Taylor dispersion in non-Darcy porous media with bulk chemical reaction : a model for drug transport in impeded blood vessels

Roy, AK; Beg, OA; Saha, AK; Ramana Murthy, JV

Abstract

The present article discusses the solute transport process in unsteady laminar blood flow through
a non-Darcy porous medium, as a model for drug movement in blood vessels containing deposits.
The Darcy-Brinkman-Forchheimer drag force formulation is adopted to mimic a sparsely packed
porous domain, and the vessel is approximated as an impermeable cylindrical conduit. The
conservation equations are implemented in an axisymmetric system (R,Z) with suitable boundary
conditions, assuming constant tortuosity and porosity of the medium. Newtonian flow is assumed,
which is physically realistic for large vessels at high shear rates. The velocity field is expanded
asymptotically, and the concentration field decomposed. Advection and dispersion coefficient
expressions are rigorously derived. Extensive visualization of the influence of effective Péclet
number, Forchheimer number, reaction parameter on velocity, asymptotic dispersion coefficient,
mean concentration, and transverse concentration at different axial locations and times are
provided. Increasing reaction parameter and Forchheimer number both decrease the dispersion
coefficient, although the latter exhibits a linear decay. The maximum mean concentration is
enhanced with greater Forchheimer numbers, although the centre of the solute cloud is displaced
in the backward direction. Peak mean concentration is suppressed with the reaction parameter,
although the centroid of the solute cloud remains unchanged. Peak mean concentration
deteriorates over time since the dispersion process is largely controlled by diffusion at the large
time, and therefore the breakthrough curve is more dispersed. A similar trend is computed with
increasing Péclet number (large Péclet numbers imply diffusion-controlled transport). The
computations provide some insight into a drug (pharmacological agents) reacting linearly with
blood.

Citation

Roy, A., Beg, O., Saha, A., & Ramana Murthy, J. (2021). Taylor dispersion in non-Darcy porous media with bulk chemical reaction : a model for drug transport in impeded blood vessels. Journal of Engineering Mathematics, 127(1), 24. https://doi.org/10.1007/s10665-021-10120-8

• Journal Article Type: Article
• Acceptance Date: Feb 26, 2021
• Publication Date: Mar 23, 2021
• Deposit Date: Feb 17, 2021
• Publicly Available Date: Mar 23, 2022
• Journal: Journal of Engineering Mathematics
• Print ISSN: 0022-0833
• Electronic ISSN: 1573-2703
• Publisher: Springer Verlag
• Volume: 127
• Issue: 1
• Pages: 24
• DOI: https://doi.org/10.1007/s10665-021-10120-8
• Publisher URL: https://doi.org/10.1007/s10665-021-10120-8
• Related Public URLs: http://link.springer.com/journal/10665
• Additional Information: Access Information : This is a post-peer-review, pre-copyedit version of an article published in Journal of Engineering Mathematics. The final authenticated version is available online at: http://dx.doi.org/10.1007/s10665-021-10120-8