### Abstract

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

Article number | 20170524 |

Journal | Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences |

Volume | 473 |

Issue number | 2207 |

DOIs | |

Publication status | Published - 15 Nov 2017 |

### Fingerprint

### Keywords

- mathematical modelling
- advection
- Taylor-Aris dispersion
- rivulet

### Cite this

*Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences*,

*473*(2207), [20170524]. https://doi.org/10.1098/rspa.2017.0524

}

*Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences*, vol. 473, no. 2207, 20170524. https://doi.org/10.1098/rspa.2017.0524

**Advection and Taylor-Aris dispersion in rivulet flow.** / Al Mukahal, F. H. H.; Duffy, B. R.; Wilson, S. K.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Advection and Taylor-Aris dispersion in rivulet flow

AU - Al Mukahal, F. H. H.

AU - Duffy, B. R.

AU - Wilson, S. K.

PY - 2017/11/15

Y1 - 2017/11/15

N2 - Motivated by the need for a better understanding of the transport of solutes in microfluidic flows with free surfaces, the advection and dispersion of a passive solute in steady unidirectional flow of a thin uniform rivulet on an inclined planar substrate driven by gravity and/or a uniform longitudinal surface shear stress are analysed. Firstly, we describe the short-time advection of both an initially semi-infinite and an initially finite slug of solute of uniform concentration. Secondly, we describe the long-time Taylor-Aris dispersion of an initially finite slug of solute. In particular, we obtain the general expression for the effective diffusivity for Taylor-Aris dispersion in such a rivulet, and discuss in detail its different interpretations in the special case of a rivulet on a vertical substrate.

AB - Motivated by the need for a better understanding of the transport of solutes in microfluidic flows with free surfaces, the advection and dispersion of a passive solute in steady unidirectional flow of a thin uniform rivulet on an inclined planar substrate driven by gravity and/or a uniform longitudinal surface shear stress are analysed. Firstly, we describe the short-time advection of both an initially semi-infinite and an initially finite slug of solute of uniform concentration. Secondly, we describe the long-time Taylor-Aris dispersion of an initially finite slug of solute. In particular, we obtain the general expression for the effective diffusivity for Taylor-Aris dispersion in such a rivulet, and discuss in detail its different interpretations in the special case of a rivulet on a vertical substrate.

KW - mathematical modelling

KW - advection

KW - Taylor-Aris dispersion

KW - rivulet

UR - http://rspa.royalsocietypublishing.org/

U2 - 10.1098/rspa.2017.0524

DO - 10.1098/rspa.2017.0524

M3 - Article

VL - 473

JO - Proceedings A: Mathematical, Physical and Engineering Sciences

JF - Proceedings A: Mathematical, Physical and Engineering Sciences

SN - 1364-5021

IS - 2207

M1 - 20170524

ER -