Pramod Kumar Yadav

ON HYDRODYNAMIC PERMEABILITY OF A MEMBRANE BUILT UP BY POROUS DEFORMED SPHEROIDAL PARTICLES

This paper concerns the slow viscous flow of an incompressible fluid past a swarm of identically oriented porous deformed spheroidal particles, using particle-in-cell method. The Brinkman’s equation in the porous region and the Stokes equation for clear fluid region in their stream function formulations are used. Explicit expressions are investigated for both the inside and outside flow fields to the first order in a small parameter characterizing the deformation. The flow through the porous oblate spheroid is considered as the particular case of the porous deformed spheroid. The hydrodynamic drag force experienced by a porous oblate spheroid and permeability of a membrane built up by porous oblate spheroids having parallel axis are evaluated. The dependence of the hydrodynamic drag force and the hydrodynamic permeability on particle volume fraction, deformation parameter and viscosity of porous fluid are also discussed. Four known boundary conditions on the hypothetical surface are considered and compared: Happel’s, Kuwabara’s, Kvashnin’s and Cunningham’s (Mehta-Morse’s condition). Some previous results for hydrodynamic drag force and hydrodynamic permeability have been verified. The model suggested can be used for evaluation of changing hydrodynamic permeability of a membrane under applying unidirectional loading in pressure-driven processes (reverse osmosis, nano-, ultra- and microfiltration).

A Jeffrey-fluid model of blood flow in tubes with stenosis

In this paper, we discuss the two-layered Jeffrey-fluid model with mild stenosis in narrow tubes. The blood flow in narrow arteries is treated as a two-fluid model with the suspension of erythrocytes, leukocytes, etc., as a Jeffrey fluid, which is a non-Newtonian fluid, in the core region and plasma, a Newtonian fluid, in the peripheral region. An analytical solution has been obtained for the velocity in the core and peripheral region, volume flow rate, resistance to flow, and wall-shear stress. The effect of Jeffrey-fluid parameters, like the height of stenosis, viscosity, etc., on volume flow rate, resistance to flow (impedance), and wall-shear stress has been discussed graphically. Through the present study, it is found that the wall-shear stress and resistance to flow increases with the increase in height of stenosis and decreases with the increase in the ratio of relaxation time. It is also found that the velocity decreases with an increase in stenosis height in both the core and the peripheral region. A previous result has been also verified.

Effect of magnetic field on the hydrodynamic permeability of a membrane built up by porous spherical particles

In this paper, an analysis of steady, axi-symmetric Stokes flow of an electrically conducting viscous incompressible fluid through spherical particle covered by porous shell in presence of uniform magnetic field is presented. To model flow through the swarm of spherical particles, cell model technique has been used, i.e. porous spherical shell is assumed to be confined within a hypothetical cell of the same geometry. At the fluid-porous interface, the stress jump boundary condition for tangential stresses along with continuity of normal stress and velocity components are used. Four known boundary conditions on the hypothetical surface were considered and compared: Happel’s, Kuwabara’s, Kvashnin’s and Cunningham’s (Mehta−Morse’s) condition. The effect of stress jump coefficient, Hartmann number, and dimensionless permeability of the porous region as well as particle volume fraction on the hydrodynamic permeability and streamlines were discussed. The patterns of streamlines were also obtained.

A Two-Layer Mathematical Model of Blood Flow in Porous Constricted Blood Vessels

In this paper, we discussed a mathematical model for two-layered non-Newtonian blood flow through porous constricted blood vessels. The core region of blood flow contains the suspension of erythrocytes as non-Newtonian Casson fluid and the peripheral region contains the plasma flow as Newtonian fluid. The wall of porous constricted blood vessel configured as thin transition Brinkman layer over layered by Darcy region. The boundary of fluid layer is defined as stress jump condition of Ocha-Tapiya and Beavers–Joseph. In this paper, we obtained an analytic expression for velocity, flow rate, wall shear stress. The effect of permeability, plasma layer thickness, yield stress and shape of the constriction on velocity in core & peripheral region, wall shear stress and flow rate is discussed graphically. This is found throughout the discussion that permeability and plasma layer thickness have accountable effect on various flow parameters which gives an important observation for diseased blood vessels.