The stability ratio for a dispersion of particles covered by an ion-penetrable charged membrane

The electrostatic interaction between two particles covered by an ion-penetrable charged membrane suspended in an a:b electrolyte solution is estimated. A perturbation method is employed to solve the governing nonlinear Poisson-Boltzmann equation. The approximate analytical expression derived for potential distribution yields a sufficiently accurate estimate, Both the stability ratio and the critical coagulation concentration of the counterions of the system under consideration are derived. The results of a numerical simulation reveal that the stability ratio decreases with an increase in the size of a particle and increases with the total amount of fixed charges in the membrane phase. For a constant total amount of fixed charges and particle size, the stability ratio increases with a decrease in the thickness of the membrane. We show that monodispersed particles are more stable than polydispersed particles. (C) 1996 Academic Press, Inc.