Petsev Dimiter N, Lopez Gabriel P
Department of Chemical and Nuclear Engineering, University of New Mexico, Albuquerque, NM 87131, USA.
J Colloid Interface Sci. 2006 Feb 15;294(2):492-8. doi: 10.1016/j.jcis.2005.07.037. Epub 2005 Aug 8.
The electrostatic potential in a capillary filled with electrolyte is derived by solving the nonlinear Poisson-Boltzmann equation using the method of matched asymptotic expansions. This approach allows obtaining an analytical result for arbitrary high wall potential if the double layer thickness is smaller than the capillary radius. The derived expression for the electrostatic potential is compared to numerical solutions of the Poisson-Boltzmann equation and it is shown that the agreement is excellent for capillaries with radii greater or equal to four times the electrical double layer thickness. The knowledge of the electrostatic potential distribution inside the capillary enables the derivation of the electroosmotic velocity flow profile in an analytical form. The obtained results are applicable to capillaries with radii ranging from nanometers to micrometers depending on the ionic strength of the solution.
通过使用匹配渐近展开法求解非线性泊松 - 玻尔兹曼方程，得出充满电解质的毛细管中的静电势。如果双层厚度小于毛细管半径，这种方法能够得到任意高壁电势的解析结果。将导出的静电势表达式与泊松 - 玻尔兹曼方程的数值解进行比较，结果表明，对于半径大于或等于电双层厚度四倍的毛细管，二者吻合度极佳。毛细管内部静电势分布的知识使得能够以解析形式推导电渗流速度剖面。根据溶液的离子强度，所得结果适用于半径从纳米到微米不等的毛细管。
