Advection and Taylor-Aris dispersion in rivulet flow

F. H. H. Al Mukahal, B. R. Duffy, S. K. Wilson

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

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.
LanguageEnglish
Article number20170524
JournalProceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
Volume473
Issue number2207
DOIs
Publication statusPublished - 15 Nov 2017

Fingerprint

Advection
advection
solutes
Substrate
Microfluidics
Substrates
Steady flow
Inclined
Diffusivity
Steady Flow
Shear Stress
Free Surface
Shear stress
Gravity
Gravitation
steady flow
Vertical
shear stress
diffusivity
gravitation

Keywords

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

Cite this

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

In: Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol. 473, No. 2207, 20170524, 15.11.2017.

Research output: Contribution to journalArticle

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

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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

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