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描述多离子在电化学梯度作用下运移的Poisson-Nernst-Planck方程在很多领域都有重要的应用,由于浓度场和电势场的强烈耦合影响,方程求解困难。现有的求解一般基于Nernst-Planck方程,耦合电中性条件或者常电位假定,进行简化分析,且一般为稳态问题。采用多物理场耦合分析软件COMSOLMultiphysics进行求解,软件强大的多场耦合分析能力使求解该方程的稳态、非稳态问题以及全耦合分析成为可能,并和已有的分析结果进行了验证。
The Poisson-Nernst-Planck equation, which describes the migration of multi-ions under the action of an electrochemical gradient, is of great importance in many fields. Due to the strong coupling between the concentration and the potential fields, the equation is difficult to solve. Existing solutions are generally based on the Nernst-Planck equation, coupled neutral conditions or the assumption of constant potential for simplified analysis and are generally steady-state problems. The multi-physics coupled analysis software COMSOLMultiphysics is used to solve the problem. The powerful multi-field coupling analysis capability of the software makes it possible to solve the steady-state and unsteady problems and the full coupling analysis of the equation, and verifies with the existing analysis results.