Analytical solution of the Poisson-Nernst-Planck equations for an electrochemical system close to electroneutrality

Pabst, Michael

doi:10.1063/1.4881599

Journal Article

FZJ-2014-03663

Analytical solution of the Poisson-Nernst-Planck equations for an electrochemical system close to electroneutrality

Pabst, M. (Corresponding Author)FZJ*

2014
American Institute of Physics Melville, NY

The journal of chemical physics 140(22), 224113 (2014) [10.1063/1.4881599]

This record in other databases:

Please use a persistent id in citations: http://hdl.handle.net/2128/19015 doi:10.1063/1.4881599

Abstract: Single charge densities and the potential are used to describe models of electrochemical systems. These quantities can be calculated by solving a system of time dependent nonlinear coupled partial differential equations, the Poisson-Nernst-Planck equations. Assuming small deviations from the electroneutral equilibrium, the linearized and decoupled equations are solved for a radial symmetric geometry, which represents the interface between a cell and a sensor device. The densities and the potential are expressed by Fourier-Bessels series. The system considered has a ratio between the Debye-length and its geometric dimension on the order of 10−4 so the Fourier-Bessel series can be approximated by elementary functions. The time development of the system is characterized by two time constants, τ c and τ g . The constant τ c describes the approach to the stationary state of the total charge and the potential. τ c is several orders of magnitude smaller than the geometry-dependent constant τ g , which is on the order of 10 ms characterizing the transition to the stationary state of the single ion densities.

Classification: