Qualitative Properties of Steady-State Poisson-Nernst-Planck Systems: Perturbation and Simulation Study
نویسندگان
چکیده
Poisson-Nernst-Planck (PNP) systems are considered in the case of vanishing permanent charge. A detailed case study, based on natural categories described by system boundary conditions and flux, is carried out via simulation and singular perturbation analysis. Our results confirm the rich structure inherent in these systems. A natural quantity, the quotient of the Debye and characteristic length scales, serves as the singular perturbation parameter. The regions of validity are carefully analyzed by critical comparisons and contrasts between the simulation and the perturbation solution, which can be represented in closed form.
منابع مشابه
M ar 2 00 8 A singular perturbation approach to the steady - state 1 D Poisson - Nernst - Planck modeling
The reduced 1D Poisson-Nernst-Planck (PNP) model of artificial nanopores in the presence of a permanent charge on the channel wall is studied. More specifically, we consider the limit where the channel length exceed much the Debye screening length and channel’s charge is sufficiently small. Ion transport is described by the nonequillibrium steady-state solution of the PNP system within a singul...
متن کاملQualitative Properties of Ionic Flows via Poisson-nernst-planck Systems with Bikerman’s Local Hard-sphere Potential: Ion Size Effects
We study a quasi-one-dimensional steady-state Poisson-NernstPlanck model for ionic flows through membrane channels with fixed boundary ion concentrations and electric potentials. We consider two ion species, one positively charged and one negatively charged, and assume zero permanent charge. Bikerman’s local hard-sphere potential is included in the model to account for ion size effects on the i...
متن کاملQualitative Properties of Steady-State Poisson-Nernst-Planck Systems: Mathematical Study
We examine qualitative properties of solutions of self-consistent Poisson-NernstPlanck (PNP) systems, including uniqueness. In the case of vanishing permanent charge, the predominant case studied, our results unveil a rich structure inherent in these systems, one that is determined by the boundary conditions and the signs of the oppositely charged carrier fluxes. A particularly significant spec...
متن کاملAsymptotic Expansions and Numerical Simulations of I-v Relations via a Steady State Poisson-nernst-planck System
A steady state Poisson-Nernst-Planck (PNP) system is studied both analytically and numerically with particular attention on I-V relations of ion channels. Assuming the dielectric constant ε is small, the PNP system can be viewed as a singularly perturbed system. Due to the special structures of the zeroth order inner and outer systems, one is able to derive more explicit expressions of higher o...
متن کاملN ov 2 00 8 A singular perturbation approach to the steady - state 1 D Poisson - Nernst - Planck modeling
The reduced 1D Poisson-Nernst-Planck (PNP) model of artificial nanopores in the presence of a permanent charge on the channel wall is studied. More specifically, we consider the limit where the channel length exceed much the Debye screening length and channel’s charge is sufficiently small. Ion transport is described by the nonequillibrium steady-state solution of the PNP system within a singul...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- SIAM Journal of Applied Mathematics
دوره 57 شماره
صفحات -
تاریخ انتشار 1997