TY  - JOUR
AU  - Pabst, Michael
TI  - Analytical solution of the Poisson-Nernst-Planck equations for an electrochemical system close to electroneutrality
JO  - The journal of chemical physics
VL  - 140
IS  - 22
SN  - 1089-7690
CY  - Melville, NY
PB  - American Institute of Physics
M1  - FZJ-2014-03663
SP  - 224113
PY  - 2014
AB  - 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.
LB  - PUB:(DE-HGF)16
UR  - <Go to ISI:>//WOS:000337806100016
DO  - DOI:10.1063/1.4881599
UR  - https://juser.fz-juelich.de/record/154315
ER  -