%0 Journal Article
%A Pabst, Michael
%T Analytical solution of the Poisson-Nernst-Planck equations for an electrochemical system close to electroneutrality
%J The journal of chemical physics
%V 140
%N 22
%@ 1089-7690
%C Melville, NY
%I American Institute of Physics
%M FZJ-2014-03663
%P 224113
%D 2014
%X 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.
%F PUB:(DE-HGF)16
%9 Journal Article
%U <Go to ISI:>//WOS:000337806100016
%R 10.1063/1.4881599
%U https://juser.fz-juelich.de/record/154315