Electrical potentials of two identical planar, cylindrical, and spherical colloidal particles in a salt-free medium

Electrical potentials of two identical particles with fixed surface charge density in a salt-free medium

“…A comparison between the present results and those of Hsu and Huang [10] reveals that the performance of the perturbation method adopted for the case of constant surface charge density is better than that for the case of constant surface potential.…”

“…As pointed out by Hsu and Huang [10], if k is sufficiently small, then using the first-order approximation is satisfactory. That is, y n , n P 2 can be neglected, yielding y ffi y 0 þ ky 1 :…”

“…These include, for example, electrical potential distribution [10][11][12][13][14], electrophoresis [15][16][17][18][19], electrical double layer [20,21], equilibrium sedimentation [22], and critical coagulation concentration or stability [23][24][25][26].…”

“…In a recent study, we derived an approximate perturbation solution for the electrical potential of two identical planar, cylindrical, and spherical particles in a salt-free dispersion [10]. The derivation was based on a constant surface potential model; that is, the surface potential of a particle is uninfluenced by the neighboring environment such as the presence of another particle or surface.…”

“…In this study, the perturbation method adopted previously for the resolution of the electrical potential of two identical planes, cylinders, and spheres maintained at constant surface potentials [10] is applied to solve that at constant surface charge densities. Mathematically, the former belongs to a Dirichlet-type problem, and the latter is a Neumann type.…”