Electro-kinetically modulated peristaltic mechanism of Jeffrey liquid through a micro-channel with variable viscosity

A theoretical model is developed to stimulate electro-kinetic transfer through peristaltic movement in a micro-channel. The effect of variable viscosity and wall properties are considered. The long wavelength and small Reynolds number approximations are supposed to simplify the governing formulas. Debye-Huckel linearization is also utilized. The perturbation technique is utilized to solve the governing non-linear equations. The graphical outcomes are presented for velocity and streamlines.

Mixed convection analysis of cilia-driven flow of a Jeffrey fluid in a vertical tube

In this article, effects of cilia-driven flow of a Jeffrey fluid in a vertical tube are discussed. Mixed convection effects are also considered. Jeffrey fluid equations are simplified by the well-known assumptions of small Reynolds number and large wavelength. An exact solution has been managed for the simplified equations. The ciliated motion features are investigated by plots and are discussed in detail. The consequences show that the pumping machinery functions more competently drive forward Jeffrey fluid than Newtonian fluid. The results may help us better understand the transportation of bio-fluids in the human body.

Viscous Flows

Here some solutions of Navier–Stokes equations are found.The flow of a fluid along a pipe (Poisseuille flow) and that between two rotating cylinders (Couette flow) are the simplest. In the limit of large viscosity (small Reynolds number) the equations become linear: Stokes equations. Flow past a sphere is solved in detail. It is used to calculate the drag on a sphere, a classic formula of Stokes. An exact solution of the Navier–Stokes equation describing a dissipating vortex is also found. It is seen that viscosity cannot be ignored at the boundary or at the core of vortices.

The Navier–Stokes Equations

When different layers of a fluid move at different velocities, there is some friction which results in loss of energy and momentum to molecular degrees of freedom. This dissipation is measured by a property of the fluid called viscosity. The Navier–Stokes (NS) equations are the modification of Euler’s equations that include this effect. In the incompressible limit, the NS equations have a residual scale invariance. The flow depends only on a dimensionless ratio (the Reynolds number). In the limit of small Reynolds number, the NS equations become linear, equivalent to the diffusion equation. Ideal flow is the limit of infinite Reynolds number. In general, the larger the Reynolds number, the more nonlinear (complicated, turbulent) the flow.

Influence of Inclined Magnetic Field on the Peristaltic Flow of a Jeffrey Fluid in an Inclined Porous Channel

In this paper we have studied the effects of inclined magnetic field, porous medium and wall properties on the peristaltic transport of a Jeffry fluid in an inclined non-uniform channel. The basic governing equations are solved by using the infinite wave length and small Reynolds number assumptions. The analytical solutions have obtained for velocity and stream function. The variations in velocity for different values of important parameters have presented in graphs. The results are discussed for both uniform and non-uniform channels.

Locomotion inside a surfactant-laden drop at low surface Péclet numbers

We investigate the dynamics of a swimming microorganism inside a surfactant-laden drop for axisymmetric configurations under the assumptions of small Reynolds number and small surface Péclet number $(Pe_{s})$. Expanding the variables in $Pe_{s}$, we solve the Stokes equations for the concentric configuration using Lamb’s general solution, while the dynamic equation for the stream function is solved in the bipolar coordinates for the eccentric configurations. For a two-mode squirmer inside a drop, the surfactant redistribution can either increase or decrease the magnitude of swimmer and drop velocities, depending on the value of the eccentricity. This was explained by analysing the influence of surfactant redistribution on the thrust and drag forces acting on the swimmer and the drop. The far-field representation of a surfactant-covered drop enclosing a pusher swimmer at its centre is a puller; the strength of this far field is reduced due to the surfactant redistribution. The advection of surfactant on the drop surface leads to a time-averaged propulsion of the drop and the time-reversible swimmer that it engulfs, thereby causing them to escape from the constraints of the scallop theorem. We quantified the range of parameters for which an eccentrically stable configuration can be achieved for a two-mode squirmer inside a clean drop. The surfactant redistribution shifts this eccentrically stable position towards the top surface of the drop, although this shift is small.