Keh Huan J, Ma Hsien Chen
Department of Chemical Engineering, National Taiwan University, Taipei 10617, Taiwan, Republic of China.
Langmuir. 2007 Feb 27;23(5):2879-86. doi: 10.1021/la062683n. Epub 2007 Jan 30.
A theoretical study is presented for the steady diffusioosmotic flow of an electrolyte solution in a fine capillary tube generated by a constant concentration gradient imposed in the axial direction. The capillary wall may have either a constant surface potential or a constant surface charge density of an arbitrary quantity. The electric double layer adjacent to the charged wall may have an arbitrary thickness, and its electrostatic potential distribution is determined by an analytical approximation to the solution of the Poisson-Boltzmann equation. Solving a modified Navier-Stokes equation with the constraint of no net electric current arising from the cocurrent diffusion, electric migration, and diffusioosmotic convection of the electrolyte ions, the macroscopic electric field and the fluid velocity along the axial direction induced by the imposed electrolyte concentration gradient are obtained semianalytically as a function of the radial position in a self-consistent way. The direction of the diffusioosmotic flow relative to the concentration gradient is determined by the combination of the zeta potential (or surface charge density) of the wall, the properties of the electrolyte solution, and other relevant factors. For a prescribed concentration gradient of an electrolyte, the magnitude of fluid velocity at a position in general increases with an increase in its distance from the capillary wall, but there are exceptions. The effect of the radial distribution of the induced tangential electric field and the relaxation effect due to ionic convection in the double layer on the diffusioosmotic flow are found to be very significant.
本文针对由轴向施加的恒定浓度梯度所产生的、在细毛细管中电解质溶液的稳态扩散渗透流进行了理论研究。毛细管壁可以具有恒定的表面电势或任意量的恒定表面电荷密度。与带电壁相邻的双电层可以具有任意厚度，并且其静电势分布由泊松 - 玻尔兹曼方程解的解析近似确定。通过求解修正的纳维 - 斯托克斯方程，并考虑到电解质离子的共流扩散、电迁移和扩散渗透对流不会产生净电流这一约束条件，以自洽的方式半解析地获得了由施加的电解质浓度梯度引起的宏观电场和沿轴向的流体速度作为径向位置的函数。扩散渗透流相对于浓度梯度的方向由壁的zeta电势（或表面电荷密度）、电解质溶液的性质以及其他相关因素共同决定。对于规定的电解质浓度梯度，一般来说，某一位置处流体速度的大小会随着其与毛细管壁距离的增加而增大，但也存在例外情况。发现感应切向电场的径向分布以及双层中离子对流引起的弛豫效应对扩散渗透流的影响非常显著。
