cylinders, and spheres. Although the mathematical treatment The Poisson-Boltzmann equation describing the electrical pobecomes much simpler, using these one-dimensional simulatential distribution around a charged spheroidal surface in an tions can be unrealistic for a wide class of dispersed entities. electrolyte solution is solved analytically under the Debye-Huckel Biocolloids, for instance, can be rod-like, olivary, and varicondition. A general boundary value problem is discussed in which ous other shapes. Attempts were made to extend the results an arbitrary combination of potential and charge density is specifor simple surfaces to spheroidal surfaces (2-4). The analyfied at the surface. The method of reflections is proposed for the ses, however, were limited to thin electrical double layers. resolution of the governing Poisson-Boltzmann equation. The This is largely due to the complicated nature of spheroidal conventional constant potential (Dirichlet) problem and constant coordinates and the spheroidal wave functions involved in surface charge (Neumann) problem can be recovered as special cases of the present model. The problem of nonuniformly distrib-the expression of electrical potential distribution. Although uted potential/charges over a surface is also analyzed. A typical spheroidal wave functions have been investigated extenexample in practice is that the distribution of charges is patchwise. sively in the literature (5, 6), their applications in the de-We show that neglecting the nonuniformity of the charged condiscription of charged surfaces in electrolyte solutions are still tion over a surface may lead to a significant deviation. ᭧ 1996 very limited. Yoon and Kim (7) analyzed the electrophoretic Academic Press, Inc. phenomena of spheroidal particles by employing these func-Key Words: surface, charged, spheroidal, in electrolyte solution; tions. The eigenvalues and the coefficients associated with Poisson-Boltzmann equation, linearized; surface condition, mixed the solution to the two-dimensional electrical potential distripotential and charge density, nonuniform; analytical solution, bution needed to be evaluated through finding the roots of a spheroidal wave functions, reflection method.
transcendental equation. A more explicit and straightforward approach was suggested by Hsu and Liu (8) to the description of two-dimensional electrical potential distributions for spheroidal surfaces.