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Cite Details

R. A. Zimmerman, G. Severino and D. M. Tartakovsky, "Hydrodynamic dispersion in a tube with diffusive losses through its walls", J. Fluid Mech., vol. 837, doi:10.1017/jfm.2017.870, pp. 546-561, 2018


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.

BibTeX Entry

author = {R. A. Zimmerman and G. Severino and D. M. Tartakovsky},
title = {Hydrodynamic dispersion in a tube with diffusive losses through its walls},
year = {2018},
urlpdf = {},
journal = {J. Fluid Mech.},
volume = {837},
doi = {10.1017/jfm.2017.870},
pages = {546-561}