Keh Huan J, Ding Jau M
Department of Chemical Engineering, National Taiwan University, Taipei 106-17, Taiwan, Republic of China.
J Colloid Interface Sci. 2003 Jul 15;263(2):645-60. doi: 10.1016/s0021-9797(03)00354-0.
An analytical study of the steady electrokinetic flow in a long uniform capillary tube or slit is presented. The inside wall of the capillary is covered by a layer of adsorbed or covalently bound charge-regulating polymer in equilibrium with the ambient electrolyte solution. In this solvent-permeable and ion-penetrable surface polyelectrolyte layer, ionogenic functional groups and frictional segments are assumed to distribute at uniform densities. The electrical potential and space charge density distributions in the cross section of the capillary are obtained by solving the linearized Poisson-Boltzmann equation. The fluid velocity profile due to the application of an electric field and a pressure gradient through the capillary is obtained from the analytical solution of a modified Navier-Stokes/Brinkman equation. Explicit formulas for the electroosmotic velocity, the average fluid velocity and electric current density on the cross section, and the streaming potential in the capillary are also derived. The results demonstrate that the direction of the electroosmotic flow and the magnitudes of the fluid velocity and electric current density are dominated by the fixed charge density inside the surface polymer layer, which is determined by the regulation characteristics such as the dissociation equilibrium constants of the ionogenic functional groups in the surface layer and the concentration of the potential-determining ions in the bulk solution.
本文对长均匀毛细管或狭缝中的稳态电动流动进行了分析研究。毛细管的内壁覆盖有一层吸附或共价结合的电荷调节聚合物，该聚合物与周围电解质溶液处于平衡状态。在这个溶剂可渗透且离子可穿透的表面聚电解质层中，假设离子ogenic官能团和摩擦链段以均匀密度分布。通过求解线性化的泊松-玻尔兹曼方程，得到了毛细管横截面上的电势和空间电荷密度分布。通过修正的纳维-斯托克斯/布林克曼方程的解析解，得到了由于施加电场和压力梯度通过毛细管而产生的流体速度分布。还推导了毛细管横截面上电渗速度、平均流体速度和电流密度以及流动电势的显式公式。结果表明，电渗流的方向、流体速度和电流密度的大小由表面聚合物层内的固定电荷密度决定，而固定电荷密度由调节特性决定，如表面层中离子ogenic官能团的解离平衡常数和本体溶液中电位决定离子的浓度。
