### Abstract

A new 3-D periodic Stokes flow has been imagined and realized experimentally. It consists of axial Poiseuille flow superimposed on the 2-D tangential motion between two confocal ellipses that glide circumferentially so that the geometry is invariant. Using a numerical experiment to study the advection of a passive scalar. we show that for a given 3-D mixer geometry and flow rate there is an optimum modulation frequency of the boundary displacement protocol for which the mixing process is most efficient. Furthermore, it is shown that chaotic advection can be regarded as a frequency-selective amplifier. This behavior is not unlike that of fluid stability where external perturbations are amplified for a certain frequency range. For values above or below this range. perturbations are damped and the system is stable.

Original language | English |
---|---|

Pages (from-to) | 271-276 |

Number of pages | 6 |

Journal | Computer Aided Chemical Engineering |

Volume | 18 |

Issue number | C |

DOIs | |

Publication status | Published - 2004 |

Event | 14th European Symposium on Computer Aided Process Engineering (ESCAPE-14) - Lisbon, Portugal Duration: 16 May 2004 → 19 May 2004 |

### Keywords

- CHAOTIC ADVECTION
- CONFOCAL ELLIPSES
- TRANSPORT

### Cite this

*Computer Aided Chemical Engineering*,

*18*(C), 271-276. https://doi.org/10.1016/S1570-7946(04)80111-1

}

*Computer Aided Chemical Engineering*, vol. 18, no. C, pp. 271-276. https://doi.org/10.1016/S1570-7946(04)80111-1

**Optimization of mixing protocol in a 3-D time-periodic Stokes flow.** / Rodrigo, A. J. S.; Rodrigues, R. C. R.; Formiga, N. F. C.; Mota, José Paulo Barbosa; Lefevre, A.; Saatdjian, E.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Optimization of mixing protocol in a 3-D time-periodic Stokes flow

AU - Rodrigo, A. J. S.

AU - Rodrigues, R. C. R.

AU - Formiga, N. F. C.

AU - Mota, José Paulo Barbosa

AU - Lefevre, A.

AU - Saatdjian, E.

PY - 2004

Y1 - 2004

N2 - A new 3-D periodic Stokes flow has been imagined and realized experimentally. It consists of axial Poiseuille flow superimposed on the 2-D tangential motion between two confocal ellipses that glide circumferentially so that the geometry is invariant. Using a numerical experiment to study the advection of a passive scalar. we show that for a given 3-D mixer geometry and flow rate there is an optimum modulation frequency of the boundary displacement protocol for which the mixing process is most efficient. Furthermore, it is shown that chaotic advection can be regarded as a frequency-selective amplifier. This behavior is not unlike that of fluid stability where external perturbations are amplified for a certain frequency range. For values above or below this range. perturbations are damped and the system is stable.

AB - A new 3-D periodic Stokes flow has been imagined and realized experimentally. It consists of axial Poiseuille flow superimposed on the 2-D tangential motion between two confocal ellipses that glide circumferentially so that the geometry is invariant. Using a numerical experiment to study the advection of a passive scalar. we show that for a given 3-D mixer geometry and flow rate there is an optimum modulation frequency of the boundary displacement protocol for which the mixing process is most efficient. Furthermore, it is shown that chaotic advection can be regarded as a frequency-selective amplifier. This behavior is not unlike that of fluid stability where external perturbations are amplified for a certain frequency range. For values above or below this range. perturbations are damped and the system is stable.

KW - CHAOTIC ADVECTION

KW - CONFOCAL ELLIPSES

KW - TRANSPORT

U2 - 10.1016/S1570-7946(04)80111-1

DO - 10.1016/S1570-7946(04)80111-1

M3 - Article

VL - 18

SP - 271

EP - 276

JO - Computer Aided Chemical Engineering

JF - Computer Aided Chemical Engineering

SN - 1570-7946

IS - C

ER -