Phenomenological adsorption isotherm for a binary system based on Poisson-Boltzmann equation

A model for the binary adsorption phenomenon of cations by a porous adsorbent in an isotropic liquid taking into account a localized adsorption energy is proposed. It consists of a set of algebraic and differential equations aiming at determining the profile of the electric field, the chemical potential, and the concentration of cations in the adsorbent material. The mathematical development of this model is based on the Poisson-Boltzmann equation to describe the electric field profile of a sample limited at one side by a flat surface adsorbent. This geometrical simplification is necessary to reduce the mathematical complexity and yields a more physical, even if still phenomenological, isotherm unlike Langmuir and many others. The proposed model was tested to represent data of binary biosorption equilibrium. To represent adequately the experimental data, it was necessary to use a mixing rule in the adsorption energy-related term. The model was able to accurately describe the case investigated showing results similar to those obtained by means of conventional isotherms.