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

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Abstract

The present article discusses the solute transport process in steady 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 is 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.

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Acknowledgements

The authors wish to thank Prof. Pradeep. G. Siddheshwar, for his excellent advice in the development of the mathematical model. We thank the referees for useful comments that refined the paper to the present form. All the authors also appreciate the helpful comments of the reviewers which have improved the manuscript in clarity.

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Authors and Affiliations

  1. Department of Science & Humanities, Tripura Institute of Technology, Agartala, Tripura, 799009, India

    Ashis Kumar Roy

  2. Multi-Physical Engineering Sciences Group, Mechanical Engineering Department, School of Science, Engineering and Environment (SEE), University of Salford, Manchester, UK

    O. Anwar Bég

  3. Department of Mathematics, National Institute of Technology Agartala, Tripura, 799046, India

    Apu Kumar Saha

  4. Department of Mathematics, National Institute of Technology Warangal, Warangal, Telangana, 506004, India

    J. V. Ramana Murthy

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  1. Ashis Kumar Roy
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Roy, A.K., Bég, O.A., Saha, A.K. et al. Taylor dispersion in non-Darcy porous media with bulk chemical reaction: a model for drug transport in impeded blood vessels. J Eng Math 127, 24 (2021). https://doi.org/10.1007/s10665-021-10120-8

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