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Electrophoresis in dilute polymer solutions

Published online by Cambridge University Press:  05 December 2019

Gaojin Li  and
Donald L. Koch Open the ORCID record for Donald L. Koch [Opens in a new window]
Gaojin Li
Affiliation:
Robert Frederick Smith School of Chemical and Biomolecular Engineering, Cornell University, Olin Hall, Ithaca, NY14853, USA
Donald L. Koch*
Affiliation:
Robert Frederick Smith School of Chemical and Biomolecular Engineering, Cornell University, Olin Hall, Ithaca, NY14853, USA
*
†Email address for correspondence: [email protected]
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Abstract

We analyse the electrophoresis of a weakly charged particle with a thin double layer in a dilute polymer solution. The particle velocity in polymer solutions modelled with different constitutive equations is calculated using a regular perturbation in the polymer concentration and the generalized reciprocal theorem. The analysis shows that the polymer is strongly stretched in two regions, the birefringent strand and the high-shear region inside the double layer. The electrophoretic velocity of the particle always decreases with the addition of polymers due to both increased viscosity and fluid elasticity. At a small Weissenberg number ($Wi$), which is the product of the polymer relaxation time and the shear rate, the polymers inside the double layer contribute to most of the velocity reduction by increasing the fluid viscosity. With increasing $Wi$, viscoelasticity decreases and shear thinning increases the particle velocity. Polymer elasticity alters the fluid velocity disturbance outside the double layer from that of a neutral squirmer to a puller-type squirmer. At high $Wi$, the strong extensional stress inside the birefringent strand downstream of the particle dominates the velocity reduction. The scaling of the birefringent strand is used to estimate the particle velocity.

JFM classification

Non-Newtonian Flows: Viscoelasticity
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 884 , 10 February 2020 , A9
Copyright
© 2019 Cambridge University Press

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