不均勻帶電膠體粒子電泳之邊界效應

Abstract

本論文探討當邊界存在時，在外加一均勻電場下，一表面帶電不均勻之球形或圓柱形膠體粒子之電泳，假設電雙層厚度相較於粒子半徑與粒子到邊界之距離皆為非常薄，求得粒子電泳速度之解析解。邊界存在可能對粒子周圍之流場及電場造成以下三個影響：(1)粒子表面之電場會因邊界存在而增強或減弱；(2)邊界存在會增強粒子運動時所受之黏滯力；(3)邊界表面上之電荷與邊界切線方向之電場作用將使流體做電滲透流動。 本文先將探討當粒子與孔壁皆可為不均勻帶電時，一球形粒子位於一球孔中心之電泳。利用Laplace及 Stokes 方程式可求得電場與流場分佈之解析解，進而求得粒子移動及轉動速度與粒子距離邊界遠近之關係式。分別計算粒子與孔壁所帶任意表面電位之multipole moments後，即可利用這些關係式得到粒子電泳與轉動速度。因所求解之方程式皆為線性，所以結果顯示粒子速度可由疊加球孔上電滲透流動對粒子速度之影響和經邊界效應修正後之粒子速度而得。 本文另一部份探討一表面存在隨角度變化之帶電分佈圓柱形粒子在鄰近與其中心軸相平行之一平板，且外加電場為垂直或平行此平板時所進行之電泳。利用Laplace及 Stokes 方程式與雙極座標系統，可求得在此二維電場與流場分佈下，圓柱粒子移動與轉動速度之解析解。計算粒子所帶不均勻表面電位之multipole moments，即可利用這些解析解得到粒子移動與轉動速度。吾人發現當粒子鄰近邊界時，邊界效應可使得無邊界存在時不做移動或轉動運動之粒子產生移動或轉動速度。

The boundary effects on electrophoresis of a spherical or cylindrical colloidal particle with a nonuniform zeta potential distribution in the vicinity of a confining wall at quasisteady state are analyzed. The applied electric field is constant and the electric double layers adjacent to the solid surfaces are assumed to be much thinner than the particle radius and the gap width between the surfaces. The presence of a confining wall causes three basic effects on the particle velocity: (a) the local electric field on the particle surface is enhanced or reduced by the wall; (b) the wall increases viscous retardation of the moving particle; (c) an electroosmotic flow of the suspending fluid may exist due to the interaction between the charged wall and the tangential electric field. In the first part of the thesis, a study is presented for the electrophoretic motion of a dielectric sphere situated at the center of a spherical cavity when both surface potentials are nonuniform. The Laplace and Stokes equations are solved analytically for the electric potential and velocity fields, respectively, in the fluid phase, and explicit formulas for the electrophoretic and angular velocities of the particle are obtained. To apply these formulas, one only has to calculate the multipole moments of the zeta potential distributions at the particle and cavity surfaces. It is found that the contribution from the electroosmotic flow developing from the interaction of the imposed electric field with the thin double layer adjacent to the cavity wall and the contribution from the wall-corrected electrophoretic driving force to the particle velocities can be superimposed due to the linearity of the problem. In the other part of the thesis, an investigation of the electrophoretic motion of a long dielectric circular cylinder with an angular distribution of its surface potential under a transversely imposed electric field in the vicinity of a large plane wall parallel to its axis is made, where the applied electric field can be either perpendicular or parallel to the plane wall. Through the use of cylindrical bipolar coordinates, the Laplace and Stokes equations are solved analytically for the two-dimensional electric potential and velocity fields, respectively, in the fluid phase, and explicit formulas for the electrophoretic and angular velocities of the cylindrical particle are obtained. To apply these formulas, one only has to calculate the multipole moments of the zeta potential distribution at the particle surface. It is found that the existence of a nearby plane wall can cause the translation or rotation of a particle which does not exist in an unbounded fluid under the applied electric field.