Postler T, Slouka Z, Svoboda M, Pribyl M, Snita D
Center for Nonlinear Dynamics of Chemical and Biological Systems, Department of Chemical Engineering, Institute of Chemical Technology, Technická 5, 166 28 Prague 6, Czech Republic.
J Colloid Interface Sci. 2008 Apr 1;320(1):321-32. doi: 10.1016/j.jcis.2007.10.056. Epub 2008 Jan 16.
Spatially two-dimensional nonequilibrium mathematical model describing electroosmotic flow through a submicrometer channel with an electric charge fixed on the channel walls is presented. This system is governed by the hydrodynamic, electrostatic, and mass transport phenomena. The model is based on the coupled mass balances, Poisson, Navier-Stokes, and Nernst-Planck equations. Nonslip boundary conditions are employed. The effect of an imposed electric field on the system behavior is studied by means of a numerical analysis of the model equations. We have obtained the following findings. If the channel width is comparable to the thickness of the electric double layer, the system behaves as an ion-exchange membrane and the dependence of the electric current passing through the channel on the applied voltage is strongly nonlinear. In the case of negatively (positively) charged walls, a narrow region of very low conductivity (so-called ionic gate) is formed in the free electrolyte near the channel entry facing the anode (cathode) side. For a wide channel, the electric current is proportional to the applied voltage and the velocity of electrokinetic flow is linearly proportional to the electric field strength. Complex hydrodynamics (eddy formation and existence of ionic gates) is the most interesting characteristics of the studied system. Hence, current-voltage and velocity-voltage curves and the corresponding spatial distributions of the model variables at selected points are studied and described in detail.
提出了一种二维非平衡数学模型，用于描述电渗流通过壁面固定有电荷的亚微米通道的情况。该系统由流体动力学、静电学和质量传输现象控制。该模型基于耦合的质量平衡、泊松方程、纳维 - 斯托克斯方程和能斯特 - 普朗克方程。采用无滑移边界条件。通过对模型方程的数值分析研究了外加电场对系统行为的影响。我们得到了以下结果。如果通道宽度与电双层厚度相当，系统表现得像离子交换膜，并且通过通道的电流与施加电压的关系呈强烈非线性。在壁面带负（正）电荷的情况下，在面向阳极（阴极）侧的通道入口附近的自由电解质中会形成一个电导率极低的狭窄区域（所谓的离子门）。对于宽通道，电流与施加电压成正比，电动流速度与电场强度呈线性比例关系。复杂的流体动力学（漩涡形成和离子门的存在）是所研究系统最有趣的特征。因此，详细研究并描述了电流 - 电压和速度 - 电压曲线以及所选点处模型变量的相应空间分布。
