Journal of Colloid and Interface Science 260 (2003) 118–125 www.elsevier.com/locate/jcis Dynamic electrophoretic mobility of a sphere in a spherical cavity Cheng-Pang Tung, Eric Lee, and Jyh-Ping Hsu ∗ Department of Chemical Engineering, National Taiwan University, Taipei 10617, Taiwan, ROC Received 13 August 2002; accepted 5 December 2002 Abstract Dynamic electrophoresis is a powerful analytical tool for the description of the surface properties of the charged entities in a concentrated dispersion. In our study the boundary effect on this dynamic phenomenon is investigated theoretically for the case, when the surface potential is low. In particular, the dynamic electrophoresis of a sphere in a spherical cavity is discussed as are the effects of the key factors on the phenomenon under consideration, which include the thickness of the double layer, the frequency of the applied electric field, the ratio of particle radius to cavity radius, and the boundary conditions of the surfaces of the particle and the cavity. The results of numerical simulation reveal that these key factors can have both quantitative and qualitative influence on the electrophoretic behavior of the particle. As an example, for the case of a positively charged particle placed in a negatively charged cavity if the double layer surrounding the particle is thin, the magnitude of the electrophoretic mobility of the particle increases with an increase in the frequency of the applied electric field and a phase lead may occur, but the opposite is true if the double layer is thick. These effects are not observed for the case of a positively charged particle placed in an uncharged cavity or for a positively charged particle placed in a positively charged cavity.  2003 Elsevier Science (USA). All rights reserved. Keywords: Electrophoresis, dynamic; Boundary effect, sphere in spherical cavity; Double-layer thickness, arbitrary; Surface potential, low; Applied electric field, frequency, phase angle 1. Introduction When a sound wave passes through an electrolyte solu- tion, a dynamic electric field will be induced. This phenom- enon is observed for the case of a colloidal dispersion, the so-called colloid vibration potential (CVP) effect. Although the CVP effect was investigated extensively, its development was limited due to the lack of an appropriate experimen- tal apparatus for its quantification. The problem remained unsolved until around 1980 when several devices become available. One of these is that used to measure the inverse effect of CVP; that is, a dynamic electric field is applied to a colloidal dispersion to induce a sound wave, the so-called electrokinetic sonic amplitude (ESA) effect. For both CVP and ESA effects, the frequency of the applied electric field is the same as that of the response frequency. The combination of CVP and ESA effects is called the electroacoustic effect by O’Brien [1]. He analyzed theoretically the dynamic elec- trophoretic mobility for the case of high surface potential and dilute dispersion, and he showed that an inverse relation * Corresponding author. E-mail address: jphsu@ccms.ntu.edu.tw (J.-P. Hsu). exists between CVP and ESA. Corresponding experimental work was also conducted in which the surface potential of a particle was estimated based on electroacoustic measure- ment. A thorough review of the experimental development was provided by Hunter [2]. In the theoretical counterpart, Sawatzky and Babchin [3] were able to derive an approxi- mate expression for the dynamic electrophoretic mobility for the case of low surface potential and arbitrary double layer thickness. Applying the numerical method of O’Brien [1], Magelsdorf and White [4] obtained an approximate numer- ical solution for the general electrokinetic equations for the case of a spherical particle at low potential but with a rel- atively thick double layer. Ohshima [5] derived a more ac- curate analytical expression for the electrophoretic mobility for the case of low potential and arbitrary double layer thick- ness. These discussions focused mainly on the dynamic behav- ior of particles in an infinite fluid. In practice, however, the presence of a boundary is almost always inevitable. The wall of a container, for instance, may be important for the move- ment of nearby particles. The porosity of a porous medium should be considered in the modeling of the motion of a par- ticle passing through it. A concentrated dispersion is another 0021-9797/03/$ – see front matter  2003 Elsevier Science (USA). All rights reserved. doi:10.1016/S0021-9797(02)00186-8