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000154315 037__ $$aFZJ-2014-03663
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000154315 1001_ $$0P:(DE-Juel1)128714$$aPabst, Michael$$b0$$eCorresponding Author$$ufzj
000154315 245__ $$aAnalytical solution of the Poisson-Nernst-Planck equations for an electrochemical system close to electroneutrality
000154315 260__ $$aMelville, NY$$bAmerican Institute of Physics$$c2014
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000154315 520__ $$aSingle 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.
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