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

2021 ◽  
Vol 87 (3) ◽  
pp. 134-147
Author(s):  
Siti Nurulaifa Mohd ZainulAbidin ◽  
Zuhaila Ismail ◽  
Nurul Aini Jaafar
Keyword(s):  
Blood Flow ◽  
Dispersion Model ◽  
Fluid Model ◽  
Momentum Equation ◽  
Bingham Fluid ◽  
Dispersion Function ◽  
Solute Dispersion ◽  
Stenosed Artery ◽  
Flow Through ◽  
Height Increase

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.

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.

scholarly journals UNSTEADY TWO-LAYERED BLOOD FLOW THROUGH A -SHAPED STENOSED ARTERY USING THE GENERALIZED OLDROYD-B FLUID MODEL

2016 ◽  
Vol 58 (1) ◽  
pp. 96-118 ◽  
Author(s):  
AKBAR ZAMAN ◽  
NASIR ALI ◽  
O. ANWAR BEG ◽  
M. SAJID
Keyword(s):  
Blood Flow ◽  
Differential Equations ◽  
Newtonian Fluid ◽  
Numerical Solutions ◽  
Fluid Model ◽  
Initial Boundary ◽  
Momentum Conservation ◽  
Rheological Parameters ◽  
Stenosed Artery ◽  
Flow Through

A theoretical study of an unsteady two-layered blood flow through a stenosed artery is presented in this article. The geometry of a rigid stenosed artery is assumed to be$w$-shaped. The flow regime is assumed to be laminar, unsteady and uni-directional. The characteristics of blood are modelled by the generalized Oldroyd-B non-Newtonian fluid model in the core region and a Newtonian fluid model in the periphery region. The governing partial differential equations are derived for each region by using mass and momentum conservation equations. In order to facilitate numerical solutions, the derived differential equations are nondimensionalized. A well-tested explicit finite-difference method (FDM) which is forward in time and central in space is employed for the solution of a nonlinear initial boundary value problem corresponding to each region. Validation of the FDM computations is achieved with a variational finite element method algorithm. The influences of the emerging geometric and rheological parameters on axial velocity, resistance impedance and wall shear stress are displayed graphically. The instantaneous patterns of streamlines are also presented to illustrate the global behaviour of the blood flow. The simulations are relevant to haemodynamics of small blood vessels and capillary transport, wherein rheological effects are dominant.

scholarly journals On Two-Fluid Blood Flow through Stenosed Artery with Permeable Wall

2014 ◽  
Vol 11 (1-2) ◽  
pp. 39-45
Author(s):  
Rupesh K. Srivastav ◽  
V. P. Srivastava
Keyword(s):  
Blood Flow ◽  
Present Model ◽  
Fluid Model ◽  
Flow Characteristics ◽  
Mechanical Study ◽  
Stenosed Artery ◽  
Flow Through ◽  
Flowing Blood ◽  
Two Fluid Model ◽  
Two Fluid

The present investigation concerns the fluid mechanical study on the effects of the permeability of the wall through an axisymmetric stenosis in an artery assuming that the flowing blood is represented by a two-fluid model. The expressions for the blood flow characteristics, the impedance, the wall shear stress distribution in the stenotic region and the shearing stress at the stenosis throat have been derived. Results for the effects of permeability as well as of the peripheral layer on these blood flow characteristics are quantified through numerical computations and presented graphically and discussed comparatively to validate the applicability of the present model.

scholarly journals Herschel-Bulkley Model of Blood Flow through a Stenosed Artery with the Effect of Chemical Reaction on Solute Dispersion

2021 ◽  
Vol 17 (4) ◽  
pp. 457-474
Author(s):  
Siti Nurul Aifa Mohd Zainul Abidin ◽  
Nurul Aini Jaafar ◽  
Zuhaila Ismail
Keyword(s):  
Blood Flow ◽  
Chemical Reaction ◽  
Fluid Model ◽  
Plug Flow ◽  
Circulatory System ◽  
Mean Velocity ◽  
Axial Diffusivity ◽  
Length Increase ◽  
Stenosed Artery ◽  
Flow Through

A non-Newtonian mathematical model of blood described as a Hershel-Bulkley fluid model flowing in a stenosed artery with the effect of a chemical reaction is mathematically studied. The expressions of the shear stress, mean velocity and absolute velocity in the plug and non-plug flow field are evaluated analytically. The convective-diffusion equation is solved using the Taylor-Aris technique subject to the relevant boundary constraint in determining the concentration, relative and effective axial diffusivity. The efficiency of the dispersion process is affected by the presence of chemical reaction and stenosis in blood flow. The normalized velocity decreases as stenosis height and stenosis length increase. The relative axial diffusivity is significantly lower while the effective axial diffusivity decreases considerably as the chemical reaction rate, the height of the stenosis and the length of the stenosis increase. Besides, it is observed that as the solute disperses in the presence of stenosis, the flow quantities are lesser than in the absence of stenosis. Further, this study helps in understanding many physiological processes for instance dispersion of drugs or nutrients in the circulatory system. Also, to enhance the dispersion of a solute in blood flow through narrow arteries in the presence of chemical reaction and stenosis.

scholarly journals Numerical Modeling of Blood Flow in Irregular Stenosed Artery with the Effects of Gravity

2013 ◽  
Vol 62 (3) ◽  
Author(s):  
Tan Yan Bin ◽  
Norzieha Mustapha
Keyword(s):  
Blood Flow ◽  
Gravitational Force ◽  
Stokes Equations ◽  
Numerical Study ◽  
Momentum Equation ◽  
Navier Stokes ◽  
Governing Equations ◽  
Navier Stokes Equations ◽  
Stenosed Artery ◽  
Flow Through

A numerical study on the influences of gravitational force on an unsteady two–dimensional nonlinear model of blood flow through a stenosed artery is presented. Blood flow through the constricted region with an irregular stenosis is considered as incompressible Newtonian fluid. The governing equations are derived from the Navier–Stokes equations, which also comprise a significant term for gravitational force in the axial momentum equation. The numerical method chosen in this study is the finite difference approximations based on Marker and Cell (MAC) method at which governing equations are develop in staggered grids for discretization. The Poisson equation of pressure is solved by successive–over–relaxation (S.O.R.) method. Pressure–velocity corrector is imposed to increase accuracy. Streamlines, wall shear stress and axial velocity profiles are plotted.

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