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Experimental and computational studies of mixing in complex Stokes flows: the vortex mixing flow and multicellular cavity flows

Published online by Cambridge University Press:  26 April 2006

Sadhan C. Jana ,
Guy Metcalfe  and
J. M. Ottino
Sadhan C. Jana
Affiliation:
Department of Chemical Engineering, Robert R. McCormick School of Engineering and Applied Science, Northwestern University, Evanston, IL 60208–3120, USA Present address: The Benjamin Levich Institute, Steinman Hall, 1M, City University of New York, 140th Street & Convent Avenue, New York, NY 10031, USA.
Guy Metcalfe
Affiliation:
Department of Chemical Engineering, Robert R. McCormick School of Engineering and Applied Science, Northwestern University, Evanston, IL 60208–3120, USA
J. M. Ottino
Affiliation:
Department of Chemical Engineering, Robert R. McCormick School of Engineering and Applied Science, Northwestern University, Evanston, IL 60208–3120, USA
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Abstract

A complex Stokes flow has several cells, is subject to bifurcation, and its velocity field is, with rare exceptions, only available from numerical computations. We present experimental and computational studies of two new complex Stokes flows: a vortex mixing flow and multicell flows in slender cavities. We develop topological relations between the geometry of the flow domain and the family of physically realizable flows; we study bifurcations and symmetries, in particular to reveal how the forcing protocol's phase hides or reveals symmetries. Using a variety of dynamical tools, comparisons of boundary integral equation numerical computations to dye advection experiments are made throughout. Several findings challenge commonly accepted wisdom. For example, we show that higher-order periodic points can be more important than period-one points in establishing the advection template and extended regions of large stretching. We demonstrate also that a broad class of forcing functions produces the same qualitative mixing patterns. We experimentally verify the existence of potential mixing zones for adiabatic forcing and investigate the crossover from adiabatic to non-adiabatic behaviour. Finally, we use the entire array of tools to address an optimization problem for a complex flow. We conclude that none of the dynamical tools alone can successfully fulfil the role of a merit function; however, the collection of tools can be applied successively as a dynamical sieve to uncover a global optimum.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 269 , 25 June 1994 , pp. 199 - 246
Copyright
© 1994 Cambridge University Press

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