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

Bhargav Rallabandi, Cheng Wang, Sascha Hilgenfeldt

Research output: Contribution to journalArticle

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.

Original languageEnglish (US)
Article number064501
JournalPhysical Review Fluids
Volume2
Issue number6
DOIs
StatePublished - Jun 1 2017

Fingerprint

Vortex
Vortex flow
Vortex Flow
Cycling
Streaming
Secondary Flow
Cross-flow
Residence Time
Secondary flow
Unsteady Flow
Unsteady flow
Superposition
Decay
Prediction
Experiment
Simulation
Experiments

ASJC Scopus subject areas

  • Computational Mechanics
  • Modeling and Simulation
  • Fluid Flow and Transfer Processes

Cite this

Analysis of optimal mixing in open-flow mixers with time-modulated vortex arrays. / Rallabandi, Bhargav; Wang, Cheng; Hilgenfeldt, Sascha.

In: Physical Review Fluids, Vol. 2, No. 6, 064501, 01.06.2017.

Research output: Contribution to journalArticle

@article{d72d469620be43a399c602fd786b1c67,
title = "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.",
author = "Bhargav Rallabandi and Cheng Wang and Sascha Hilgenfeldt",
year = "2017",
month = "6",
day = "1",
doi = "10.1103/PhysRevFluids.2.064501",
language = "English (US)",
volume = "2",
journal = "Physical Review Fluids",
issn = "2469-990X",
publisher = "American Physical Society",
number = "6",

}

TY - JOUR

T1 - Analysis of optimal mixing in open-flow mixers with time-modulated vortex arrays

AU - Rallabandi, Bhargav

AU - Wang, Cheng

AU - Hilgenfeldt, Sascha

PY - 2017/6/1

Y1 - 2017/6/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=85035123614&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85035123614&partnerID=8YFLogxK

U2 - 10.1103/PhysRevFluids.2.064501

DO - 10.1103/PhysRevFluids.2.064501

M3 - Article

VL - 2

JO - Physical Review Fluids

JF - Physical Review Fluids

SN - 2469-990X

IS - 6

M1 - 064501

ER -