Sedimentation Potential of Charged Spherical Colloidal Particles in an Uncharged Polymer Gel Medium: An Onsager Reciprocal Relation Approach

ABSTRACT A theoretical analysis is presented for the sedimentation potential of a dilute suspension of charged spherical colloidal particles in an uncharged polymer gel medium saturated with an electrolyte solution. The polymer gel is described by the Brinkman–Debye–Bueche model, in which the polymer network provides hydrodynamic resistance to the flow of the electrolyte solution. An important advantage of sedimentation‐potential measurements for determining the zeta potential is that, unlike electrophoretic mobility measurements, they do not require an externally applied electric field, since the potential arises from the gravitational sedimentation of charged particles. In the present study, rather than deriving the sedimentation potential directly from the coupled electrokinetic equations, we employ the Onsager reciprocal relation between sedimentation and electrophoresis. The sedimentation potential is therefore obtained directly from the electrophoretic mobility of a spherical particle in the same gel medium, for which an analytical expression has been derived previously. This approach leads to a simple analytical expression for the sedimentation potential and establishes a direct connection between sedimentation and electrophoresis in an uncharged polymer gel medium. The result reduces to the corresponding expression for a particle in a free electrolyte solution in the limit of vanishing hydrodynamic resistance of the polymer network. The present analysis demonstrates that the Onsager reciprocal relation provides a simple and useful route for obtaining sedimentation potentials from established gel electrophoresis theories.