Electrokinetics of spherical colloidal particles with a slip surface in a concentrated suspension
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ORIGINAL CONTRIBUTION
Electrokinetics of spherical colloidal particles with a slip surface in a concentrated suspension Hiroyuki Ohshima 1 Received: 29 March 2020 / Revised: 10 September 2020 / Accepted: 24 September 2020 # Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract A theory is developed of the electrophoresis of a spherical colloidal particle with a slip surface in a concentrated suspension on the basis of Kuwabara’s cell model. We introduce the slipping length on the particle surface, which is the measure of the particle surface hydrophobicity. We derive the general expression of the particle electrophoretic mobility and its approximate analytic expressions for a particle carrying a low zeta potential. Expressions for other electrokinetics, that is, electrical conductivity, sedimentation velocity, and potential in concentrated suspensions, are also derived. Furthermore, it is shown that as in the case of a dilute suspension, a similarity is found between the electrokinetics of charged spherical solid particles with a slip surface in a concentrated suspension and that for liquid drops. Keywords Electrokinetics . Electrophoretic mobility . Zeta potential . Spherical particle . Slip surface . Concentrated suspension
Introduction The purpose of the present paper is to derive the general expression of the electrophoretic mobility of a spherical colloidal particle with a slip surface in a concentrated suspension on the basis of a cell model [1–16] and its approximate formula for the low zeta potential case. The standard theory of the electrophoresis of colloidal particles in dilute/concentrated suspensions usually assumes that no liquid slip occurs on the particle surface [17–32]. Instead of the no-slip boundary condition, which can be applied only to a hydrophilic surface, we here employ the slip boundary condition (i.e., the Navier boundary condition) suitable for a hydrophobic surface [33–46]. The hydrophobicity of the particle surface is characterized by the slipping length Λ. Many experiments have been conducted over the past two decades to show that hydrodynamic slip occurs on the hydrophobic surface, demonstrating that Λ is of the order of nanometers. In particular, Churaev et al. [34] reported enhancement of the electroosmotic flow on a hydrophobic surface due to the hydrodynamic slip. Bouzigues et al. [37] performed novel experiments to measure slip lengths Λ
over hydrophilic and hydrophobic surfaces. Recently, Kobayashi [38] analyzed the electrophoretic mobility of hydrophobic polystyrene particles in aqueous monovalent electrolyte solutions using standard electrokinetic equations with the Navier boundary condition. He showed that the introduction of the slip length of a few nanometers increases the magnitude of the electrophoretic mobility of polystyrene particles, leading to better agreement between experimental mobility and theoretical mobility. A detailed theoretical study on the electrophoretic mobility of a spherical particle with a slip surface was made by Khair and Squires
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