Electrophoretic Mobility of a Spherical Particle in a Spherical Cavity

✍ Scribed by Eric Lee; Jhih-Wei Chu; Jyh-Ping Hsu

• Publisher: Elsevier Science
• Year: 1997
• Tongue: English
• Weight: 139 KB
• Volume: 196
• Category: Article
• ISSN: 0021-9797
• DOI: 10.1006/jcis.1997.5220

✦ Synopsis

ARTICLE NO. CS975220 NOTE Electrophoretic Mobility of a Spherical Particle in a Spherical Cavity where Ç 2 is the Laplace operator, r the space charge density, e the permittivity of the liquid phase, N the number of ionic species, z j and The electrophoretic mobility U of a spherical particle in a n 0 j the valence and bulk concentration of ion species j , respectively, e spherical cavity for the case of low electric field is estimated the elementary charge, and k and T the Boltzmann constant and absolute for an arbitrary thick electrical double layer. We show that if temperature, respectively. Following Zydney's treatment ( 1 ) , F is dethe particle is uncharged and the cavity negatively charged, composed into F 1 and F 2 . The former denotes the electrical potential the deviation in the mobility based on the linearized Poissondistribution in the absence of the applied electric field, and the latter,

Boltzmann equation, U L , can be serious even at a low electrical the potential distribution outside the particle due to the presence of the potential. In this case, the variation of the absolute deviation, electric field. Suppose that the surface potentials of particle and cavity ÉU 0 U L É as a function of ka , k and a being, respectively, the are fixed at F a and F b , respectively. Then, we have ( 1 ) reciprocal Debye length and particle radius, has a maximum. The ka at which the maximal absolute deviation occurs increases with l ( particle size / cavity size ) , and the maximal ab-

solute deviation decreases with l. The latter increases with the absolute surface potential of cavity. If the particle is positively

charged and the cavity uncharged, U L is sufficiently accurate [4] if the electrical potential is low.