TY - JOUR

T1 - Nonlinear electrophoresis of a tightly fitting sphere in a cylindrical tube

AU - Sherwood, J. D.

AU - Ghosal, S.

N1 - Funding Information:
We thank our anonymous referees for suggestions that led to improvement of this paper. J.D.S. thanks the Department of Applied Mathematics and Theoretical Physics, University of Cambridge, for hospitality.
Publisher Copyright:
© 2018 Cambridge University Press.

PY - 2018/5/25

Y1 - 2018/5/25

N2 - 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.

AB - 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.

KW - colloids

KW - lubrication theory

KW - micro-/nano-fluid dynamics

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U2 - 10.1017/jfm.2018.212

DO - 10.1017/jfm.2018.212

M3 - Article

AN - SCOPUS:85044454121

VL - 843

SP - 847

EP - 871

JO - Journal of Fluid Mechanics

JF - Journal of Fluid Mechanics

SN - 0022-1120

ER -