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Hydrodynamic dispersion in a tube with diffusive losses through its walls

Published online by Cambridge University Press:  05 January 2018

R. A. Zimmerman ,
G. Severino  and
D. M. Tartakovsky Open the ORCID record for D. M. Tartakovsky [Opens in a new window]
R. A. Zimmerman
Affiliation:
Applied Engineering and Technology – 1, Los Alamos National Laboratory, Los Alamos, NM 87545, USA
G. Severino
Affiliation:
Department of Agricultural Sciences, University of Naples – Federico II, via Università 100, 80055 Portici (NA), Italy
D. M. Tartakovsky*
Affiliation:
Department of Energy Resources Engineering, Stanford University, 367 Panama Street, Stanford, CA 94305, USA
*
†Email address for correspondence: tartakovsky@stanford.edu
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Abstract

Advective–diffusive transport of passive or reactive scalars in confined environments (e.g. tubes and channels) is often accompanied by diffusive losses/gains through the confining walls. We present analytical solutions for transport of a reactive solute in a tube, whose walls are impermeable to flow but allow for solute diffusion into the surrounding medium. The solute undergoes advection, diffusion and first-order chemical reaction inside the tube, while diffusing and being consumed in the surrounding medium. These solutions represent a leading-order (in the radius-to-length ratio) approximation, which neglects the longitudinal variability of solute concentration in the surrounding medium. A numerical solution of the full problem is used to demonstrate the accuracy of this approximation for a physically relevant range of model parameters. Our analysis indicates that the solute delivery rate can be quantified by a dimensionless parameter, the ratio of a solute’s residence time in a tube to the rate of diffusive losses through the tube’s wall.

JFM classification

Biological Fluid Dynamics: Biological Fluid Dynamics Biological Fluid Dynamics: Biomedical flows
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 837 , 25 February 2018 , pp. 546 - 561
Copyright
© 2018 Cambridge University Press 

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