平板帶電對硬球粒子及液滴電泳之影響

Abstract

本論文探討非導體硬球粒子與液滴垂直於一帶電平板的電泳運動現象，以假性光譜法對膠體粒子進行數值模擬。為了適當描述系統，使用雙球座標進行多區聯解，並在弱外加電場的假設下，將部分相互耦合的電動力學方程組線性化，再利用牛頓-拉福生疊代法求得系統之穩態解。本研究突破過去使用雙球座標無法處理帶電平板在無窮遠處數值畸點的問題，利用一維系統「平板─電解質溶液」之解析解進行變數變換，成功計算出高電位下粒子與平板皆帶電之電泳速度，並進一步探討平板帶電對電泳現象的影響。 研究結果發現，當低電位的時候帶電平板的電泳動度滿足粒子帶電、平板不帶電與粒子不帶電、平板帶電之線性加成結果，與以往學者所做之假設相符合。而平板帶電對無因次電泳動度的影響大致小於粒子本身電荷的影響，只有在粒子相當靠近平板時會比較明顯，因屆時會產生一電滲透浮力，此力的大小與粒子平板間距離有關，而方向由平板的電性決定。此外，當電位越高、粒子平板間距離靠近時，有別於在單一粒子中極化效應減少無因次電泳動度的現象，此時極化效應增加電滲透浮力，反而使無因次電泳動度增加，亦或是使無因次電泳動度反轉。 另一方面，當液滴內外黏度比愈小，液滴內部的拖曳力越小，其電泳速度隨之增加，反之當內外黏度比越大的時候，其電泳速度越接近硬球膠體粒子的結果。在定性上與硬球粒子相差無幾，但定量上卻有顯著之差異，亦即液滴的電泳運動受邊界影響甚為重要。

The electrophoretic behavior of a spherical rigid particle or a non-conducting liquid drop normal to a charged plane is investigated in this study. Due to the particular physical configurations, the systems were characterized by bipolar and sphere coordinates respectively. The coupled electrical potential, ion conservation and hydrodynamic equations, or the so-called electrokinetic equations, are linearized by assuming the applied external electric field is weak. A pseudo-spectral method based on Chebyshev polynomials and Newton-Raphson iteration scheme are adopted to solve the resulting electrokinetic equations numerically. When the particle is near a solid boundary, the presence of the boundary will affect the particle motion significantly. The electrophoretic mobility of the particle is affected by the distance to the charged plane. We conclude that the thinner the double layer and/or the larger the particle-surface distance, the greater the mobility of the particle. Moreover, a charged plane can exert electro-osmosis flow so dominant that sometimes it may even reverse the direction of the particle motion. This phenomenon can be enhanced by the effect of electro-osmotic buoyancy, and will affect the particle motion significantly. For the liquid drop, without considering the polarization effect, the magnitude of the scaled electrophoretic mobility increases with the decrease of viscosity ratio. This is because the flow inside the drop enhances the hydrodynamic drag on the liquid drop. It is also very interesting that the electrophoresis of the liquid drop will be very similar to the colloid particle if the viscosity ratio is very large. Besides, we find that the closer the particle to the plane, the more significant the distortion of electric double layer. The electrophoretic mobility becomes slow.