Effect of boundary absorption on dispersion in Casson fluid flow in an annulus: application to catheterized artery (original) (raw)
Related papers
Effect of Boundary Absorption in Dispersion in Casson Fluid Flow in a Tube
Annals of Biomedical Engineering, 2004
The combined effect of yield stress and irreversible boundary reaction on dispersion process in a Casson fluid flowing in a conduit (pipe/channel) is studied using the generalized dispersion model proposed by Sankarasubramanian and Gill (Sankarasubramanian, R., and W. N. Gill. Proc. R. Soc. London, Ser. A 333:115–132, 1973). The study describes the development of dispersive transport following the injection of a tracer in terms of the three effective transport coefficients, viz., exchange, convection, and dispersion coefficients. The exchange coefficient does not depend on yield stress but the convection and dispersion coefficients depend on yield stress or equivalently plug flow region. For large times, when the plug flow radius is one-tenth of pipe radius, the convective coefficient is reduced by 0.41 times of the corresponding value for a Newtonian fluid at equivalent wall absorption parameter; in channel case the reduction is by 39%. It is seen that the asymptotic dispersion coefficient decreases with increase in wall absorption parameter and yield stress of the fluid. When the plug radius in pipe (channel) is 0.1, depending upon the values of wall absorption parameter, say (0.01–100) the reduction factor in dispersion coefficient is in the range (0.1–0.3) in comparison to the values of the Newtonian case. The results reduce to those of Sankarasubramanian and Gill (Sankarasubramanian, R., and W. N. Gill. Proc. R. Soc. London, Ser. A 333:115–132, 1973) when there is no yield stress for the pipe flow analysis and to those of Dash et al. (Dash, R. K., G. Jayaraman, and K. N. Mehta. Ann. Biomed. Eng. 28:373–385, 2000) when there is no interphase mass transfer. The study can be used as a starting first approximation solution for studying the dispersion in the cardiovascular system.
Acta Mechanica, 2006
The dispersion of a solute in the flow of a Casson fluid in an annulus is studied. The generalized dispersion model is employed to study the dispersion process. The effective diffusion coefficient, which describes the whole dispersion process in terms of a simple diffusion process, is obtained as a function of time, in addition to its dependence on the yield stress of the fluid and on the annular gap between the two cylinders. It is observed that the dispersion coefficient changes very rapidly for small values of time and becomes essentially constant as time takes large values. In non–Newtonian fluids the steady state is reached at earlier instants of time when compared to the Newtonian case and the time taken to reach the steady state is seen to depend on the values of the yield stress. It is observed that a decrease in the annular gap inhibits the dispersion process for all times both in Newtonian as well as in non–Newtonian fluids. When the yield stress is 0.05, depending upon the size of the annular gap (0.9–0.7) the reduction factor in the dispersion coefficient varies in the range 0.58–0.08. The application of this study for understanding the dispersion of an indicator in a catheterized artery is discussed.
A Study on Solute Dispersion in a Three Layer Blood-like Liquid Flowing through a Rigid Artery
Periodica Polytechnica Mechanical Engineering
The unsteady dispersion of a solute has been discussed by the method of generalized dispersion technique in a blood-like liquid flowing through a pipe under the combined effects of finite yield stress and irreversible absorption into the wall.The solvent is enacted as a three-layered liquid by considering the center liquid as a Casson liquid (a core of red blood cell suspension) and a peripheral layer of plasma as a Newtonian liquid. An asymptotic representation for the convection and dispersion coefficients has been shown only for large values of time, which will not hamper the study of physical behavior of the system. The objective of the present study is to examine the nature of exchange coefficient, convective coefficient and in particular, dispersion coefficient together with mean concentration distribution under the effect of absorption parameter (β), yield stress (τy) (equivalently the plug radius (Rp)) and peripheral layer variation (i.e., ratio of central core ...
Journal of Advanced Research in Fluid Mechanics and Thermal Sciences, 2021
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. Henc...
Malaysian Journal of Fundamental and Applied Sciences, 2021
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 presenc...
Nonlinear Analysis for Shear Augmented Dispersion of Solutes in Blood Flow through Narrow Arteries
Journal of Applied Mathematics, 2012
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.
Applied Mathematics and Computation, 2007
Presented herein is the study of diffusion phenomenon in modelled normal and stenosed capillary-tissue exchange system. The model incorporates modified Casson's fluid representation for the blood flow through an axially non-symmetrical but radially symmetric stenosis. Assessment of the severity of the disease could be made possible through the variation of a parameter named as retention parameter. Symmetry of the distribution of the wall shearing stress and resistive impedance and their growth with the developing stenosis is another important feature of this analysis. The concentration profiles and associated physiological diffusion variables involved in the analysis for normal and diseased state have been determined.
Hydrodynamic Dispersion of Solute under Homogeneous and Heterogeneous Reactions
International Journal of Heat and Technology, 2019
The present investigation deals with Taylor dispersion of reactive species in Casson liquid in an oscillatory flow because of the pulsatile pressure gradient. The solute is considered to be chemically active at the boundary and also participate a first order reaction within the bulk flow. To evaluate transport coefficients, Aris-Barton moment technique is considered. The solute transport process is discoursed in detailed with respect to yield stress, chemical reaction parameter, Womersly number etc. The study reveals that both wall absorption and bulk flow reaction have a significant response on dispersion phenomena. Both the chemical reactions agree to diminish the negative exchange coefficient and the apparent dispersion coefficient, however, increases the negative convection coefficient. The negative exchange coefficient is independent of yield stress but a significant variation is observed due to yield stress in the cases of negative convection coefficient and the apparent dispersion coefficient. The axial distribution of mean concentration is approximated by using the Hermite polynomial representation of central moments as a function of reaction rate parameters, wall absorbing parameter, yield stress etc. The present article may be useful for the studies related to physiological blood flow analysis.
ijcem.org
The study focuses on the behavior of diffusion phenomenon in the normal and stenosed capillarytissue exchange system where the rheology of flowing blood in the capillary is characterized by the generalized Casson's fluid model. Assessment of the severity of the disease could be made possible through the variation of a parameter named as retention parameter. The concentration profile and associated physiological diffusion variable involved in the study for normal and diseased state have been analyzed. The model is also employed to study the effect of shape of stenosis on flow characteristics. An extensive quantitative analysis is performed through numerical computations of the desired quantities having physiological relevance through their graphical representations so as to validate the applicability of the present model.
Dispersion of a solute in pulsatile non-Newtonian fluid flow through a tube
Acta Mechanica, 2012
The unsteady dispersion of a solute by an imposed pulsatile pressure gradient in a tube is studied by modeling the flowing fluid as a Casson fluid. The generalized dispersion model is applied to study the dispersion process, and according to this process, the entire dispersion process is expressed in terms of two coefficients, the convection and the dispersion coefficients. This model mainly brings out the effects of yield stress and flow pulsatility on the dispersion process. It is observed that the dispersion phenomenon in the pulsatile flow inherently differs from the steady flow, which is due to a change in the plug flow radius during a cycle of oscillation. Also, it was found that the dispersion coefficient fluctuates due to the oscillatory nature of the velocity. It is seen that the dispersion coefficient changes cyclically, and the amplitude and magnitude of the dispersion coefficient increases initially with time and reaches a non-transient state after a certain critical time. It is also seen that this critical time varies with Womersley frequency parameter and Schmidt number and is independent of yield stress and fluctuating pressure component. It is observed that the yield stress and Womersley frequency parameter inhibit the dispersion of a solute. It is also observed that the dispersion coefficient decreased approximately 4 times as the Womersley frequency parameter increases from 0.5 to 1. The study can be used in the understanding of the dispersion process in the cardiovascular system and blood oxygenators.