(250j) Validation of A Novel Algorithmic Approach To Solve The Poisson-Boltzmann Equations In Electrokinetics

Many exploratory studies rely on the ability to make accurate estimations of the variable under study. In electrokinetics applications, appropriate prediction of electro-osmotic velocity profiles is crucial to the study of electrokinetic processes, such as electro-assisted drug delivery, micro-electrophoretic separations, soil remediation, and material processing. All these applications require the mathematical solution of the complete Poisson Boltzmann (P-B) equation for the systems under study. This equation is a complex mathematical expression characterized as a secondary nonlinear ordinary differential equation. Not long ago, Arce and Oyanader* proposed a novel and simpler solution of the P-B equation using a recursive function, ƒ_AO. In this work, the previous contribution of Arce and Oyanader will be revisited using a new, more analytical approach, but validating the simple predictor-corrector method developed and introduced by Arce and Oyanader as an alternative tool for nonlinear phenomena problems.

This validation seeks to persuade practitioners from different discipline areas, such as hydrodynamics, electrostatics, and mass and heat transfer that the recursive function, ƒ_AO, is of simple and practical use. In particular, this novel approach has proven to be an exceptional tool in modeling the electrical field for applications of interest such as the separation of a mixture of macromolecules and the removal of contaminants on soil cleaning processes. Several examples will illustrate the benefits of the methodology. Comparisons to numerical solutions are also included.

(*) Oyanader, M., Arce, P., “A New and Simpler Approach for the Solution of the Electrostatic Potential Differential Equation. Enhanced Solution for Planar, Cylindrical and Annular Geometries,” Journal of Colloid and Interface Science, 2005, 284, 315.