Page 34 - programme book

AM-007
Exact Analysis of Unsteady Solute Dispersion in Blood Flow – A
Theoretical Study

Siti Nurul Aifa Mohd Zainul Abidin 1, a) , Nurul Aini Jaafar 1, b) and Zuhaila Ismail 1, c)

1,2,3 Department of Mathematical Sciences, Faculty of Science, Universiti Teknologi Malaysia,
81310 UTM Skudai, Johor, Malaysia.

c) Corresponding author: zuhaila@utm.my
a) nurulaifa@graduate.utm.my
b) nurulaini.jaafar@utm.my

Abstract. An artery narrowing referred to as atherosclerosis or stenosis causes a reduction in the
diameter of the artery. When blood flow through an artery consists of stenosis, the issue of solute
dispersion is more challenging to solve. A mathematical model is developed to examine the
unsteady solute dispersion in an overlapping stenosed artery portraying blood as Herschel-
Bulkley fluid model. The governing and the constitutive equation is solved analytically to get the
velocity of fluid. The generalized dispersion model (GDM) is imposed to solve the convective-
diffusion equation and to describe the entire dispersion process. The peak of mean concentration
of solute increases with an increase in the slug input of solute length, power-law index, yield
stress and stenosis height. The maximum mean concentration is the effective dose for therapeutic
concentration. The existence of stenosis restricted the blood flow and drug dispersion. In short,
this study improved the understanding of the physiological processes involved in transporting
the drugs and nutrients to the targeted stenosed region in the circulatory system.

Keywords: Blood flow, Solute, Dispersion, Herschel-Bulkley fluid, Concentration.

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