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Discontinuity, Nonlinearity, and Complexity 11(3) (2022) 553--568 | DOI:10.5890/DNC.2022.09.015

Annah J. Moitoi, Sachin Shaw

Department of Mathematics and Statistical Sciences, Botswana International University of Science \&

Technology, Private Bag 16, Palapye, Botswana

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Abstract

The study of the longitudinal dispersion of a drug delivered through a microvessel is irreversibly absorbed or undergoes an exchange process at the boundary and has many applications in the field of chemical engineering, environmental dynamics, biomedical engineering and physiological fluid dynamics. The dispersion of nanoparticles plays a vital role in medical science during drug delivery through a microvessel. The current problem deals with the dispersion characteristic of blood during drug delivery through a microvessel. The nature of the blood flow is considered as a two phase fluid model, where clear region is considered as non-Newtonian Herschel-Bulkley fluid which followed a nonlinear relation between the shear stress and shear rate, while the peripheral region is considered as Newtonian fluid. The governing equations are solved analytically in the form of Bessel functions while others are solved in the form of numerical integration method. Several factors that influence the dispersion of nanoparticles during drug delivery in a microvessel, such as pressure distribution, nanoparticles volume fraction, the permeability of the blood vessel, yield stress and the radius of the nanoparticle were considered in the present problem. It is observed that the effective diffusion of the nanoparticles reduces with increase in nanoparticles volume fraction and the permeability of the blood vessels increases the effective dispersion at the inlet.

Acknowledgments

Authors Annah Moitoi and Sachin Shaw gives thanks to Botswana International University of Science and Technology (Project no.DVC/RDI/2/1/161(35)) and Simons Foundation for its support.

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