Peristaltic Pumping of Blood Through Small Vessels of Varying Cross-section

The paper is devoted to a study of the peristaltic motion of blood in the micro-circulatory system. The vessel is considered to be of varying cross-section. The progressive peristaltic waves are taken to be of sinusoidal nature. Blood is considered to be a Herschel-Bulkley fluid. Of particular concern here is to investigate the effects of amplitude ratio, mean pressure gradient, yield stress and the power law index on the velocity distribution, streamline pattern and wall shear stress. On the basis of the derived analytical expression, extensive numerical calculations have been made. The study reveals that velocity of blood and wall shear stress are appreciably affected due to the non-uniform geometry of blood vessels. They are also highly sensitive to the magnitude of the amplitude ratio and the value of the fluid index.Comment: Accepted for publication in ASME journal of Applied Mechanics. arXiv admin note: text overlap with arXiv:1108.1285v

Impact of Permeable Lining of the Wall on the Peristaltic Flow of Herschel Bulkley Fluid

The peristaltic motion is modeled for the Herschel Bulkley fluid, considered to flow in a non-uniform inclined channel. The channel wall is supposed to be lined with a non-erodible porous material. The flow is considered to be moving in a wave frame of reference moving with same velocity as of the sinusoidal wave. Low Reynolds number and long wave length assumptions are made to solve the model. Analytical solution is obtained for the pressure difference and also for the frictional force. Graphs are plotted, using Mathematica software, for both the results of pressure difference and frictional force against time average velocity. We observe that increasing the porous thickening, increases the pressure difference while, it decreases the frictional force. It is seen that the behavior of the pressure difference is opposite to the behavior of the frictional force for all the parameters considered

Peristaltic Pumping of a Non-Newtonian Fluid

The flow induced by sinusoidal peristaltic motion of the tube wall of a non-Newtonian fluid obeying Herschel-Bulkley equation (a general rheological equation that represents a powerlaw, Bingham and Newtonian fluid for particular choice of parameters) under long wavelength and low Reynolds number approximation is investigated. The results obtained for flow rate, pressure drop and friction force are discussed both qualitatively and quantitatively and compared with other related studies. It is found that the pressure drop increases with the flow rate and yield stress but decreases with the increasing amplitude ratio. The flow behaviour index shows significant impact on the magnitude of the pressure drop. The pressure-flow rate relationships in Bingham and Newtonian fluid models are found to be linear whereas the same are non-linear in power- law and Herschel-Bulkley models. The friction force possesses the character similar to the pressure drop (an opposite character to the pressure rise) with respect to any parameter

Non-Newtonian characteristics of peristaltic flow of blood in micro-vessels

Of concern in the paper is a generalized theoretical study of the non-Newtonian characteristics of peristaltic flow of blood through micro-vessels, e.g. arterioles. The vessel is considered to be of variable cross-section and blood to be a Herschel-Bulkley type of fluid. The progressive wave front of the peristaltic flow is supposed sinusoidal/straight section dominated (SSD) (expansion/contraction type); Reynolds number is considered to be small with reference to blood flow in the micro-circulatory system. The equations that govern the non-Newtonian peristaltic flow of blood are considered to be non-linear. The objective of the study has been to examine the effect of amplitude ratio, mean pressure gradient, yield stress and the power law index on the velocity distribution, wall shear stress, streamline pattern and trapping. It is observed that the numerical estimates for the aforesaid quantities in the case of peristaltic transport of the blood in a channel are much different from those for flow in an axisymmetric vessel of circular cross-section. The study further shows that peristaltic pumping, flow velocity and wall shear stress are significantly altered due to the non-uniformity of the cross-sectional radius of blood vessels of the micro-circulatory system. Moreover, the magnitude of the amplitude ratio and the value of the fluid index are important parameters that affect the flow behaviour. Novel features of SSD wave propagation that affect the flow behaviour of blood have also been discussed.Comment: Accepted for publication in Communications in Nonlinear Science and Numerical Simulation, Elsevier. arXiv admin note: text overlap with arXiv:1006.017

Mathematical Modelling of Swallowing of Viscoelastic Nature Food Through the Oesophagus Affected by Hiatus Hernia

Peristaltic transport of viscoelastic fluid through a divergent tube is studied by approximations of long wavelength and low Reynolds number. This type of study explains the interesting phenomenon of swallowing food bolus through the oesophagus affected by hiatus hernia. The amplitude of peristaltic waves is increase exponentially, the food bolus to be a viscoelastic fluid and the affected oesophagus a diverging tube. The expressions for axial and radial velocities, pressure and reflux limit are obtained. Both cases have been considered when the whole tube diverges and when it diverges only near the end. Another case in which the tube converges near the last end has also been analysed

Peristaltic transport of Johnson–Segalman fluid in a curved channel with compliant walls

The present investigation deals with the peristaltic flow of an incompressible Johnson–Segalman fluid in a curved channel. Effects of the channel wall properties are taken into account. The associated equations for peristaltic flow in a curved channel are modeled. Mathematical analysis is simplified under long wavelength and low Reynolds number assumptions. The solution expressions are established for small Weissenberg number. Effects of several embedded parameters on the flow quantities are discussed

(R1480) Heat Transfer in Peristaltic Motion of Rabinowitsch Fluid in a Channel with Permeable Wall

This paper is intended to investigate the effect of heat transfer on the peristaltic flow of Rabinowitsch fluid in a channel lined with a porous material. The Navier -Stokes equation governs the channel\u27s flow, and Darcy\u27s law describes the permeable boundary. The Rabinowitsch fluid model\u27s governing equations are solved by utilizing approximations of the long-wavelength and small number of Reynolds. The expressions for axial velocity, temperature distribution, pressure gradient, friction force, stream function are obtained. The influence on velocity, pressure gradient, friction force, and temperature on pumping action of different physical parameters is explored via graphs

Peristaltic Pumping of a Generalized Newtonian Fluid in an Elastic Tube

The paper investigates the peristaltic pumping of an incompressible non-Newtonian fluid in an elastic tube with long wavelengths and low Reynolds number approximations. Carreau fluid model is considered for present study to describe the peristaltic flow characteristics of non- Newtonian fluid in an elastic tube. Carreau fluid is a generalized Newtonian fluid which exhibits Newtonian behaviour for and it resembles as a power-law model at higher shear rates. For it exhibits shear-thinning property, i.e., the apparent viscosity reduces with increasing shear rate. The equations governing the fluid flow are solved with usual perturbation expansion by taking Weissenberg number as a perturbation parameter. The expressions for axial velocity, stream function and volume flow rate as function of pressure difference are derived. The effects of various pertinent parameters on variation of flux for a Carreau fluid flow through an elastic tube along with peristalsis are calculated and interpreted through graphs. The pressure rise per wavelength and shear stress distribution for different values of physical parameters are calculated and presented. Trapping phenomenon is presented graphically to understand the physical behaviour of various parameters. The difference in flux variation is examined by two different models of Rubinow and Keller (1972) and Mazumdar (1992). It is observed that in elastic tubes, the flux of Carreau fluid with peristalsis is more when the tension relation is a fifth degree polynomial as compared to exponential curve. When the power-law index or Weissenberg number and without peristalsis, the present results are similar to the observations of Rubinow and Keller (1972). Further, the relation between the function and radius of the elastic tube for both Newtonian, non-Newtonian cases are discussed graphically and these findings are identical with the investigations of Mazumdar (1992). The results observed for the present flow characteristics reports several interesting behaviours that warrant further study of physiological fluids in elastic tubes with peristalsis

Electro-Osmotic Flow of MHD Jeffrey Fluid in a Rotating Microchannel by Peristalsis: Thermal Analysis

In this study, we examine the rotating and heat transfer on the peristaltic and electro-osmatic flow of a Jeffery fluid in an asymmetric microchannel with slip impact. A pressure gradient and anal axially imposed electric field work together to impact the electro-osmotic flow (EOF). Mathematical modeling is imported by employing the low Reynolds number and long wavelength approximation. The exact solution has been simplified for the stream function, temperature, and velocity distributions. The effects of diverse egress quantities on the gush virtue are exhibited and discussed with the help of graphs. The shear stress and trapping phenomena have been investigated. The characterization of results has been resolved for the flow governing ingrained appropriate parameters by employing the table. Our findings can be summarized as follows: (i) Debye length has a strong influence on the conducting viscous fluid of EOF in non-uniform micro-channel. (ii) The temperature field is enhanced through the elevated values of the rotation parameter and EOF. (iii) The shear stress has oscillatory behavior and the heat transmission rate increases with the magnitude of larger values of EOF. Finally, there is good agreement between the current results and those that have already been published. This model applies to the study of chemical fraternization/separation procedures and bio-microfluidic devices for the resolution of diagnosis

MHD dissipative flow and heat transfer of casson fluids due to metachronal wave propulsion of beating cilia with thermal and velocity slip effects under an oblique magnetic field

A theoretical investigation of magnetohydrodynamic (MHD) flow and heat transfer of electrically-conducting viscoplastic fluids through a channel is conducted. The robust Casson model is implemented to simulate viscoplastic behavior of fluids. The external magnetic field is oblique to the fluid flow direction. Viscous dissipation effects are included. The flow is controlled by the metachronal wave propagation generated by cilia beating on the inner walls of the channel. The mathematical formulation is based on deformation in longitudinal and transverse velocity components induced by the ciliary beating phenomenon with cilia assumed to follow elliptic trajectories. The model also features velocity and thermal slip boundary conditions. Closed-form solutions to the non-dimensional boundary value problem are obtained under physiological limitations of low Reynolds number and large wavelength. The influence of key hydrodynamic and thermo-physical parameters i.e. Hartmann (magnetic) number, Casson (viscoplastic) fluid parameter, thermal slip parameter and velocity slip parameter on flow characteristics are investigated. A comparative study is also made with Newtonian fluids (corresponding to massive values of plastic viscosity). Stream lines are plotted to visualize trapping phenomenon. The computations reveal that velocity increases with increasing the magnitude of Hartmann number near the channel walls whereas in the core flow region (centre of the channel) significant deceleration is observed. Temperature is elevated with greater Casson parameter, Hartmann number, velocity slip, eccentricity parameter, thermal slip and also Brinkmann (dissipation) number. Furthermore greater Casson parameter is found to elevate the quantity and size of the trapped bolus. In the pumping region, the pressure rise is reduced with greater Hartmann number, velocity slip, and wave number whereas it is enhanced with greater cilia length