Nonlinear electrophoresis of a tightly fitting sphere in a cylindrical tube

J. D. Sherwood*, Sandip Ghosal

*Corresponding author for this work

Research output: Contribution to journalArticle

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Abstract

We investigate electrophoresis of a tightly fitting sphere of radius on the axis of a circular tube of radius , using lubrication theory and ideas due to Schnitzer & Yariv (Phys. Fluids, vol. 26, 2014, 122002). The electrical charge clouds on both the cylindrical wall and the surface of the sphere are assumed thin compared to the gap between the sphere and cylinder, so that charge clouds do not overlap and ion exclusion effects are minimal. Nevertheless, non-uniform pumping of counter-ions within the charge clouds leads to a change in the ionic concentration outside the charge clouds in the narrow gap between sphere and cylinder. The electro-osmotic slip velocities at the two surfaces are modified, leading to a decrease in the electrophoretic velocity of the sphere at low Péclet numbers and an increase in the velocity at high Péclet numbers. When the field strength is low, it is known that the electrophoretic velocity is proportional to which is zero when the zeta potential on the sphere surface is equal to the zeta potential on the cylinder. The perturbation to the above low field strength electrophoretic velocity (at high Péclet number) is predicted to be proportional to , where and are the surface charge densities on the sphere and cylinder. The choice of materials with similar or identical zeta potentials (and surface charge densities) for the cylinder and sphere should therefore facilitate the observation of velocities nonlinear in the field strength , since the reference linear electrophoretic velocity will be small.

Original languageEnglish (US)
Pages (from-to)847-871
Number of pages25
JournalJournal of Fluid Mechanics
Volume843
DOIs
StatePublished - May 25 2018

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Keywords

  • colloids
  • lubrication theory
  • micro-/nano-fluid dynamics

ASJC Scopus subject areas

  • Condensed Matter Physics
  • Mechanics of Materials
  • Mechanical Engineering

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