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 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 Mechanics of non-Newtonian blood flow in an artery having multiple stenosis and electroosmotic effects

2021 ◽  
Vol 104 (3) ◽  
pp. 003685042110316
Author(s):  
Salman Akhtar ◽  
Luthais B McCash ◽  
Sohail Nadeem ◽  
Salman Saleem ◽  
Alibek Issakhov
Keyword(s):  
Blood Flow ◽  
Flow Problem ◽  
Fluid Model ◽  
Casson Fluid ◽  
Viscous Effects ◽  
Heating Effects ◽  
Casson Fluid Model ◽  
Flow Through ◽  
Mathematical Equations ◽  
Mathematica Software

The electro-osmotically modulated hemodynamic across an artery with multiple stenosis is mathematically evaluated. The non-Newtonian behaviour of blood flow is tackled by utilizing Casson fluid model for this flow problem. The blood flow is confined in such arteries due to the presence of stenosis and this theoretical analysis provides the electro-osmotic effects for blood flow through such arteries. The mathematical equations that govern this flow problem are converted into their dimensionless form by using appropriate transformations and then exact mathematical computations are performed by utilizing Mathematica software. The range of the considered parameters is given as [Formula: see text]. The graphical results involve combine study of symmetric and non-symmetric structure for multiple stenosis. Joule heating effects are also incorporated in energy equation together with viscous effects. Streamlines are plotted for electro-kinetic parameter [Formula: see text] and flow rate [Formula: see text]. The trapping declines in size with incrementing [Formula: see text], for symmetric shape of stenosis. But the size of trapping increases for the non-symmetric case.

Mathematical analysis of Phan-Thien–Tanner fluid model for blood in arteries

2015 ◽  
Vol 08 (05) ◽  
pp. 1550064
Author(s):  
Noreen Sher Akbar ◽  
S. Nadeem
Keyword(s):  
Blood Flow ◽  
Shear Stress ◽  
Wall Shear Stress ◽  
Fluid Model ◽  
Shearing Stress ◽  
Small Arteries ◽  
Tapered Artery ◽  
Impedance Wall ◽  
Flow Through ◽  
Parameters Of Interest

In the present paper, we have studied the blood flow through tapered artery with a stenosis. The non-Newtonian nature of blood in small arteries is analyzed mathematically by considering the blood as Phan-Thien–Tanner fluid. The representation for the blood flow is through an axially non-symmetrical but radially symmetric stenosis. Symmetry of the distribution of the wall shearing stress and resistive impedance and their growth with the developing stenosis is another important feature of our analysis. Exact solutions have been evaluated for velocity, resistance impedance, wall shear stress and shearing stress at the stenosis throat. The graphical results of different type of tapered arteries (i.e. converging tapering, diverging tapering, non-tapered artery) have been examined for different parameters of interest.

scholarly journals The Effects of Magnetic Casson Blood Flow in an Inclined Multi-stenosed Artery by using Caputo-Fabrizio Fractional Derivatives

2021 ◽  
Vol 82 (2) ◽  
pp. 28-38
Author(s):  
Dzuliana Fatin Jamil ◽  
Salah Uddin ◽  
Muhamad Ghazali Kamardan ◽  
Rozaini Roslan
Keyword(s):  
Blood Flow ◽  
Fractional Derivatives ◽  
Magnetic Particles ◽  
Hartmann Number ◽  
Fluid Model ◽  
Casson Fluid ◽  
Medical Problems ◽  
Casson Fluid Model ◽  
Stenosed Artery ◽  
Fractional Differential

This paper investigates the magnetic blood flow in an inclined multi-stenosed artery under the influence of a uniformly distributed magnetic field and an oscillating pressure gradient. The blood is modelled using the non-Newtonian Casson fluid model. The governing fractional differential equations are expressed by using the fractional Caputo-Fabrizio derivative without singular kernel. Exact analytical solutions are obtained by using the Laplace and finite Hankel transforms for both velocities. The velocities of blood flow and magnetic particles are graphically presented. It shows that the velocity increases with respect to the Reynolds number and the Casson parameter. Meanwhile, the velocity decreases as the Hartmann number increases. These results are useful for the diagnosis and treatment of certain medical problems.

Generalized Brinkman Type Dusty Fluid Model for Blood Flow

2020 ◽  
pp. 154-170
Author(s):  
Muhammad Saqib ◽  
Sharidan Shafie ◽  
Ilyas Khan
Keyword(s):  
Blood Flow ◽  
Magnetic Parameter ◽  
Fluid Model ◽  
Cylindrical Tube ◽  
Hankel Transform ◽  
Governing Equations ◽  
Two Phase ◽  
Cylindrical Coordinate ◽  
Long Time ◽  
Fractional Parameter

This chapter is dedicated to studying the magnetic blood flow with uniformly distributed magnetite dusty particles (MDP) in a cylindrical tube. For this purpose, the two-phase fractional Brinkman type fluid model is considered. The fractional governing equations are modeled in the cylindrical coordinate system taking into consideration the magnetization of the fluid due to the applied magnetic field. The fractional governing equations are subjected to physical initial and boundary conditions. The joint Laplace and Hankel transform is employed to develop exact analytical solutions. The obtained solutions are computed numerically and plotted in different graphs. It is noticed that for a long time the blood and MDP velocities increase with increasing values of the fractional parameter. In contrast, this effect reverses for a shorter time. In the case of the magnetic parameter, both velocities are decreased with increasing values of the magnetic parameter.

The Effect of Shape Factor on the Magnetic Targeting in the Permeable Microvessel With Two-Phase Casson Fluid Model

2011 ◽  
Vol 2 (4) ◽  
Author(s):  
Sachin Shaw ◽  
P. V. S. N. Murthy
Keyword(s):  
Magnetic Field ◽  
Volume Fraction ◽  
Fluid Model ◽  
Casson Fluid ◽  
Magnetic Drug Targeting ◽  
Magnetic Targeting ◽  
Two Phase ◽  
Coupled Equations ◽  
Casson Fluid Model ◽  
Phase Fluid

The present investigation deals with magnetic drug targeting in a microvessel of radius 5 μm using two-phase fluid model. The microvessel is divided into the endothelial glycocalyx layer wherein the blood obeys Newtonian character and a core region wherein the blood obeys the non-Newtonian Casson fluid character. The carrier particles, bound with nanoparticles and drug molecules, are injected into the vascular system upstream from the malignant tissue and are captured at the tumor site using a local applied magnetic field near the tumor position. Brinkman model is used to characterize the permeable nature of the inner wall of the microvessel. The expressions for the fluidic force for the carrier particle traversing in the two-phase fluid in the microvessel and the magnetic force due to the external magnetic field are obtained. Several factors that influence the magnetic targeting of the carrier particles in the microvasculature, such as the size and shape of the carrier particle, the volume fraction of embedded magnetic nanoparticles, and the distance of separation of the magnet from the axis of the microvessel, are considered in the present problem. The system of coupled equations is solved to obtain the trajectories of the carrier particle in the noninvasive case.

scholarly journals Nonlinear Analysis for Shear Augmented Dispersion of Solutes in Blood Flow through Narrow Arteries

2012 ◽  
Vol 2012 ◽  
pp. 1-24 ◽  
Author(s):  
D. S. Sankar ◽  
Nurul Aini Binti Jaafar ◽  
Yazariah Yatim
Keyword(s):  
Blood Flow ◽  
Circular Tube ◽  
Fluid Model ◽  
Nonlinear Differential Equations ◽  
Outer Region ◽  
Casson Fluid ◽  
Flat Plates ◽  
Axial Diffusivity ◽  
Casson Fluid Model ◽  
Relative Diffusivity

The shear augmented dispersion of solutes in blood flow (i) through circular tube and (ii) between parallel flat plates is analyzed mathematically, treating blood as Herschel-Bulkley fluid model. The resulting system of nonlinear differential equations are solved with the appropriate boundary conditions, and the expressions for normalized velocity, concentration of the fluid in the core region and outer region, flow rate, and effective axial diffusivity are obtained. It is found that the normalized velocity of blood, relative diffusivity, and axial diffusivity of solutes are higher when blood is modeled by Herschel-Bulkley fluid rather than by Casson fluid model. It is also noted that the normalized velocity, relative diffusivity, and axial diffusivity of solutes are higher when blood flows through circular tube than when it flows between parallel flat plates.

Solute dispersion in pulsatile Casson fluid flow in a tube with wall absorption

2016 ◽  
Vol 793 ◽  
pp. 877-914 ◽  
Author(s):  
Jyotirmoy Rana ◽  
P. V. S. N. Murthy
Keyword(s):  
Pulsatile Flow ◽  
Dispersion Model ◽  
Fluid Model ◽  
Critical Time ◽  
Transient State ◽  
Casson Fluid ◽  
Small Time ◽  
Dispersion Process ◽  
Pulsatile Pressure ◽  
Casson Fluid Model

The analysis of axial dispersion of solute is presented in a pulsatile flow of Casson fluid through a tube in the presence of interfacial mass transport due to irreversible first-order reaction catalysed by the tube wall. The theory of dispersion is studied by employing the generalized dispersion model proposed by Sankarasubramanian & Gill (Proc. R. Soc. Lond. A, vol. 333 (1592), 1973, pp. 115–132). This dispersion model describes the whole dispersion process in terms of three effective transport coefficients, i.e. exchange, convection and dispersion coefficients. In the present study, the effects of yield stress of Casson fluid ${\it\tau}_{y}$, wall absorption parameter ${\it\beta}$, amplitude of fluctuating pressure component $e$ and Womersley frequency parameter ${\it\alpha}$ on the dispersion process are discussed under the influence of pulsatile pressure gradient. In a pulsatile flow, the plug flow radius changes during the period of oscillation and it has an effect on the dispersion process. Even with the Casson fluid model also, in an oscillatory flow, for small values of ${\it\alpha}$, the dispersion coefficient $K_{2}$ is positive, but when the value of ${\it\alpha}$ is as large as 3, $K_{2}$ takes both positive and negative values due to the fluctuations in the velocity profiles. This nature becomes more predominant for ${\it\tau}_{y}$, $e$ and ${\it\beta}$. It is observed that initially, for small time, the amplitude and magnitude of fluctuations of $K_{2}$ becomes more rapid and increases with time but it decreases after certain time and reaches a non-transient state for large time. Like in the case of Newtonian model, double frequency period for $K_{2}$ is observed at small time for large values of ${\it\alpha}$ with the Casson model for blood. It is seen that critical time for which $K_{2}$ reaches a non-transient state is independent of ${\it\tau}_{y}$ and $e$ but is dependent on ${\it\alpha}$. It is also observed that the axial distribution of mean concentration $C_{m}$ of solute depends on ${\it\tau}_{y}$ and ${\it\beta}$. But the effect of $e$ and ${\it\alpha}$ on $C_{m}$ is not very significant. This dispersion model in non-Newtonian pulsatile flow can be applied to study the dispersion process in the cardiovascular system and blood oxygenators.

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