电动不稳定性及向混沌运动转变的直接数值模拟
Direct Numerical Simulation of Electrokinetic Instability and Transition to Chaotic Motion
摘要：
通过对Nernst-Planck-Poisson-Stokes系统的数值积分和不稳定性阈值附近的弱非线性分析，研究了一种新的不稳定性--动电不稳定性，以及在电荷选择表面附近向混沌运动的异常转变.考虑了两种初始条件：（a）白噪声初始条件，以模拟“房间干扰”和随后的自然演变的解决方案;（b）一个人工单色离子分布与一个固定的波数，以模拟规则的波图案。从流体动力学稳定性和分叉理论的角度对结果进行了研究。利用线性谱稳定性理论确定了系统的电对流运动阈值，并对整个系统进行了数值模拟。以下制度，取代彼此之间的选择性表面的电位降的增加，得到：一维稳定的解决方案;二维稳定的电对流涡（在适当的相空间中的固定点）;非定常涡非周期性地改变其参数（同宿轮廓）;周期性运动（极限环）;和混沌运动。向混沌运动的过渡不包括Hopf分岔。薄浓度极化层的数值分辨率显示沿表面的尖峰状电荷分布，这可能是，取决于政权，无论是稳定的或非周期性的合并。数值研究证实了实验观察到的规则（近正弦）振荡的超限制度的情况下。有一个定性的协议的实验和理论值的阈值的不稳定性，所观察到的相干结构的主导尺寸，和实验和理论的电压-电流特性。
英文摘要：
A new type of instability - electrokinetic instability - and an unusual transition to chaotic motion near a charge-selective surface was studied by numerical integration of the Nernst-Planck-Poisson-Stokes system and a weakly nonlinear analysis near the threshold of instability. Two kinds of initial conditions were considered: (a) white noise initial conditions to mimic "room disturbances" and subsequent natural evolution of the solution; (b) an artificial monochromatic ion distribution with a fixed wave number to simulate regular wave patterns. The results were studied from the viewpoint of hydrodynamic stability and bifurcation theory. The threshold of electroconvective movement was found by the linear spectral stability theory, the results of which were confirmed by numerical simulation of the entire system. The following regimes, which replace each other as the potential drop between the selective surfaces increases, were obtained: one-dimensional steady solution; two-dimensional steady electroconvective vortices (stationary point in a proper phase space); unsteady vortices aperiodically changing their parameters (homoclinic contour); periodic motion (limit cycle); and chaotic motion. The transition to chaotic motion did not include Hopf bifurcation. Numerical resolution of the thin concentration polarization layer showed spike-like charge profiles along the surface, which could be, depending on the regime, either steady or aperiodically coalescent. The numerical investigation confirmed the experimentally observed absence of regular (near-sinusoidal) oscillations for the overlimiting regimes. There is a qualitative agreement of the experimental and the theoretical values of the threshold of instability, the dominant size of the observed coherent structures, and the experimental and theoretical volt-current characteristics.
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