Analysis of optimal mixing in open-flow mixers with time-modulated vortex arrays

Analysis of optimal mixing in open-flow mixers with time-modulated vortex arrays In this work, a systematic approach to efficient open flow mixing is introduced, using general theoretical concepts to identify optimized parameters of a deliberately introduced unsteady flow component. The method is applied in detail to two-dimensional (2D) advective mixing in flows resulting from the superposition of a transport flow through a channel and secondary localized cross-flows, here the vortical streaming due to a microbubble array. A simple description of stirring in a steady 2D vortex identifies the characteristic time beyond which vortex stirring becomes ineffective, with slow algebraic decay of the mix-variance. Duty cycling of the vortices introduces flow unsteadiness, for which optimum duty cycling protocols are identified, following analytically from a few selected Eulerian properties of the combined transport and vortex stirring flow. In comparison with experiments and simulations, it is shown that this simple formalism allows for the accurate prediction of optimal advective mixing, exponential in time, in the microbubble streaming case and, by extension, for any open-flow mixer with modulated secondary flow. Taking into account the effect of diffusion, estimated residence times required for complete mixing in such optimized devices are obtained. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Physical Review Fluids American Physical Society (APS)

Analysis of optimal mixing in open-flow mixers with time-modulated vortex arrays

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Analysis of optimal mixing in open-flow mixers with time-modulated vortex arrays

Abstract

In this work, a systematic approach to efficient open flow mixing is introduced, using general theoretical concepts to identify optimized parameters of a deliberately introduced unsteady flow component. The method is applied in detail to two-dimensional (2D) advective mixing in flows resulting from the superposition of a transport flow through a channel and secondary localized cross-flows, here the vortical streaming due to a microbubble array. A simple description of stirring in a steady 2D vortex identifies the characteristic time beyond which vortex stirring becomes ineffective, with slow algebraic decay of the mix-variance. Duty cycling of the vortices introduces flow unsteadiness, for which optimum duty cycling protocols are identified, following analytically from a few selected Eulerian properties of the combined transport and vortex stirring flow. In comparison with experiments and simulations, it is shown that this simple formalism allows for the accurate prediction of optimal advective mixing, exponential in time, in the microbubble streaming case and, by extension, for any open-flow mixer with modulated secondary flow. Taking into account the effect of diffusion, estimated residence times required for complete mixing in such optimized devices are obtained.
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Publisher
The American Physical Society
Copyright
Copyright © ©2017 American Physical Society
eISSN
2469-990X
D.O.I.
10.1103/PhysRevFluids.2.064501
Publisher site
See Article on Publisher Site

Abstract

In this work, a systematic approach to efficient open flow mixing is introduced, using general theoretical concepts to identify optimized parameters of a deliberately introduced unsteady flow component. The method is applied in detail to two-dimensional (2D) advective mixing in flows resulting from the superposition of a transport flow through a channel and secondary localized cross-flows, here the vortical streaming due to a microbubble array. A simple description of stirring in a steady 2D vortex identifies the characteristic time beyond which vortex stirring becomes ineffective, with slow algebraic decay of the mix-variance. Duty cycling of the vortices introduces flow unsteadiness, for which optimum duty cycling protocols are identified, following analytically from a few selected Eulerian properties of the combined transport and vortex stirring flow. In comparison with experiments and simulations, it is shown that this simple formalism allows for the accurate prediction of optimal advective mixing, exponential in time, in the microbubble streaming case and, by extension, for any open-flow mixer with modulated secondary flow. Taking into account the effect of diffusion, estimated residence times required for complete mixing in such optimized devices are obtained.

Journal

Physical Review FluidsAmerican Physical Society (APS)

Published: Jun 26, 2017

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