Diffusioosmosis of electrolyte solutions along a charged plane wall
Diffusioosmosis of electrolyte solutions along a charged plane wall
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作者：
Keh, HJ;Ma, HC
分析了由外加浓度梯度引起的电解质溶液沿介质平面壁的稳定扩散渗流。平面壁可以具有恒定的表面电势或任意量的恒定的表面电荷密度。与带电壁相邻的双电层可以有任意厚度，其静电势分布由泊松-玻尔兹曼方程决定。得到了由施加的电解液浓度梯度沿切向方向产生的宏观电场，作为横向位置的函数。通过求解修正的Navier-Stokes方程，推导出了流体速度分布的封闭公式。相对于浓度梯度的扩散渗透流的方向由壁面的Zeta电位和电解质溶液的性质相结合来确定。对于给定浓度梯度的电解液沿平面壁面，流体速度的大小一般随着其与壁面的电动距离的增加而增加，但也有例外。双层中感应切向电场的横向分布对扩散渗流的影响是非常显著的，不能忽略。
The steady diffusioosmotic flow of an electrolyte solution along a dielectric plane wall caused by an imposed tangential concentration gradient is analytically examined. The plane 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 the Poisson-Boltzmann equation. The macroscopic electric field along the tangential direction induced by the imposed electrolyte concentration gradient is obtained as a function of the lateral position. A closed-form formula for the fluid velocity profile is derived as the solution of a modified Navier-Stokes equation. The direction of the diffusioosmotic flow relative to the concentration gradient is determined by the combination of the zeta potential of the wall and the properties of the electrolyte solution. For a given concentration gradient of an electrolyte along a plane wall, the magnitude of fluid velocity at a position in general increases with an increase in its electrokinetic distance from the wall, but there are exceptions. The effect of the lateral distribution of the induced tangential electric field in the double layer on the diffusioosmotic flow is found to be very significant and cannot be ignored.