帶電多孔球形粒子懸浮液的電泳可動度與導電度

Abstract

本論文探討在一均勻外加電場下，帶電多孔球形粒子在與電解質溶液中的懸浮系統的電泳可動度及導電度。多孔粒子是具有溶劑與離子通透性，並且電荷與流動阻力均勻分布的聚電解質分子。 解析的過程中，吾人考慮在任意電雙層厚度但低電位的條件下，利用單元小室模型來探討粒子之間彼此的作用，並且允許相鄰電雙層間的重疊。藉由假設系統在外加電場作用之下，與平衡狀態相較僅有微小的擾動量，可將原來交互聯立非線性的Poisson -Boltzmann方程式和加入靜電力修正項的Stokes方程式予以線性化。如此，以多孔粒子內固定電荷密度為微小參數，使用正規微擾法將線性化後的電動力方程式，分別轉化為不同階數的線性方程組，再結合相對應的邊界條件，可以求得多孔粒子在內部及外部的平衡電位、流場以及電化學位能分布的數學解析解。利用在單元小室外邊界上的電力及流體阻力的淨合力為零，以及體積平均電場與電流密度之線性關係式，可分別求得帶電粒子的電泳可動度和懸浮液的有效導電度。本研究發現，無論是電雙層的厚度、多孔粒子的內部阻力和粒子在懸浮液中的體積分率，對於電泳可動度及導電度均有複雜的影響。

The electrophoresis and electric conduction of a suspension of charged porous spheres in an electrolyte solution with an arbitrary thickness of the electric double layers are analytically studied. The porous particle can be a solvent-permeable and ion-penetrable polyelectrolyte molecule or charged floc with uniformly distributed frictional segments and fixed charges. The effects of particle interactions are taken into account by employing a unit cell model, and the overlap of the electric double layers of adjacent particles is allowed. The electrokinetic equations, which govern the electrostatic potential profile, the ionic concentration (or electrochemical potential energy) distributions, and the fluid velocity field inside and outside the porous particle in a unit cell, are linearized by assuming that the system is only slightly distorted from equilibrium. Through the use of a regular perturbation method, these linearized equations are solved with the density of the fixed charges as the small perturbation parameter. Analytical expressions for the electrophoretic mobility of each charged porous sphere and for the effective electric conductivity of the suspension correct to the first and second orders, respectively, of the fixed charge density are obtained. Comparisons of the results of the cell model with different conditions at the outer boundary of the cell are made. The dependence of the electrophoretic mobility and the electric conductivity on the particle volume fraction and other properties of the particle-solution system is found to be quite complicated.