Electrophoresis of tightly fitting spheres along a circular cylinder of finite length

Electrophoresis of a tightly fitting sphere of radius $a$ along the centreline of a liquid-filled circular cylinder of radius $R$ is studied for a gap width $h_0=R-a\ll a$. We assume a Debye length $\kappa ^{-1}\ll h_0$, so that surface conductivity is negligible for zeta potentials typically seen i...

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Bibliographic Details
Published in:Journal of fluid mechanics 2021-12, Vol.929, Article A45
Main Authors: Sherwood, J.D., Ghosal, S.
Format: Article
Language:English
Subjects:
Analytical methods
Boundary conditions
Circular cylinders
Cylinders
Debye length
Electric fields
Electrophoresis
Fluid mechanics
JFM Papers
Slip velocity
Solid surfaces
Spheres
Velocity
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Summary:Electrophoresis of a tightly fitting sphere of radius $a$ along the centreline of a liquid-filled circular cylinder of radius $R$ is studied for a gap width $h_0=R-a\ll a$. We assume a Debye length $\kappa ^{-1}\ll h_0$, so that surface conductivity is negligible for zeta potentials typically seen in experiments, and the Smoluchowski slip velocity is imposed as a boundary condition at the solid surfaces. The pressure difference between the front and rear of the sphere is determined. If the cylinder has finite length $L$, this pressure difference causes an additional volumetric flow of liquid along the cylinder, increasing the electrophoretic velocity of the sphere, and an analytic prediction for this increase is found when $L\gg R$. If $N$ identical, well-spaced spheres are present, the electrophoretic velocity of the spheres increases with $N$, in agreement with the experiments of Misiunas & Keyser (Phys. Rev. Lett., vol. 122, 2019, 214501).
ISSN:0022-1120
1469-7645
DOI:10.1017/jfm.2021.892