Abstract
An iterative solution scheme is proposed for solving the electrical double-layer interactions governed by the linearized Poisson–Boltzmann equation. The method is based on the indirect integral equation formulation with the double-layer potential kernel of the linearized Poisson–Boltzmann equation. In contrast to the conventional direct integral equation approach that yields Fredholm integral equations of the first kind, the indirect integral equation approach yields well-posed Fredholm integral equations of the second kind. The eigenvalue analysis reveals that the spectral radius of the double-layer integral operator is always less than one. Thus, iterative solution schemes can be successfully implemented for solving the electrical double-layer interactions for very large and complex systems. The utility of the iterative indirect method is demonstrated for several examples which include spherical and spheroidal particles.
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