### Abstract

Relative (effective) lateral dispersion of a passive solute was examined at transitional Reynolds numbers within a two-dimensional array of randomly distributed circular cylinders of uniform diameter d. The present work focuses on dense arrays, for which previously developed theory [Y. Tanino and H. M. Nepf, J. Fluid Mech. 600, 339 (2008)] implies that the asymptotic (long-time/long-distance) dispersion coefficient, when normalized by the mean interstitial fluid velocity, u, and d, will only exhibit a weak dependence on Reynolds number, Re-d equivalent to ud/nu, where nu is the kinematic viscosity. However, the advective distance required to reach asymptotic dispersion is expected to be controlled by pore-scale mixing, which is strongly Re-d-dependent prior to the onset of full turbulence. Laser-induced fluorescence was used to measure the time-averaged lateral concentration profiles of solute released continuously from a point source in arrays of solid volume fraction phi=0.20 and 0.35 at Re-d=48-120. Results are compared to previous measurements at higher Re-d. Lateral dispersion reaches the same rate as asymptotic dispersion in fully turbulent flow at x approximate to 154d at (phi,Re-d)=(0.20,110-120) and at x approximate to 87d at (phi,Re-d)=(0.35,300-390). In contrast, dispersion does not reach the fully turbulent flow limit at Re-d < 100 within the range of x considered. Also, concentration profiles deviate further from a Gaussian distribution at phi=0.35 than at 0.20 for similar Re-d and x phi/d. From these observations, it can be inferred that the pre-asymptotic regime extends farther downstream, in terms of the number of cylinders spanned, at lower Re-d and at larger phi.

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

Article number | 046603 |

Number of pages | 10 |

Journal | Physics of Fluids |

Volume | 21 |

Issue number | 4 |

DOIs | |

Publication status | Published - Apr 2009 |

### Keywords

- turbulent flows
- laminar flows
- solution processes
- turbulent diffusion
- laser induced fluorescence

### Cite this

**Laboratory investigation of lateral dispersion within dense arrays of randomly distributed cylinders at transitional Reynolds number.** / Tanino, Yukie; Nepf, Heidi M.

Research output: Contribution to journal › Article

*Physics of Fluids*, vol. 21, no. 4, 046603. https://doi.org/10.1063/1.3119862

}

TY - JOUR

T1 - Laboratory investigation of lateral dispersion within dense arrays of randomly distributed cylinders at transitional Reynolds number

AU - Tanino, Yukie

AU - Nepf, Heidi M.

N1 - This material is based on work supported by the National Science Foundation under Grant No. EAR0309188. Any opinions, conclusions, or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the National Science Foundation. We thank the three anonymous reviewers for their comments.

PY - 2009/4

Y1 - 2009/4

N2 - Relative (effective) lateral dispersion of a passive solute was examined at transitional Reynolds numbers within a two-dimensional array of randomly distributed circular cylinders of uniform diameter d. The present work focuses on dense arrays, for which previously developed theory [Y. Tanino and H. M. Nepf, J. Fluid Mech. 600, 339 (2008)] implies that the asymptotic (long-time/long-distance) dispersion coefficient, when normalized by the mean interstitial fluid velocity, u, and d, will only exhibit a weak dependence on Reynolds number, Re-d equivalent to ud/nu, where nu is the kinematic viscosity. However, the advective distance required to reach asymptotic dispersion is expected to be controlled by pore-scale mixing, which is strongly Re-d-dependent prior to the onset of full turbulence. Laser-induced fluorescence was used to measure the time-averaged lateral concentration profiles of solute released continuously from a point source in arrays of solid volume fraction phi=0.20 and 0.35 at Re-d=48-120. Results are compared to previous measurements at higher Re-d. Lateral dispersion reaches the same rate as asymptotic dispersion in fully turbulent flow at x approximate to 154d at (phi,Re-d)=(0.20,110-120) and at x approximate to 87d at (phi,Re-d)=(0.35,300-390). In contrast, dispersion does not reach the fully turbulent flow limit at Re-d < 100 within the range of x considered. Also, concentration profiles deviate further from a Gaussian distribution at phi=0.35 than at 0.20 for similar Re-d and x phi/d. From these observations, it can be inferred that the pre-asymptotic regime extends farther downstream, in terms of the number of cylinders spanned, at lower Re-d and at larger phi.

AB - Relative (effective) lateral dispersion of a passive solute was examined at transitional Reynolds numbers within a two-dimensional array of randomly distributed circular cylinders of uniform diameter d. The present work focuses on dense arrays, for which previously developed theory [Y. Tanino and H. M. Nepf, J. Fluid Mech. 600, 339 (2008)] implies that the asymptotic (long-time/long-distance) dispersion coefficient, when normalized by the mean interstitial fluid velocity, u, and d, will only exhibit a weak dependence on Reynolds number, Re-d equivalent to ud/nu, where nu is the kinematic viscosity. However, the advective distance required to reach asymptotic dispersion is expected to be controlled by pore-scale mixing, which is strongly Re-d-dependent prior to the onset of full turbulence. Laser-induced fluorescence was used to measure the time-averaged lateral concentration profiles of solute released continuously from a point source in arrays of solid volume fraction phi=0.20 and 0.35 at Re-d=48-120. Results are compared to previous measurements at higher Re-d. Lateral dispersion reaches the same rate as asymptotic dispersion in fully turbulent flow at x approximate to 154d at (phi,Re-d)=(0.20,110-120) and at x approximate to 87d at (phi,Re-d)=(0.35,300-390). In contrast, dispersion does not reach the fully turbulent flow limit at Re-d < 100 within the range of x considered. Also, concentration profiles deviate further from a Gaussian distribution at phi=0.35 than at 0.20 for similar Re-d and x phi/d. From these observations, it can be inferred that the pre-asymptotic regime extends farther downstream, in terms of the number of cylinders spanned, at lower Re-d and at larger phi.

KW - turbulent flows

KW - laminar flows

KW - solution processes

KW - turbulent diffusion

KW - laser induced fluorescence

U2 - 10.1063/1.3119862

DO - 10.1063/1.3119862

M3 - Article

VL - 21

JO - Physics of Fluids

JF - Physics of Fluids

SN - 1070-6631

IS - 4

M1 - 046603

ER -