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Shear-augmented solute dispersion during drug delivery for three-layer flow through microvessel under stress jump and momentum slip-Darcy model

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Abstract

Nanoparticle (drug particle) dispersion is an important phenomenon during nanodrug delivery in the bloodstream by using multifunctional carrier particles. The aim of this study is to understand the dispersion of drug particle (nanoparticle) transport during steady blood flow through a microvessel. A two-phase fluid model is considered to define blood flow through a microvessel. Plug and intermediate regions are defined by a non-Newtonian Herschel-Bulkley fluid model where the plug region appears due to the aggregation of red blood cells at the axis in the vessel. The peripheral (porous in nature) region is defined by the Newtonian fluids. The wall of the microvessel is considered to be permeable and characterized by the Darcy model. Stress-jump and velocity slip conditions are incorporated respectively at the interface of the intermediate and peripheral regions and at the inner surface of the microvessel. The effects of the rheological parameter, the pressure constant, the particle volume fraction, the stress jump constant, the slip constant, and the yield stress on the dispersion are analyzed and discussed. It is observed that the non-dimensional pressure gradient and the yield stress enhance the dispersion rate of the nanoparticle, while the opposite trends are observed for the velocity slip constant, the nanoparticle volume fraction, the rheological parameter, and the stress-jump constant.

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Acknowledgments

Authors G. BASHAGA and S. SHAW extend their uppermost gratitude to the Simons Foundation and Botswana International University of Science and Technology (No. DVC/RDI/2/1/161(35)) for their unwavering support.

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Authors and Affiliations

  1. Department of Mathematics and Statistical Sciences, Botswana International University of Science and Technology, Private Bag 16, Palapye, Botswana

    G. Bashaga & S. Shaw

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  1. G. Bashaga
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  2. S. Shaw
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Correspondence to S. Shaw.

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Project supported by the Botswana International University of Science and Technology (No. DVC/RDI/2/1/161(35))

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Bashaga, G., Shaw, S. Shear-augmented solute dispersion during drug delivery for three-layer flow through microvessel under stress jump and momentum slip-Darcy model. Appl. Math. Mech.-Engl. Ed. 42, 901–914 (2021). https://doi.org/10.1007/s10483-021-2737-8

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  • DOI: https://doi.org/10.1007/s10483-021-2737-8

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