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

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

Peristaltic Transport of a Particle–Fluid Suspension through a Uniform and Non-Uniform Annulus

This study looks at the influence of an endoscope on the peristaltic flow of a particle–fluid suspension (as blood model) through tubes. A long wavelength approximation through a uniform and non-uniform infinite annulus filled with an incompressible viscous and Newtonian fluid mixed with rigid spherical particles of identical size is investigated theoretically. The inner tube is uniform, rigid and moving with a constant velocity V0, whereas the outer non-uniform tube has a sinusoidal wave travelling down its wall. The axial velocity of the fluid phase uf, particulate phase up and the pressure gradients have been obtained in terms of the dimensionless flow rate Q, the amplitude ratio ɸ, particle concentration C, the velocity constant V0 and the radius ratio ϵ (the ratio between the radius of the inner tube and the radius of the outer one at the inlet). Numerical calculations for various values of the physical parameters of interest are carried out for the pressure rise and the friction force on the inner and the outer tubes

Peristaltic transport of a particle-fluid suspension through a uniform and non-uniform annulus

This study looks at the influence of an endoscope on the peristaltic flow of a particle-fluid suspension (as blood model) through tubes. A long wavelength approximation through a uniform and non-uniform infinite annulus filled with an incompressible viscous and Newtonian fluid mixed with rigid spherical particles of identical size is investigated theoretically. The inner tube is uniform, rigid and moving with a constant velocity V 0 , whereas the outer non-uniform tube has a sinusoidal wave travelling down its wall. The axial velocity of the fluid phase u f , particulate phase u p and the pressure gradients have been obtained in terms of the dimensionless flow rate Q, the amplitude ratio φ, particle concentration C, the velocity constant V 0 and the radius ratio (the ratio between the radius of the inner tube and the radius of the outer one at the inlet). Numerical calculations for various values of the physical parameters of interest are carried out for the pressure rise and the friction force on the inner and the outer tubes