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A comparative computational and experimental study of chaotic mixing of viscous fluids

Published online by Cambridge University Press:  26 April 2006

P. D. Swanson  and
J. M. Ottino
P. D. Swanson
Affiliation:
Departments of Chemical Engineering and Polymer Science and Engineering, University of Massachusetts, Amherst, MA 01003, USA
J. M. Ottino
Affiliation:
Departments of Chemical Engineering and Polymer Science and Engineering, University of Massachusetts, Amherst, MA 01003, USA
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Abstract

The objective of this work is to develop techniques to predict the results of experiments involving chaotic dispersion of passive tracers in two-dimensional low Reynolds number flows. We present the design of a flow apparatus which allows the unobstructed observation of the entire flow region. Whenever possible we compare the experimental results with those of computations. Conventional tracking of the boundaries of the tracer is inefficient and works well only for low stretches (order 102 at most). However, most mixing experiments involve extremely large perturbations from steady flow since this is where the best mixing occurs. The best prediction of widespread mixing and large stretching (order 104–105) is provided by lineal stretching plots; surprisingly the technique also works for relatively low numbers of periods (as low as 2 or 3). The second best prediction is provided by a combination of low-order unstable manifolds – which indicate where the tracer goes, especially for short times – and the eigendirections of low-order hyperbolic periodic points – which indicate the alignment of striations in the flow. On the other hand, Poincaré sections provide only a gross picture of the spreading: they can be used primarily to detect what regions are inaccessible to the dye. Comparison of computations and experiments invariably reveals that bifurcations within islands have little impact in the mixing process.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 213 , April 1990 , pp. 227 - 249
Copyright
© 1990 Cambridge University Press

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