MATHEMATICAL ANALYSIS OF UNSTEADY SOLUTE DISPERSION IN BLOOD FLOW WITH REVERSIBLE AND IRREVERSIBLE BOUNDARY ABSORPTION

2017 ◽  
Vol 102 (1) ◽  
pp. 1-54
Author(s):  
Nurul Aini Jaafar ◽  
Yazariah Mohd Yatim ◽  
D. S. Sankar
Keyword(s):  
Blood Flow ◽  
Mathematical Analysis ◽  
Solute Dispersion ◽  
Boundary Absorption

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

2021 ◽  
Vol 86 (2) ◽  
pp. 56-73
Author(s):  
Nurul Aini Jaafar ◽  
Siti NurulAifa Mohd ZainulAbidin ◽  
Zuhaila Ismail ◽  
Ahmad Qushairi Mohamad
Keyword(s):  
Blood Flow ◽  
Chemical Reaction ◽  
Power Law ◽  
Plug Flow ◽  
Arterial Disease ◽  
Arterial Stenosis ◽  
Dispersion Function ◽  
Dispersion Process ◽  
Solute Dispersion ◽  
Power Law Index

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.

scholarly journals Mathematical Analysis of Non-Newtonian Blood Flow in Stenosis Narrow Arteries

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Somchai Sriyab
Keyword(s):  
Blood Flow ◽  
Skin Friction ◽  
Yield Stress ◽  
Newtonian Fluid ◽  
Mathematical Analysis ◽  
Viscosity Coefficient ◽  
Plasma Viscosity ◽  
Casson Model ◽  
Mild Stenosis ◽  
Normal Artery

The flow of blood in narrow arteries with bell-shaped mild stenosis is investigated that treats blood as non-Newtonian fluid by using the K-L model. When skin friction and resistance of blood flow are normalized with respect to non-Newtonian blood in normal artery, the results present the effect of stenosis length. When skin friction and resistance of blood flow are normalized with respect to Newtonian blood in stenosis artery, the results present the effect of non-Newtonian blood. The effect of stenosis length and effect of non-Newtonian fluid on skin friction are consistent with the Casson model in which the skin friction increases with the increase of ither stenosis length or the yield stress but the skin friction decreases with the increase of plasma viscosity coefficient. The effect of stenosis length and effect of non-Newtonian fluid on resistance of blood flow are contradictory. The resistance of blood flow (when normalized by non-Newtonian blood in normal artery) increases when either the plasma viscosity coefficient or the yield stress increases, but it decreases with the increase of stenosis length. The resistance of blood flow (when normalized by Newtonian blood in stenosis artery) decreases when either the plasma viscosity coefficient or the yield stress increases, but it decreases with the increase of stenosis length.

scholarly journals Unsteady solute dispersion in small blood vessels using a two-phase Casson model

2017 ◽  
Vol 473 (2204) ◽  
pp. 20170427 ◽  
Author(s):  
Jyotirmoy Rana ◽  
P. V. S. N. Murthy
Keyword(s):  
Blood Flow ◽  
Dispersion Model ◽  
Fluid Model ◽  
Two Phase ◽  
Small Arteries ◽  
Solute Dispersion ◽  
Small Vessels ◽  
Significant Difference ◽  
Casson Fluid Model ◽  
Mean Concentration

This study explores the transport of a solute in an unsteady blood flow in small arteries with and without absorption at the wall. The Casson fluid model is suitable for blood flow in small vessels. Owing to the aggregation of red cells in the central region of the small vessels, a two-phase model is considered in this investigation. Using the generalized dispersion model (Sankarasubramanian & Gill 1973 Proc. R. Soc. Lond. A 333 , 115–132. (doi:10.1098/rspa.1973.0051)), the convection, dispersion and mean concentration of the solute are analysed at all times in small arteries of different radii. The effects of the yield stress, wall absorption, the amplitude of the fluctuating pressure gradient component, the peripheral layer thickness, the Womersley frequency parameter, the Schmidt number and the Peclet number on the dispersion process are discussed. A comparative study of solute dispersion among single- and two-phase fluid models is presented. For small vessels, a significant difference between these models is observed during the solute dispersion; however, this difference becomes insignificant for large vessels. The mean concentration of solute reduces with increasing radius of the vessels. The present investigation is more realistic for understanding the transportation process of drugs in blood flow in small arteries using the non-Newtonian fluid model.

Attempts in the Mathematical Analysis of Blood Flow

1963 ◽  
Vol 7 (1) ◽  
pp. 25-31 ◽  
Author(s):  
E. A. Fox ◽  
Edward Saibel
Keyword(s):  
Blood Flow ◽  
Mathematical Analysis
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