动电不稳定性的线性和非线性演化及扩散层选择
Linear and Nonlinear Evolution and Diffusion Layer Selection in Electrokinetic Instability
摘要：
本文通过对NPPS系统的直接数值模拟，将动电不稳定性划分为四个非平凡阶段：i）初始条件影响阶段（毫秒）; ii）一维自相似演化阶段（毫秒-秒）; iii）自相似解的初级不稳定性阶段（秒）; iv）具有次级不稳定性的非线性阶段。在中等大的时间演化的自相似字符被证实。Rubinstein和Zaltzman不稳定性和噪声驱动的非线性演化的超限制制度的离子交换膜进行了数值模拟，并与理论和实验预测。发现在此阶段期间发生的主要不稳定性阻止扩散层的自相似生长，并指定其特征长度，如Yossifon和Chang（PRL 101，254501（2008））首次实验预测的。提出了一种从宽带初始噪声中选择特征波数的新原则。
英文摘要：
In the present work fournontrivial stages of electrokinetic instability are identified by direct numerical simulation (DNS) of the full Nernst-Planck-Poisson-Stokes (NPPS) system: i) The stage of the influence of the initial conditions (milliseconds); ii) 1D self-similar evolution (milliseconds-seconds); iii) The primary instability of the self-similar solution (seconds); iv) The nonlinear stage with secondary instabilities. The self-similar character of evolution at intermediately large times is confirmed. Rubinstein and Zaltzman instability and noise-driven nonlinear evolution to over-limiting regimes in ion-exchange membranes are numerically simulated and compared with theoretical and experimental predictions. The primary instability which happens during this stage is found to arrest self-similar growth of the diffusion layer and specifies its characteristic length as was first experimentally predicted by Yossifon and Chang (PRL 101, 254501 (2008)). A novel principle for the characteristic wave number selection from the broadbanded initial noise is established.
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