © 1995
by The American Society of Mechanical Engineers
You do not currently have access to this content.
