Diffusive dynamics of charge-regulated macro-ion solutions

Abstract

Onsager’s variational principle is generalized to address the diffusive dynamics of an electrolyte solution composed of charge-regulated macro-ions and counterions. The free energy entering the Rayleighian corresponds to the Poisson–Boltzmann theory augmented by the charge-regulation mechanism. The dynamical equations obtained by minimizing the Rayleighian include the classical Poisson–Nernst–Planck equations, the Debye–Falkenhagen equation, and their modifications in the presence of charge regulation. By analyzing the steady state, we show that the charge regulation impacts the non-equilibrium macro-ion spatial distribution and their effective charge, deviating significantly from their equilibrium values. Our model, based on Onsager’s variational principle, offers a unified approach to the diffusive dynamics of electrolytes containing components that undergo various charge association/dissociation processes.