Advection and Taylor-Aris dispersion in rivulet flow

Al Mukahal, F. H. H. and Duffy, B. R. and Wilson, S. K. (2017) Advection and Taylor-Aris dispersion in rivulet flow. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 473 (2207). 20170524. ISSN 1471-2962 (

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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.