Peristaltic Transport of a Couple Stress Fluid: Some Applications to Hemodynamics

The present paper deals with a theoretical investigation of the peristaltic transport of a couple stress fluid in a porous channel. The study is motivated towards the physiological flow of blood in the micro-circulatory system, by taking account of the particle size effect. The velocity, pressure gradient, stream function and frictional force of blood are investigated, when the Reynolds number is small and the wavelength is large, by using appropriate analytical and numerical methods. Effects of different physical parameters reflecting porosity, Darcy number, couple stress parameter as well as amplitude ratio on velocity profiles, pumping action and frictional force, streamlines pattern and trapping of blood are studied with particular emphasis. The computational results are presented in graphical form. The results are found to be in good agreement with those of Shapiro et. al \cite{r25} that was carried out for a non-porous channel in the absence of couple stress effect. The present study puts forward an important observation that for peristaltic transport of a couple stress fluid during free pumping when the couple stress effect of the fluid/Darcy permeability of the medium, flow reversal can be controlled to a considerable extent. Also by reducing the permeability it is possible to avoid the occurrence of trapping phenomenon

Mathematical modelling of nonlinear thermal radiation effects on EMHD peristaltic pumping of viscoelastic dusty fluid through a porous medium duct

Biologically-inspired propulsion systems are currently receiving significant interest in the aerospace sector. Since many spacecraft propulsion systems operate at high temperatures, thermal radiation is important as a mode of heat transfer. Motivated by these developments, in the present article, the influence of nonlinear thermal radiation (via the Rosseland diffusion flux model) has been studied on the laminar, incompressible, dissipative EMHD (Electro-magneto-hydrodynamic) peristaltic propulsive flow of a non-Newtonian (Jefferys viscoelastic) dusty fluid containing solid particles through a porous planar channel. The fluid is electrically-conducting and a constant static magnetic field is applied transverse to the flow direction (channel walls). Slip effects are also included. Magnetic induction effects are neglected. The mathematical formulation is based on continuity, momentum and energy equations with appropriate boundary conditions, which are simplified by neglecting the inertial forces and taking the long wavelength and lubrication approximations. The boundary value problem is then rendered non-dimensional with appropriate variables and the resulting system of reduced ordinary differential equations is solved analytically. The impact of various emerging parameters dictating the non-Newtonian propulsive flow i.e. Prandtl number, radiation parameter, Hartmann number, permeability parameter, Eckert number, particle volume fraction, electric field and slip parameter are depicted graphically. Increasing particle volume fraction is observed to suppress temperature magnitudes. Furthermore the computations demonstrate that an increase in particle volume fraction reduces the pumping rate in retrograde pumping region whereas it causes the opposite effect in the co-pumping region. The trapping mechanism is also visualized with the aid of streamline contour plots. Increasing thermal radiation elevates temperatures. Increasing Hartmann (magnetic body force) number decreases the size of the trapping bolus whereas the quantity of the does not effected. Conversely increasing particle volume fraction reduces the magnitude of the trapping bolus whereas the number of trapped bolus remains constant

(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

Analytical study of electro-osmosis modulated capillary peristaltic hemodynamics

A mathematical model is developed to analyse electro-kinetic effects on unsteady peristaltic transport of blood in cylindrical vessels of finite length. The Newtonian viscous model is adopted. The analysis is restricted under Debye-Hückel linearization (i.e. wall zeta potential less than or equal to 25mV is sufficiently small). The transformed, non-dimensional conservation equations are derived via lubrication theory and long wavelength and the resulting linearized boundary value problem is solved exactly. The case of a thin electric double layer (i.e. where only slip electro-osmotic velocity considered) is retrieved as a particular case of the present model. The response in pumping characteristics (axial velocity, pressure gradient or difference, volumetric flow rate, local wall shear stress) to the influence of electro-osmotic effect (inverse Debye length) and Helmholtz-Smoluchowski velocity is elaborated in detail. Visualization of trapping phenomenon is also included and the bolus dynamics evolution with electro-kinetic effects examined. A comparative study of train wave propagation and single wave propagation is presented under the effects of thickness of EDL and external electric field. The study is relevant to electrophoresis in haemotology, electrohydrodynamic therapy and biomimetic electro-osmotic pumps

Peristaltic transport of bi-viscosity fluids through a curved tube : a mathematical model for intestinal flow

The human intestinal tract is a long curved tube constituting the final section of the digestive system in which nutrients and water are mostly absorbed. Motivated by the dynamics of chyme in the intestine, a mathematical model is developed to simulate the associated transport phenomena via peristaltic transport. Rheology of chyme is modelled using the Nakamura-Sawada bi-viscosity non-Newtonian formulation. The intestinal tract is considered as a curved tube geometric model. Low Reynolds number (creeping hydrodynamics) and long wavelength approximations are taken into consideration.Analytical solutions of the moving boundary value problem are derived for velocity field,pressure gradient and pressure rise. Streamline flow visualization is achieved with Mathematica symbolic software. Peristaltic pumping phenomenon and trapping of the bolus are also examined. The influence of curvature parameter, apparent viscosity coefficient (rheological parameter) and volumetric flow rate on flow characteristics is described. Validation of analytical solutions is achieved with a MAPLE17 numerical quadrature algorithm. The work is relevant to improving understanding of gastric hydrodynamics and provides a benchmark for further computational fluid dynamics (CFD) simulations

Electro-magneto-hydrodynamic peristaltic pumping of couple stress biofluids through a complex wavy micro-channel

Biomimetic propulsion mechanisms are increasingly being explored in engineering sciences. Peristalsis is one of the most efficient of these mechanisms and offers considerable promise in microscale fluidics. Electrokinetic peristalsis has recently also stimulated significant attention. Electrical and magnetic fields also offer an excellent mode for regulating flows. Motivated by novel applications in electro-conductive microchannel transport systems, the current article investigates analytically the electromagnetic pumping of non-Newtonian aqueous electrolytes via peristaltic waves in a two-dimensional microchannel with different peristaltic waves propagating at the upper and lower channel wall (complex wavy scenario). The Stokes couple stress model is deployed to capture micro-structural characteristics of real working fluids. The unsteady two-dimensional conservation equations for mass and momentum conservation, electro-kinetic and magnetic body forces, are formulated in two-dimensional Cartesian co-ordinates. The transport equations are transformed from the wave frame to the laboratory frame and the electrical field terms rendered into electrical potential terms via the Poisson-Boltzmann equation, Debye length approximation and ionic Nernst Planck equation. The dimensionless emerging linearized electro-magnetic boundary value problem is solved using integral methods. The influence of Helmholtz-Smoluchowski velocity (characteristic electro-osmotic velocity), couple stress length parameter (measure of the polarity of the fluid), Hartmann magnetic number, and electro-osmotic parameter on axial velocity, volumetric flow rate, time-averaged flow rate and streamline distribution are visualized and interpreted at length

Electro-osmotic flow of couple stress fluids in a microchannel propagated by peristalsis

A mathematical model is developed for electro-osmotic peristaltic pumping of a non-Newtonian liquid in a deformable micro-channel. Stokes’ couple stress fluid model is deployed to represent realistic working liquids. The Poisson-Boltzmann equation for electric potential distribution is implemented owing to the presence of an electrical double layer (EDL) in the micro-channel. Using long wavelength, lubrication theory and Debye-Huckel approximations, the linearized transformed dimensionless boundary value problem is solved analytically. The influence of electro-osmotic parameter (inversely proportional to Debye length), maximum electro-osmotic velocity (a function of external applied electrical field) and couple stress parameter on axial velocity, volumetric flow rate, pressure gradient, local wall shear stress and stream function distributions is evaluated in detail with the aid of graphs. The Newtonian fluid case is retrieved as a special case with vanishing couple stress effects. With increasing couple stress parameter there is a significant elevation in axial pressure gradient whereas the core axial velocity is reduced. An increase in electro-osmotic parameter induces both flow acceleration in the core region (around the channel centreline) and also enhances axial pressure gradient substantially. The study is relevant to simulation of novel smart bio-inspired space pumps, chromatography and medical microscale devices

Slip and hall current effects on Jeffrey fluid suspension flow in a peristaltic hydromagnetic blood micropump

The magnetic properties of blood allow it to be manipulated with an electromagnetic field. Electromagnetic blood flow pumps are a robust technology which provide more elegant and sustainable performance compared with conventional medical pumps. Blood is a complex multi-phase suspension with non-Newtonian characteristics which are significant in micro-scale transport. Motivated by such applications, in the present article a mathematical model is developed for magnetohydrodynamic (MHD) pumping of blood in a deformable channel with peristaltic waves. A Jeffery’s viscoelastic formulation is employed for the rheology of blood. A twophase fluid-particle (“dusty”) model is utilized to better simulate suspension characteristics (plasma and erythrocytes). Hall current and wall slip effects are incorporated to achieve more realistic representation of actual systems. A two-dimensional asymmetric channel with dissimilar peristaltic wave trains propagating along the walls is considered. The governing conservation equations for mass, fluid and particle momentum are formulated with appropriate boundary conditions. The model is simplified using of long wavelength and creeping flow approximations. The model is also transformed from the fixed frame to the wave frame and rendered non-dimensional. Analytical solutions are derived. The resulting boundary value problem is solved analytically and exact expressions are derived for the fluid velocity, particulate velocity, fluid/particle fluid and particulate volumetric flow rates, axial pressure gradient, pressure rise and skin friction distributions are evaluated in detail. Increasing Hall current parameter reduces bolus growth in the channel, particle phase velocity and pressure difference in the augmented pumping region whereas it increases fluid phase velocity, axial pressure gradient and pressure difference in the pumping region. Increasing the hydrodynamic slip parameter accelerates both particulate and fluid phase flow at and close to the channel walls, enhances wall skin friction, boosts pressure difference in the augmented pumping region and increases bolus magnitudes. Increasing viscoelastic parameter (stress relaxation time to retardation time ratio) decelerates the fluid phase flow, accelerates the particle phase flow, decreases axial pressure gradient, elevates pressure difference in the augmented pumping region and reduces pressure difference in the pumping region. Increasing drag particulate suspension parameter decelerates the particle phase velocity, accelerates the fluid phase velocity, strongly elevates axial pressure gradient and reduces pressure difference (across one wavelength) in the augmented pumping region. Increasing particulate volume fraction density enhances bolus magnitudes in both the upper and lower zones of the channel and elevates pressure rise in the augmented pumping region

Effects of coagulation on the two-phase peristaltic pumping of magnetized Prandtl biofluid through an endoscopic annular geometry containing a porous medium

In this article, motivated by more accurate simulation of electromagnetic blood flow in annular vessel geometries in intravascular thrombosis, a mathematical model is developed for elucidating the effects of coagulation (i.e. a blood clot) on peristaltically induced motion of an electrically-conducting (magnetized) Prandtl fluid physiological suspension through a non-uniform annulus containing a homogenous porous medium. Magnetohydrodynamics is included owing to the presence of iron in the hemoglobin molecule and also the presence of ions in real blood. Hall current which generates a secondary (cross) flow at stronger magnetic field is also considered in the present study. A small annular tube (endoscopic) with sinusoidal peristaltic waves traveling along the inner and outer walls at constant velocity with a clot present is analyzed. The governing conservation equations which comprise the continuity and momentum equations for the fluid phase and particle phase are simplified under lubrication approximations (long wavelength and creeping flow conditions). The moving boundary value problem is normalized and solved analytically (with appropriate wall conditions) for the fluid phase and particle phase using the homotopy perturbation method (HPM) with MATHEMATICA software. Validation is conducted with MAPLE numerical quadrature. A parametric study of the influence of clot height (δ), particle volume fraction (C), Prandtl fluid material parameters (α, β), Hartmann number (M), Hall parameter (m), permeability parameter (k), peristaltic wave amplitude (φ) and wave number (δ̅ ) on pressure difference and wall shear (friction forces) is included. Pressure rise is elevated with clot height, medium permeability and Prandtl rheological material parameters whereas it is reduced with increasing particle volume fraction and magnetic Hartmann number. Friction forces on the outer and inner tubes of the endoscope annulus are enhanced with clot height and particle volume fraction whereas they are decreased with Prandtl rheological material parameters, Hall parameter and permeability parameter. The simulations provide a good benchmark for more general computational fluid dynamics studies of magnetic endoscopic multi-phase peristaltic pumping

Electrothermal transport of nanofluids via peristaltic pumping in a finite micro-channel : effects of joule heating and Helmholtz-Smoluchowski velocity

The present article studies theoretically the electrokinetic pumping of nanofluids with heat and mass transfer in a micro-channel under peristaltic waves, a topic of some interest in medical nano-scale electro-osmotic devices. The microchannel walls are deformable and transmit periodic waves. The Chakraborty-Roy nanofluid electrokinetic formulation is adopted in which Joule heating effects are incorporated. Soret and Dufour cross-diffusion effects are also considered. Under low Reynolds number (negligible inertial effects), long wavelength and Debye linearization approximations, the governing partial differential equations for mass, momentum, energy and solute concentration conservation are derived with appropriate boundary conditions at the micro-channel walls. The merging model features a number of important thermo-physical, electrical and nanoscale parameter, namely thermal and solutal Grashof numbers, the Helmholtz-Smoluchowski velocity (maximum electro-osmotic velocity) and Joule heating to surface heat flux ratio. Closed-form solutions are derived for the solute concentration, temperature, axial velocity, averaged volumetric flow rate, pressure difference across one wavelength, and stream function distribution in the wave frame. Additionally expressions are presented for the surface shear stress function at the wall (skin friction coefficient), wall heat transfer rate (Nusselt number) and wall solute mass transfer rate (Sherwood number). The influence of selected parameters on these flow variables is studied with the aid of graphs. Bolus formation is also visualized and analyzed in detail