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Dynamic electric-field-induced response of charged spherical colloids in uncharged hydrogels

Published online by Cambridge University Press:  02 November 2009

MU WANG  and
REGHAN J. HILL
MU WANG
Affiliation:
Department of Chemical Engineering, McGill University, Montreal, Quebec H3A 2B2, Canada
REGHAN J. HILL*
Affiliation:
Department of Chemical Engineering, McGill University, Montreal, Quebec H3A 2B2, Canada McGill Institute for Advanced Materials, McGill University, Montreal, Quebec H3A 2B2, Canada
*
†Email address for correspondence: reghan.hill@mcgill.ca
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Abstract

Embedding colloidal particles in polymeric hydrogels often endows the polymer skeleton with appealing characteristics for microfluidics and biosensing applications. This theoretical study provides a rigorous foundation for interpreting active electrical microrheology and electroacoustic experiments on such materials. In addition to viscoelastic properties of the composites, these techniques sense physicochemical characteristics of the particle–polymer interface. Wang & Hill (Soft Matter, vol. 4, 2008, p. 1048) studied the steady response of a rigid, impenetrable sphere in a compressible hydrogel skeleton. Here, we extend their analysis to arbitrary frequencies, showing, in general, how the frequency response depends on the particle size and charge, ionic strength of the electrolyte and elastic and hydrodynamic characteristics of the polymer skeleton. Our calculations capture the transition from quasi-steady compressible to quasi-steady incompressible dynamics as the frequency passes through the reciprocal draining time of the gel. Above the reciprocal draining time, the skeleton and fluid move in unison, so the dynamics are incompressible and, thus, given to an excellent approximation by the well-known dynamic electrophoretic mobility but with the Newtonian shear viscosity replaced by a complex, frequency-dependent value.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 640 , 10 December 2009 , pp. 357 - 400
Copyright
Copyright © Cambridge University Press 2009

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