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@ARTICLE{Pabst:154315,
      author       = {Pabst, Michael},
      title        = {{A}nalytical solution of the {P}oisson-{N}ernst-{P}lanck
                      equations for an electrochemical system close to
                      electroneutrality},
      journal      = {The journal of chemical physics},
      volume       = {140},
      number       = {22},
      issn         = {1089-7690},
      address      = {Melville, NY},
      publisher    = {American Institute of Physics},
      reportid     = {FZJ-2014-03663},
      pages        = {224113},
      year         = {2014},
      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.},
      cin          = {ICS-8},
      ddc          = {540},
      cid          = {I:(DE-Juel1)ICS-8-20110106},
      pnm          = {453 - Physics of the Cell (POF2-453)},
      pid          = {G:(DE-HGF)POF2-453},
      typ          = {PUB:(DE-HGF)16},
      UT           = {WOS:000337806100016},
      doi          = {10.1063/1.4881599},
      url          = {https://juser.fz-juelich.de/record/154315},
}