Electro-osmotic and Pressure-Driven Flow in an Eccentric Microannulus

Consideration is given to steady, fully developed mixed electro-osmotic/pressure-driven flow of Newtonian fluid in an eccentric microannulus. The governing Poisson–Boltzmann and momentum equations are solved numerically in bipolar coordinates. It is shown that for a fixed aspect ratio, fully eccentric channels sustain the maximum average viscosity (i.e. flow rate) under the same dimensionless pressure gradient and electro kinetic radius. For the Debye–Hückel approximation (linearised Poisson–Boltzmann equation), we show that closed-form analytical solution can be derived for velocity field. Finally, the effect of the electrokinetic radius, pressure gradient, and eccentricity on the flow field was investigated in detail.

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.

Electrophoresis of a Cylinder in a Cylindrical Tube

Electrophoresis of a cylinder suspended in a cylindrical tube is analytically studied in the limit of thin electric double layer approximation. The electric and fluid flow fields within the annulus, and the cylinder velocities are analytically obtained in bipolar coordinates. The results are analyzed with various values of dimensionless parameters: eccentricity, cylinder-to-tube radius ratio and tube-to-cylinder zeta potential ratio (i.e., tube-to-cylinder velocity scale ratio). The analysis shows that microvortices are generated within the annulus. By changing the parameters, different flow patterns can be created, which shows potential for mixing enhancement in micro/nanofluidics. Moreover, the cylinder not only translates but also rotates when the cylinder and tube are eccentric. The cylinder rotation might be utilized as a micromotor or an electric field detector. The cylinder trajectories show that the cylinder may approach the tube wall or rest within the tube depending on the zeta potential ratio.

Slip Flow in Eccentric Annuli

A solution of the problem of Poiseuille slip flow through an eccentric cylindrical annulus is obtained in bipolar coordinates. The solution is in excellent agreement with the two published limiting cases of slip flow through concentric annuli and no-slip flow through eccentric annuli. It is shown that for a fixed aspect ratio, fully eccentric channels sustain the maximum average velocity (flow rate) under the same pressure gradient and slip conditions. For a given channel geometry, the average velocity varies linearly with Knudsen number except for small aspect ratio. It is also shown that the extrema of the friction factor Reynolds number product is determined by how this product is defined or scaled.

Magnetic levitation force exerted on the cylindrical magnet in a ferrofluid damper

The levitation phenomenon of permanent magnets immersed in ferrofluid is the foundation of ferrofluid dampers. According to the model built using bipolar coordinates, the analytical equation describing the force exerted on the cylindrical magnets in ferrofluid dampers is obtained, which is different from that of the previous results. The analysis of the equation indicates that the magnetic levitation force increases with the eccentricity of the magnet, the radius of the magnet and the permeability of ferrofluid, respectively, when other factors are definite. As a result, we can increase the permeability of ferrofluid and decrease the radius ratio of the magnet and the tube to enhance the levitation stability.

Velocity Profile of Viscous-Elastic Fluid in Eccentric Annulus with the Internal Rod Moving Axially

Using lower-convected Maxwell constitutive model, the control equation of the steady flow of viscous-elastic fluid in the eccentric annulus with inner rod moving axially in the bipolar coordinates system is established, and discreted by control-volume method, the velocity profile is solved by ADI methods, which lays theory basis for further analyzing the stress field and the reason of pumping rod eccentric wear. The result shows: eccentric ratio is the most important factor to the velocity profile.