具極化電雙層之球形膠體粒子在微圓管中之電泳運動

Abstract

本論文探討一帶電球形膠體粒子在對稱電解質溶液中，於外加電場下沿著一微圓管中心軸進行之電泳運動，其中外加之電場為均勻且平行於管壁，而管壁可為絕緣或為線性的電位分布。吾人假設固體表面之電雙層相對於粒子半徑及粒子與管壁間之距離為非常小，但仍允許粒子表面之薄電雙層存在極化效應。為了求解電解質溶液中的離子電化學位能與流體動量守衡方程式，吾人同時使用球座標和圓柱座標來建立通解，並先對管壁處的邊界條件使用傅立葉轉換來化簡通解，再使用粒子表面處的邊界條件配合邊界取點法求出通解中的待定係數。使用邊界取點法所得之數值結果與使用反射法所得之近似解析解互相吻合，而管壁存在時之粒子電泳速度會受到粒子表面、管壁表面、和電解質溶質的性質以及粒子和圓管半徑比的影響。 研究結果顯示兩種不同的管壁邊界條件，對於粒子的電泳運動影響甚為不同。在管壁不帶電的狀態下，粒子的電泳速度大致上隨粒子與管壁間之距離減少而遞減，唯在特定條件下，由於管壁存在所造成的流體力學黏滯效應以及粒子表面局部電場增強效應互相競爭，電泳速度在粒子相當靠近管壁的時候會出現隨粒子與管壁間之距離減少而遞增的現象。當管壁帶電且其表面電位相當於粒子表面電位時，粒子的電動力泳動主要是受帶電管壁引起的電滲透流動影響。

A theoretical study is presented for the electrophoretic motion of a spherical particle in an electrolyte solution along the axis of a circular microtube, whose wall may be either insulating or prescribed with the linear far-field electric potential distribution. The electric double layers adjoining the charged particle surface and tube wall are finitely thin, and the polarization of the diffuse layer at the particle surface is allowed. The general solutions to the electrostatic and hydrodynamic governing equations are constructed in combined cylindrical and spherical coordinates, and the boundary conditions are enforced on the tube wall by the Fourier transform and along the particle surface by a collocation method. The collocation results for the electrophoretic mobility of the confined particle, which agree well with the asymptotic formulas obtained by using a method of reflections, are obtained for various values of the particle, wall, and solution characteristics. An insulating tube wall and a tube wall with the far-field potential distribution affect the electrophoresis of the particle quite differently. Although the particle mobility in a tube with uncharged wall in general decreases with an increase in the particle-to-tube radius ratio , it can increase with an increase in as this ratio is close to unity for some cases because of the competition between the wall effects of hydrodynamic retardation and possible electrochemical enhancement on the particle migration. When the zeta potential of the tube wall is comparable to that of the particle, the electroosmotic flow of the bulk fluid induced by the tube wall dominates the electrokinetic migration of the particle.