Transient magneto-peristaltic flow of couple stress biofluids: A magneto-hydro-dynamical study on digestive transport phenomena

Magnetic fields are increasingly being utilized in endoscopy and gastric transport control. In this regard, the present study investigates the influence of a transverse magnetic field in the transient peristaltic rheological transport. An electrically-conducting couple stress non-Newtonian model is employed to accurately simulate physiological fluids in peristaltic flow through a sinusoidally contracting channel of finite length. This model is designed for computing the intra-bolus oesophageal and intestinal pressures during the movement of food bolus in the digestive system under magneto-hydro-dynamic effects. Long wavelength and low Reynolds number approximations have been employed to reduce the governing equations from nonlinear to linear form, this being a valid approach for creeping flows which characterizes physiological dynamics. Analytical approximate solutions for axial velocity, transverse velocity, pressure gradient, local wall shear stress and volumetric flow rate are obtained for the non-dimensional conservation equations subject to appropriate boundary conditions. The effects of couple stress parameter and transverse magnetic field on the velocity profile, pressure distribution, local wall shear stress and the averaged flow rate are discussed with the aid of computational results. The comparative study of non-integral and integral number of waves propagating along the finite length channel is also presented. Magnetic field and non-Newtonian properties are found to strongly influence peristaltic transport.     

Peristaltic transport of a couple stress fluid in a uniform and non-uniform channels

The problem of peristaltic transport of a couple stress fluid in uniform and non-uniform two-dimensional channels has been investigated under zero Reynolds number with long wavelength approximation. Blood is represented by a couple stress fluid (a fluid which its particles size are taken into account, a special case of a non-Newtonian fluid). It is found that the pressure rise decreases as the couple stress fluid parameter gamma increases (i.e., small size fluid particle). So the pressure rise for a couple stress fluid (as a blood model) is greater than that for a Newtonian fluid. Also the pressure rise increases as the amplitude ratio phi increases for different values of gamma. Further, the pressure rise in the case of non-uniform geometry is found to be much smaller than the corresponding value in the case of uniform geometry. Finally, the maximum pressure rise when the mean flow rate over one period of the wave, Q = 0, increases as phi increases and gamma decreases.     

Influence of Hall Current and Viscous Dissipation on Pressure Driven Flow of Pseudoplastic Fluid with Heat Generation: A Mathematical Study

In this paper, we study the influence of heat sink (or source) on the peristaltic motion of pseudoplastic fluid in the presence of Hall current, where channel walls are non-conducting in nature. Flow analysis has been carried out under the approximations of a low Reynolds number and long wavelength. Coupled equations are solved using shooting method for numerical solution for the axial velocity function, temperature and pressure gradient distributions. We analyze the influence of various interesting parameters on flow quantities. The present study can be considered as a mathematical presentation of the dynamics of physiological organs with stones.     

Homogeneous-Heterogeneous Reactions in Peristaltic Flow with Convective Conditions

This article addresses the effects of homogeneous-heterogeneous reactions in peristaltic transport of Carreau fluid in a channel with wall properties. Mathematical modelling and analysis have been carried out in the presence of Hall current. The channel walls satisfy the more realistic convective conditions. The governing partial differential equations along with long wavelength and low Reynolds number considerations are solved. The results of temperature and heat transfer coefficient are analyzed for various parameters of interest.     

Peristaltic Motion of Johnson-Segalman Fluid in a Curved Channel with Slip Conditions

Slip effects on the peristaltic transport of Johnson-Segalman fluid through a curved channel have been addressed. The influence of wall properties is also analyzed. Long wavelength and low Reynolds number assumptions have been utilized in the mathematical formulation of the problem. The equations so formed have been solved numerically by shooting method through computational software Mathematica 8. In addition the analytic solution for small Weissenberg number (elastic parameter) is computed through a regular perturbation method. An excellent agreement is noticed between the two solutions. The results indicate an increase in the magnitude of velocity with an intensification in the slip effect. Moreover the size and circulation of the trapped boluses increase with an increase in the slip parameter. Unlike the planar channel, the profiles of axial velocity are not symmetric about the central line of the channel.     

Effects of couple stresses on the blood flow through an artery with mild stenosis

An analysis of the effects of couple stresses on the blood flow through thin artery in the presence of very mild stenosis has been carried out with the help of two nondimensional parameters, alpha (the length ratio parameter) and eta (the parameter characterizing the antisymmetric property of the couple stress tensor). It is shown that an increase in the couple stress (small value of alpha and eta), increases the resistance to the flow and the wall shear stress. These characteristics are further enhanced by the presence of the stenosis.     

Peristaltic transport in a channel with a porous peripheral layer: model of a flow in gastrointestinal tract

Peristaltic transport in a two dimensional channel, filled with a porous medium in the peripheral region and a Newtonian fluid in the core region, is studied under the assumptions of long wavelength and low Reynolds number. The fluid flow is investigated in the waveframe of reference moving with the velocity of the peristaltic wave. Brinkman extended Darcy equation is utilized to model the flow in the porous layer. The interface is determined as a part of the solution using the conservation of mass in both the porous and fluid regions independently. A shear-stress jump boundary condition is used at the interface. The physical quantities of importance in peristaltic transport like pumping, trapping, reflux and axial velocity are discussed for various parameters of interest governing the flow like Darcy number, porosity, permeability, effective viscosity etc. It is observed that the peristalsis works as a pump against greater pressure in two-layered model with a porous medium compared with a viscous fluid in the peripheral layer. Increasing Darcy number Da decreases the pumping and increasing shear stress jump constant beta results in increasing the pumping. The limits on the time averaged flux Q for trapping in the core layer are obtained. The discussion on pumping, trapping and reflux may be helpful in understanding some of the fluid dynamic aspects of the transport of chyme in gastrointestinal tract.     

Peristaltic motion of Phan–Thien–Tanner fluid in the presence of slip condition

This investigation considers the peristaltic flow of a Phan–Thien–Tanner fluid in the presence of slip condition and induced magnetic field. By use of the long wavelength and low Reynolds number approximations, closed form series solutions for stream function, pressure gradient, magnetic force function, axial induced magnetic field, and current density were obtained. The pressure gradient and frictional forces per wavelength were computed by numerical integration. The velocity slip condition in terms of shear stress is taken into account. Graphical results show the comparison between no-slip and viscous fluid cases. Pumping and trapping phenomena are discussed.     

Flow of couple stress fluid through stenotic blood vessels

The effects of an axially symmetric mild stenosis on the flow of blood, when blood is represented by a couple stress fluid model, have been studied. It is found that, for a fixed stenosis size, the resistance to flow and wall shear stress increase as the couple stress parameter eta decreases from unity. A comparison of the results with those of the Newtonian case shows that the magnitude of resistance to flow and wall shear under a given set of conditions, is greater in the case of the couple stress fluid model. It is seen that even in the case of a mild stenosis (19% area reduction), resistance to flow and wall shear values are increased over those for no stenosis by 60% and 62%, respectively, when compared with the case of a Newtonian fluid.     

Slip Effects on Mixed Convective Peristaltic Transport of Copper-Water Nanofluid in an Inclined Channel

Peristaltic transport of copper-water nanofluid in an inclined channel is reported in the presence of mixed convection. Both velocity and thermal slip conditions are considered. Mathematical modelling has been carried out using the long wavelength and low Reynolds number approximations. Resulting coupled system of equations is solved numerically. Quantities of interest are analyzed through graphs. Numerical values of heat transfer rate at the wall for different parameters are obtained and examined. Results showed that addition of copper nanoparticles reduces the pressure gradient, axial velocity at the center of channel, trapping and temperature. Velocity slip parameter has a decreasing effect on the velocity near the center of channel. Temperature of nanofluid increases with increase in the Grashoff number and channel inclination angle. It is further concluded that the heat transfer rate at the wall increases considerably in the presence of copper nanoparticles.     

Homotopy semi-numerical simulation of peristaltic flow of generalised Oldroyd-B fluids with slip effects

This investigation deals with the peristaltic flow of generalised Oldroyd-B fluids (with the fractional model) through a cylindrical tube under the influence of wall slip conditions. The analysis is carried out under the assumptions of long wavelength and low Reynolds number. Analytical approximate solutions are obtained by using the highly versatile and rigorous semi-numerical procedure known as the homotopy analysis method. It is assumed that the cross section of the tube varies sinusoidally along the length of the tube. The effects of the dominant hydromechanical parameters, i.e. fractional parameters, material constants, slip parameter, time and amplitude on the pressure difference across one wavelength, are studied. Graphical plots reveal that the influence of both fractional parameters on pressure is opposite to each other. Interesting responses to a variation in the constants are obtained. Pressure is shown to be reduced by increasing the slip parameter. Furthermore, the pressure in the case of fractional models (fractional Oldroyd-B model and fractional Maxwell model) of viscoelastic fluids is considerably more substantial than that in the corresponding classical viscoelastic models (Oldroyd-B and Maxwell models). Applications of the study arise in biophysical food processing, embryology and gastro-fluid dynamics.     

A couple stress model of blood flow in the microcirculation

A simple mathematical model depicting blood flow in the capillary is developed with an emphasis on the permeability property of the blood vessel based on Starling's hypothesis. In this study the effect of inertia has been neglected in comparison with the viscosity on the basis of the smallness of the Reynolds number of the flow in the capillary. The capillary blood vessel is approximated by a circular cylindrical tube with a permeable wall. The blood is represented by a couple stress fluid. With such an ideal model the velocity and pressure fields are determined. It is shown that an increase in the couple stress parameter increases the resistance to the flow and thereby decreases the volume rate flow. A comparison of the results with those of the Newtonian case has also been made.     

A mathematical model for the peristaltic flow of chyme movement in small intestine

A mathematical model based on viscoelastic fluid (fractional Oldroyd-B model) flow is considered for the peristaltic flow of chyme in small intestine, which is assumed to be in the form of an inclined cylindrical tube. The peristaltic flow of chyme is modeled more realistically by assuming that the peristaltic rush wave is a sinusoidal wave, which propagates along the tube. The governing equations are simplified by making the assumptions of long wavelength and low Reynolds number. Analytical approximate solutions of problem are obtained by using homotopy analysis method and convergence of the obtained series solution is properly checked. For the realistic values of the emerging parameters such as fractional parameters, relaxation time, retardation time, Reynolds number, Froude number and inclination of tube, the numerical results for the pressure difference and the frictional force across one wavelength are computed and discussed the roles played by these parameters during the peristaltic flow. On the basis of this study, it is found that the first fractional parameter, relaxation time and Froude number resist the movement of chyme, while, the second fractional parameter, retardation time, Reynolds number and inclination of tube favour the movement of chyme through the small intestine during pumping. It is further revealed that size of trapped bolus reduces with increasing the amplitude ratio whereas it is unaltered with other parameters.     

Peristaltic biofluids flow through vertical porous human vessels using third-grade non-Newtonian fluids model

In this paper, the heat and flow characteristic of third-grade non-Newtonian biofluids flow through a vertical porous human vessel due to peristaltic wall motion are studied. The third-grade model can describe shear thinning (or shear thickening) and normal stress differences, which is acceptable for biofluids modeling. In order to solve the governing equations, the assumption of long-wavelength approximation is utilized. This hypothesis emphasizes that the wavelength of the peristaltic wall motion is large in comparison with the radius of the human vessel, which is widely acceptable in biological investigations. The analytical perturbation method is employed to solve the governing equations. Consequently, analytical expressions for the velocity profile, shear stress, temperature field, and biofluid flow rate are obtained. In addition, the effects of the governing parameters such as the third-grade non-Newtonian parameter, Grashof Number, Eckert number, and porosity, on the results are examined.     

Analysis of intra-uterine fluid motion induced by uterine contractions

Evaluation of the fluid flow pattern in a non-pregnant uterus is important for understanding embryo transport in the uterus. Fertilization occurs in the fallopian tube and the embryo (fertilized ovum) enters the uterine cavity within 3 days of ovulation. In the uterus, the embryo is conveyed by the uterine fluid for another 3 to 4 days to a successful implantation site at the upper part of the uterus. Fluid movements within the uterus may be induced by several mechanisms, but they seem to be dominated by myometrial contractions. Intra-uterine fluid transport in a sagittal cross-section of the uterus was simulated by a model of wall-induced fluid motion within a two-dimensional channel. The time-dependent fluid pattern was studied by employing the lubrication theory. A comprehensive analysis of peristaltic transport resulting from symmetric and asymmetric contractions is presented for various displacement waves on the channel walls. The results provide information on the flow field and possible trajectories by which an embryo may be transported before implantation at the uterine wall.     

Peristaltic flow in tubes

The study is concerned with the analysis of two flow domains of peristaltic motion in tubes. In the first analysis the wall disturbance wavelength is much larger than the average tube radius. There is a simple algebraic relation between the average flow rate and pressure differential across a wavelength. In the second analysis the disturbance wavelength may be as small as the average radius. A numerical technique may be used to determine the relation between average flow rate and pressure differential across a wavelength.     

A mathematical simulation of the ureter: effects of the model parameters on ureteral pressure/flow relations

Ureteral peristaltic mechanism facilitates urine transport from the kidney to the bladder. Numerical analysis of the peristaltic flow in the ureter aims to further our understanding of the reflux phenomenon and other ureteral abnormalities. Fluid-structure interaction (FSI) plays an important role in accuracy of this approach and the arbitrary Lagrangian-Eulerian (ALE) formulation is a strong method to analyze the coupled fluid-structure interaction between the compliant wall and the surrounding fluid. This formulation, however, was not used in previous studies of peristalsis in living organisms. In the present investigation, a numerical simulation is introduced and solved through ALE formulation to perform the ureteral flow and stress analysis. The incompressible Navier-Stokes equations are used as the governing equations for the fluid, and a linear elastic model is utilized for the compliant wall. The wall stimulation is modeled by nonlinear contact analysis using a rigid contact surface since an appropriate model for simulation of ureteral peristalsis needs to contain cell-to-cell wall stimulation. In contrast to previous studies, the wall displacements are not predetermined in the presented model of this finite-length compliant tube, neither the peristalsis needs to be periodic. Moreover, the temporal changes of ureteral wall intraluminal shear stress during peristalsis are included in our study. Iterative computing of two-way coupling is used to solve the governing equations. Two phases of nonperistaltic and peristaltic transport of urine in the ureter are discussed. Results are obtained following an analysis of the effects of the ureteral wall compliance, the pressure difference between the ureteral inlet and outlet, the maximum height of the contraction wave, the contraction wave velocity, and the number of contraction waves on the ureteral outlet flow. The results indicate that the proximal part of the ureter is prone to a higher shear stress during peristalsis compared with its middle and distal parts. It is also shown that the peristalsis is more efficient as the maximum height of the contraction wave increases. Finally, it is concluded that improper function of ureteropelvic junction results in the passage of part of urine back flow even in the case of slow start-up of the peristaltic contraction wave.     

Steady flow of couple stress fluid through tubes of slowly varying cross-sections--application to blood flows

Steady laminar flow of a non-Newtonian fluid based on couple stress fluid theory, through narrow tubes of varying cross-sections has been studied theoretically. Asymptotic solutions are obtained for the basic equations and the expressions for the velocity field and the wall shear stress are derived for a general cross-section. Computation and discussions are carried out for the geometries which occur in the context of physiological flows or in particular blood flows. The tapered tubes and constricted tubes are of special importance. It is observed that increase in certain parameters results in erratic flow behaviour proximal to the constricted areas which is further enhanced by the increase in the geometric parameters. This elucidates the implications of the flow in the development of vascular lesions.     

Wall stress and flow dynamics in abdominal aortic aneurysms: finite element analysis vs. fluid–structure interaction

Abdominal aortic aneurysm (AAA) rupture is the clinical manifestation of an induced force exceeding the resistance provided by the strength of the arterial wall. This force is most frequently assumed to be the product of a uniform luminal pressure acting along the diseased wall. However fluid dynamics is a known contributor to the pathogenesis of AAAs, and the dynamic interaction of blood flow and the arterial wall represents the in vivo environment at the macro-scale. The primary objective of this investigation is to assess the significance of assuming an arbitrary estimated peak fluid pressure inside the aneurysm sac for the evaluation of AAA wall mechanics, as compared with the non-uniform pressure resulting from a coupled fluid–structure interaction (FSI) analysis. In addition, a finite element approach is utilised to estimate the effects of asymmetry and wall thickness on the wall stress and fluid dynamics of ten idealised AAA models and one non-aneurysmal control. Five degrees of asymmetry with uniform and variable wall thickness are used. Each was modelled under a static pressure-deformation analysis, as well as a transient FSI. The results show that the inclusion of fluid flow yields a maximum AAA wall stress up to 20% higher compared to that obtained with a static wall stress analysis with an assumed peak luminal pressure of 117 mmHg. The variable wall models have a maximum wall stress nearly four times that of a uniform wall thickness, and also increasing with asymmetry in both instances. The inclusion of an axial stretch and external pressure to the computational domain decreases the wall stress by 17%.     

Numerical study on the flow of a non-Newtonian fluid through an axisymmetric stenosis

The laminar steady flow of non-Newtonian fluid (biviscosity fluid) through an axisymmetric stenosis is calculated using the finite element methods. The flow pattern, the separation and reattachment points, and the distributions of pressure and shear stress at the wall are obtained. Then, the axial force acting on the stenosis is evaluated. It is suggested by the authors that this force can become one of the causes of post-stenotic dilatation. Calculated results show that the non-Newtonian property of blood weakens the distortion of flow pattern, pressure and shear stress at the wall associated with the stenosis and that the non-Newtonian property of blood decreases the axial force acting on the stenosis.