Two-fluid Model For Blood Flow Research Articles

Unsteady solute dispersion in two-fluid flowing through narrow tubes: A temperature-dependent viscosity approach

The drug delivery or transportation of nutrients to our body involves the solute dispersion process through physiological systems and hence affected by the varying nature of viscosity, heat transfer and other factors. The majority of the previous works involving the solute dispersion in fluid flow through microvessels assumed the constant blood viscosity but in treatments involving temperature variations, the blood viscosity will be affected by the change in temperature and hence it is interesting to analyze its effect on the diffusion process. The motivation of the present work is to analyze the simultaneous impact of temperature-dependent viscosity and heat transfer on the solute dispersion in a two-fluid model of blood flow through narrow tubes by adopting the solution technique proposed by Sankarasubramanian and Gill (1973). Blood is considered as Herschel-Bulkley fluid with temperature-dependent viscosity filled up in a central region of the blood vessel and an outer cell free layer of plasma encircled over the central region consists of Newtonian fluid with constant viscosity. The desired flow related information using heat transfer aspect are obtained analytically for varying viscosity model and these expressions for velocity are then used to compute the diffusion coefficients and mean concentration. The entire dispersion process described by the three main diffusion coefficients known as exchange, convective and dispersion coefficients. An important observation is that the whole diffusion process (asymptotic convection, asymptotic dispersion coefficients and mean concentration) isaffected by the temperature-dependent viscosity with temperature parameters and same observation persist for three different types of fluids like Newtonian fluid (NF), Bingham-plastic fluid (BP), Power-law fluid (PL) which are specific cases of our model. A noteworthy observation is that an enhancement in viscosity index (and hence decay in viscosity of the core region fluid) affects the fluid flow velocity and hence affects the diffusion coefficients. Further, the dominance of thermal buoyancy forces expedite the diffusion process. The outcome of the results reveal the dependence of the solute dispersion on temperature-dependent viscosity and heat transfer. The study may be applicable to drug delivery through bloodstreams in the treatments involving the temperature variations such as chemotherapy.

Solute dispersion in two-fluid flowing through tubes with a porous layer near the absorbing wall: Model for dispersion phenomenon in microvessels

Present study concerns the solute dispersion analysis in a two-fluid model of blood flow through tubes with a thin porous layer near the absorbing wall. A thin porous layer near the wall represents an endothelial glycocalyx layer the composition of which may be attributed to the accumulation of carbohydrates, absorbed plasma proteins and macromolecules in a layer at the wall that affects the plasma flow (Secomb et al., 1998. A model for red blood cell motion in glycocalyx-lined capillaries. Am. J. Physiol. 274 (Heart Circ. Physiol. 43), H1016-H1022; Pries et al., 2000. The endothelial surface layer. Eur. J. Physiol. 440, 653–666). Two-fluid model for blood flow is considered in which the central region of the blood vessel is occupied by Herschel-Bulkley fluid with variable viscosity and a peripheral region of plasma surrounded over the central region is occupied by a Newtonian fluid with constant viscosity. Governing equations are solved analytically for all the regions (central, intermediate and porous regions) and the approach of Sankarasubramanian and Gill (Sankarasubramanian, R, Gill, W N, 1973. Unsteady convective diffusion with interphase mass transfer. Proc. R. Soc. London Ser. A 333, 115–132) is followed to solve the diffusion equation by series expansion method. The impact of porous layer (and hence the porous layer parameters), varying viscosity, plasma layer and wall absorption parameters on the diffusion process like convective, dispersion and mean concentration have been analyzed. A comparative investigation of solute dispersion between Newtonian and non-Newtonian fluids has also been discussed. It is perceived that the presence of such a layer reduces the convective and axial dispersion for a highly reactive wall. A remarkable observation is that a reduced porosity near the wall contributes towards reduced average concentration of the solvent. The analysis of the porous layer inside the arterial wall may be used to understand the diffusion process for flow through arteries with a deposition of a porous layer near the absorbing wall.

A micropolar-Newtonian blood flow model through a porous layered artery in the presence of a magnetic field

In this work, we present a two-phase model of blood flow through a porous layered artery in the presence of a uniform magnetic field. The characteristic of suspensions in blood allows us to assume blood as a micropolar fluid in the core region and plasma as a Newtonian fluid in the peripheral region of a blood vessel. The wall of a blood vessel is porous and composed of a thin Brinkman transition layer followed by a Darcy porous layer of different permeabilities. A magnetic field of uniform strength is transversally applied to the direction of blood flow. The authors obtained an analytical solution of the problem of blood flow through the composite porous walled artery. Analytical expressions for the flow velocity, microrotational velocity, flow rate, and stresses at the wall have been obtained in the closed form using the modified Bessel function. The effects of various flow parameters on the two-fluid model of blood flow are analyzed graphically. An important conclusion which is drawn from the solution of the present problem is that the different permeabilities of Darcy and Brinkman regions of the porous layered artery have a significant effect on the flow. The present work is validated from the previously published literature studies.

Computational model on pulsatile flow of blood through a tapered arterial stenosis with radially variable viscosity and magnetic field

An unsteady two-fluid model of blood flow through a tapered arterial stenosis with variable viscosity in the presence of variable magnetic field has been analysed in the present paper. In this article, blood in the core region is assumed to obey the law of Jeffrey fluid and plasma in the peripheral layer is assumed to be Newtonian. The values for velocity, wall shear stress, flow rate and flow resistance are numerically computed by employing finite-difference method in solving the governing equations. A comparison study between the velocity profiles obtained by the present study and the experimental data represented graphically shows that that the rheology of blood obeys the law of Jeffrey fluid rather than that of Newtonian fluid. The effects of parameters such as taper angle, radially variable viscosity, hematocrit, Jeffrey parameter, magnetic field and plasma layer thickness on physiologically important parameters such as wall shear stress distribution and flow resistance have been investigated. The results in the case of radially variable magnetic field and constant magnetic field are compared to observe the effect of magnetic field in driving the blood flow. It is observed that increase in hematocrit increases the wall shear stress. The values of wall shear stress and flow resistance are obtained at various time instances and compared. It is pertinent to note that the magnitudes of flow resistance are higher in the case of converging tapered than non-tapered and diverging tapered artery.

Two-Fluid Model for Blood Flow Through a Tapered Arterial Stenosis: Effect of Non-zero Couple Stress Boundary Condition at the Interface

The present paper concerns a mathematical model for steady flow of blood through tapered stenosed arteries with peripheral plasma layer near the wall. The model consists of a core region of suspension of all the erythrocytes assumed to be a couple stress fluid and a peripheral layer of plasma as a Newtonian fluid. A non-zero couple stress boundary condition at the interface is introduced. The values of velocity, wall shear stress and the flow resistance with respect to the non-zero couple stress condition at the interface for normal blood and diseased [polycythemia, plasmal cell dyscrasias and HBSS (sickle cell)] blood are computed. It is observed that the introduction of the non-zero couple stress boundary condition at the interface helps to increase the velocity and significantly reduces the resistive impedance which, in turn, improves or normalizes the blood flow in diseased state. This information of blood flow could be useful for the development of new diagnosis tools and medicines for many diseases.

Two-fluid model for blood flow in stenosed arteries under periodic body acceleration: a mathematical model

This study analyses the pulsatile flow of blood through narrow arteries with mild asymmetric stenosis. Blood is modeled as a two-fluid model with the suspension of all the erythrocytes in the core region being treated as Casson fluid and the plasma in the peripheral layer being assumed as Newtonian fluid. Perturbation method is used to solve the resulting coupled implicit system of non-linear partial differential equations. The expressions for shear stress, velocity, wall shear stress, plug core radius, flow rate and resistance to flow are obtained. The effects of pulsatility, stenosis shape parameter, stenosis depth, peripheral layer thickness, body acceleration and non-Newtonian behavior of blood on these flow quantities are discussed. It is noted that the plug core radius and resistance to flow decrease with the increase of the body acceleration and pressure gradient. It is observed that the velocity and flow rate increase with the increase of the peripheral layer thickness and they decrease with the increase of the stenosis shape parameter. It is recorded that the estimates of the mean flow rate of the two-fluid blood flow model are considerably higher than that of the single-fluid blood flow model. It is also noticed that the presence of body acceleration and peripheral layer influences the mean flow rate by increasing their magnitude significantly in the arteries with different radii.

Pulsatile Flow of a Two-Fluid Model for Blood Flow through Arterial Stenosis

Pulsatile flow of a two-fluid model for blood flow through stenosed narrow arteries is studied through a mathematical analysis. Blood is treated as two-phase fluid model with the suspension of all the erythrocytes in the as Herschel-Bulkley fluid and the plasma in the peripheral layer as a Newtonian fluid. Perturbation method is used to solve the system of nonlinear partial differential equations. The expressions for velocity, wall shear stress, plug core radius, flow rate and resistance to flow are obtained. The variations of these flow quantities with stenosis size, yield stress, axial distance, pulsatility and amplitude are analyzed. It is found that pressure drop, plug core radius, wall shear stress and resistance to flow increase as the yield stress or stenosis size increases while all other parameters held constant. It is observed that the percentage of increase in the magnitudes of the wall shear stress and resistance to flow over the uniform diameter tube is considerably very low for the present two-fluid model compared with that of the single-fluid model of the Herschel-Bulkley fluid. Thus, the presence of the peripheral layer helps in the functioning of the diseased arterial system.

Flow and heat transfer of a micropolar fluid sandwiched between viscous fluid layers

In the present analysis, a two-fluid model for blood flow through a horizontal channel is studied. The model essentially consists of a core region assumed to be a micropolar fluid and two viscous (Newtonian) fluid regions. Using the boundary and interface conditions proposed by Ariman et al. (J. Appl. Mech. ASME, 41, 1 (1974)), analytical expressions for velocity, microrotation velocity, and temperature are obtained. The solutions are also evaluated numerically and shown graphically for various governing parameters such as the material parameter, viscosity ratio, conductivity ratio, Eckert and Prandtl numbers on velocity, microrotation velocity, and temperature profiles. In addition, results for the rate of heat transfer, mass flow rate, and skin friction for different values of the physical parameters are presented in tabular form. It is found that effect of the material parameter is to suppress the flow and the viscosity ratio promotes the flow. It is also interesting to note that the material parameter and viscosity ratio affect the position of the point of flow separation for which the flow nature is reversed. Also, considering the solvent viscosity for air, water, and glycerin, the cell rotation on the flow has been tabulated for 0%, 20%, and 40% concentration. PACS Nos.: 44.15+a, 44.35.+c

Influence de la nature de la paroi sur un modèle d'écoulements pulsés de fluides diphasiques. Application à la microcirculation

The present work deals with a two-fluid model for blood flow through deformable tubes of small diameter. This two-f1uid model consists of a core (suspension of red cells) and peripheral red cell free plasma layer. The core has been considered as an Ostwaldian fluid and the plasma layer as a Newtonian fluid. Using an implicit finite differences method to solve the equations governing such flows, we have determined the global quantities for three kinds of ducts : rigid, elastic and viscoelastic. This study modeling the flow in blood vessels, can also contribute to other important fields such as water desalination or gel filtration.

Modélisation de la contrainte pariétale pour un écoulement pulsé de fluide diphasique en conduite déformable de faible diamètre

The present work deals with a two-fluid model for blood flow through deformable tubes of small diameter. The two-fluid flow consists of a core (suspension of red cells) and a peripheral red cell free plasma layer. From this model, taking into account the two-phase pulsatile flows, the non-Newtonian behaviour of core and the wall deformability of pipes, a wall shear-stress expression was elaborated for the Womersley numbers regarding the microcirculation. This relation allows the direct resolution of the equations governing such flows without numerical methods.

Two-layered blood flow in stenosed tubes for different diseases.

A two-fluid model for blood flow through a stenosed tube has been developed. The model consists of a core (suspension of RBCs) and peripheral plasma layer. The core is assumed to be represented by a polar fluid and the plasma layer by a Newtonian fluid. The flow is assumed to be steady and laminar, and the fluids incompressible. The flow variables are computed for normal blood and for the cases of polycythemia, plasma cell dyscrasias and for Hb SS diseases. Resistance to flow has been computed for different stenosis length and for different stenosis height. Shear stress distribution along the axial distance has been computed for different stenosis height. The impact of size effects (particle size to tube diameter) on blood diseases is discussed.

A two-fluid model for blood flow through small diameter tubes with non-zero couple stress boundary condition at interface

The present problem deals with a two-fluid model for blood flow through narrow tubes. The model basically consists of a core (substructured continuum) and a peripheral layer of plasma (Newtonian fluid). A new boundary condition has been introduced wh

Comments on “A two-fluid model for blood flow through small diameter tubes”

Comments on “A two-fluid model for blood flow through small diameter tubes”

On micropolar fluid model for blood flow through narrow tubes.

In the present analysis, a two-fluid model for blood flow through small diameter tubes has been studied. This model essentially consists of a core region (suspension of red cells, etc.), assumed to be a micropolar fluid, and a peripheral plasma layer

A two-fluid model for blood flow through small diameter tubes.

The present problem deals with a two-fluid model for blood flow through small diameter tubes. The two-fluid model consists of a core (suspension of red cells) and a peripheral red cell free plasma layer. The core has been considered as a couple stres