帶電邊界對膠體粒子電泳的影響

Abstract

本論文以有限元素法研究帶電邊界對膠體粒子電泳動的影響。文中探討的主題包含單顆球形粒子沿著圓柱形孔洞的軸心泳動、單顆球形粒子朝向無窮大的圓盤或平板泳動、以及單顆或雙顆圓柱形膠體粒子沿著圓柱形孔洞的軸心泳動，並測試了固定表面電位、固定表面電荷密度與電荷可調整三種表面荷電模式的影響。在低表面電位、弱外加電場與低雷諾數的假設下，吾人利用加疊原理求解相關電場與流場之線性化方程組，並獲得膠體粒子的電泳速度(或電泳遷移率)。 數值模擬的結果顯示，下列幾個因素對膠體粒子的電泳速度有顯著的影響：粒子與邊界的表面荷電模式、粒子與邊界的幾何形狀、粒子與邊界的距離或粒子間的距離、以及電雙層的厚度。其次，帶電邊界對膠體粒子泳動的影響是不可忽略的，因為它除了會有效增加或減少粒子的電泳速度外，在某些條件下，甚至會導致膠體粒子的電泳速度消失或產生一局部極大值。

The electrophoretic behaviors of colloidal particles near a rigid, charged boundary are investigated through solving numerically the governing electrokinetic equations by a finite element method. Four types of system are considered: a sphere along the axis of a cylindrical pore, a sphere normal to a large disk/plane, and a short cylinder or two short cylinders along the axis of a cylindrical pore. Three kinds of charged conditions on particle surface are considered: constant surface potential, constant surface charge density, and charge-regulated model. Under the conditions of low surface potential and weak applied electric field, the electrophoretic mobility of a particle is evaluated by a superposition method. The influences of the key parameters of the systems under consideration on the mobility of a particle are investigated through numerical simulation. These include the charged conditions on a particle and on a boundary, the geometries of a particle and a boundary, the separation distance between a particle and a boundary or between two particles, and the thickness of double layer. Several interesting results are observed which are of both fundamental and practical significance. For instance, we show that the presence of a charged boundary can increase, decrease, or even change the direction of the movement of a particle. Also, the mobility of a particle may exhibit a local maximum as the thickness of double layer varies.