帶電粒子無鹽懸浮液之電泳可動度與電導度

Abstract

本論文使用單元小室模型，對帶電球形粒子無鹽懸浮液，分析粒子電泳運動與懸浮液電導度，亦即圍繞於帶電球形粒子之無鹽懸浮液僅帶有一種異性離子。藉由使用線性化 Poisson-Boltzmann 方程式(適用於粒子相對表面電荷密度較低或體積分率較高之系統)與 Laplace 方程式，分別求解出小室中平衡電位分布及受外加電場所導致之擾動電位；而電化學位能分布及流體速度分布，則可分別運用離子連續方程式與修正後 Stokes 方程式求得。利用力平衡與局部體積平均電流密度可分別獲得粒子電泳可動度及懸浮液電導度，結果顯示粒子間相互作用對前述輸送性質影響顯著。在無鹽懸浮液系統中保持其他參數固定時，粒子zeta電位、粒子電泳可動度及懸浮液有效電導度會隨著粒子表面電荷密度的增加，呈現單調遞增，並會隨著粒子體積分率的增加而遞減。在使用 Debye-Hückel 近似解的情況下，無鹽懸浮液中以粒子表面電荷密度正規化後之粒子電泳可動度，隨著粒子半徑與電雙層厚度之比和粒子體積分率的變化關係，與一般電解質懸浮液之結果相似；然而無鹽懸浮液之有效電導度隨著粒子體積分率的變化關係，則與一般電解質懸浮液之結果有顯著的不同。

In this thesis, the electrophoresis and electric conduction of a suspension of charged spherical particles in a salt-free solution are analyzed by using a unit cell model. The linearized Poisson-Boltzmann equation (valid for the cases of relatively low surface charge density or high volume fraction of the particles) and Laplace equation are solved for the equilibrium electric potential profile and its perturbation caused by the imposed electric field, respectively, in the fluid containing the counterions only around the particle, and the ionic continuity equation and modified Stokes equations are solved for the electrochemical potential energy and fluid flow fields, respectively. Explicit analytical formulas for the electrophoretic mobility of the particles and effective electric conductivity of the suspension are obtained, and the particle interaction effects on these transport properties are significant and interesting. The scaled zeta potential, electrophoretic mobility, and effective electric conductivity increase monotonically with an increase in the scaled surface charge density of the particles and in general decrease with an increase in the particle volume fraction, keeping each other parameter unchanged. Under the Debye-Hückel approximation, the dependence of the electrophoretic mobility normalized with the surface charge density on the ratio of the particle radius to the Debye screening length and particle volume fraction in a salt-free suspension is same as that in a salt-containing suspension, but the variation of the effective electric conductivity with the particle volume fraction in a salt-free suspension is found to be quite different from that in a suspension containing added electrolyte.