Mathematical Modeling of Unsteady Solute Dispersion in Bingham Fluid Model of Blood Flow Through an Overlapping Stenosed Artery

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 Bingham fluid model. The governing of the momentum equation and the constitutive equation is solved analytically. The generalized dispersion model is imposed to solve the convective-diffusion equation and to describe the entire dispersion process. The dispersion function at steady-state decreases at the center of an artery as the stenosis height increase. A reverse behavior is shown at an unsteady-state. As the plug core radius, time and stenosis height increase, the dispersion function decreases at the center of an artery. There is a high amount of red blood cells at the center of the artery but no influences near the wall. Hence, this model is useful in transporting the drug or nutrients to the targeted stenosed region in the treatment of diseases and in understanding many physiological processes.

Mathematical Analysis of Unsteady Solute Dispersion with Chemical Reaction Through a Stenosed Artery

One major kind of arterial disease in blood flow that attracted many researchers is arterial stenosis. Arterial stenosis occurs when a lumen of artery is narrowed by the accumulation of fats, cholesterols and lipids plaques at the inner layer of the wall of an artery. To treat this arterial disease, the drug (solute) is injected into the blood vessels. Injection of the drug into the blood vessel cause the occurrence of chemical reaction between the drug and blood proteins and it affects the effectiveness of the solute transportation in blood flow. Hence, this study examines the unsteady dispersion of solute with the influence of chemical reaction and stenosis height through a very narrow artery with a cosine-curved stenosis. The blood is treating as Herschel-Bulkley (H-B) fluid. The momentum and constitutive equations are solved analytically to gain velocity of H-B blood flow. The convective-diffusion equation is solved by applying the generalized dispersion model to gain the dispersion function of solute. The influence of chemical reaction, power-law index, plug flow radius and stenosis height on the solute dispersion process is investigated. The results are validated with the previous solution without the effect of chemical reaction and stenosis. The results showed a good conformity between the two solutions. An increase in the chemical reaction coefficient, stenosis height, power-law index and plug flow radius reduces the dispersion function. It is observed that the solute dispersion in blood flow is affected by chemical reaction and stenosis height. H-B fluid is an appropriate fluid to investigate the blood velocity and transportation of the drug in blood flow to the targeted stenosed region through a very narrow artery for the treatment of arterial diseases. The results of the present study can potentially be used to predict the changes of blood flow behavior and dispersion process in blood flow.