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.

On the thin-film asymptotics of surface tension driven microfluidics

“…Additional studies may also consider how the peculiar patterns of flow within these devices affect chemical transport (Walsh et al 2017), building on previous studies of transport within rivulets (e.g. Darhuber et al 2004; Al Mukahal, Duffy & Wilson 2017). Throughout we have only considered straight conduits with a constant width.…”

The effect of body acceleration on the dispersion of solute in a non-Newtonian blood flow through an artery

“…In a Newtonian fluid, the dispersion theory called Taylor-Aris was used to examine the solute’s unsteady dispersion using the separation of variables (Mukahal and Habib, 2017; Kori, 2020). By treating the blood as Bingham, Power-law and Casson fluids by applying Taylor-Aris dispersion theory, Sharp (1993) analytically studied steady solute dispersion.…”

Investigation of Drift Phenomena at the Pore Scale during Flow and Transport in Porous Media

“…Mass spreading of non-reactive tracers can be described by a combination of molecular diffusion, hydrodynamic dispersion and heterogeneous advection [13]. The hydrodynamic dispersion is usually quantified by the sum of the molecular diffusion and advection components.…”

“…Many models have been developed to describe the space anomalous behaviour of dispersion coefficients (for example flow through rivulet [14], random capillaries [15]). Al Mukahal et al, 2017 provide a description of long-time Taylor-Aris dispersion of solute by using multiple scales to arrive at the expression of effective diffusivity. However, problems associated with Taylor dispersion in a capillary tube are momentous, i.e possibility of micro-macro duality and their interrelationship among scales manifest [16].…”