球形液滴對平板之電泳現象

Abstract

本論文探討非導體球形液滴垂直於一不帶電平板的電泳運動現象。在此我們突破過去求解雙球座標單一區間的情形，將原本的計算空間延伸至粒子內部，進一步探討內部流體流動對電泳現象的影響。並且在低表面電位及弱外加電場的假設下，利用正交配位法及牛頓-拉福生疊代法求解系統的非線性電場及流場方程式。 研究結果發現，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。此外，發現平板的邊界效應在電雙層厚度很大或是液滴離平板越靠近的時候相當明顯，尤其液滴太接近平板的時候會因為電雙層的變形而使得電泳速度異號，亦即液滴的電泳運動受邊界影響甚為重要。

The electrophoretic behavior of the spherical, non-conducting liquid drop normal to a plane is investigated in this study. We separate the physical region into two mathematical domains. With the aid of orthogonal collocation method and bipolar coordinates, the present study extends previous analyses in that the flow field inside the spherical particle can not be neglected, and the electric double layer thickness for the particle is arbitrary. We find that the electrophoretic mobility of the spherical drop is affected by two factors: the viscosity ratio between the fluid inside and outside the liquid drop, and the distance to the solid plane. 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.