SOLUTIONS OF THE LINEARIZED POISSON-BOLTZMANN EQUATION THROUGH THE USE OF RANDOM-WALK SIMULATION METHOD

It is shown that the random walk simulation technique, through the cho ice of a suitable set of rules, can be adapted to the problem of solvi ng the linearized Poisson-Boltzmann equation, for general cases involv ing constant surface potentials. In order to validate the technique, t he results of the method are compared to the exact solutions for a num ber of analytically tractable problems. Excellent agreements between t he two sets of results are found in all cases. Further examples of the application of the method are given by considering systems involving nonideal colloidal particles. In particular, the solutions of the line arized Poisson-Boltzmann equation for simple models of porous colloids , as well as particles with nonuniform surface potentials, have been o btained. The implication of these preliminary results for the electros tatic interactions between such nonideal colloidal particles are brief ly discussed. (C) 1995 American Institute of Physics.