邊界效應對多孔膠體粒子電泳之影響

Boundary Effects on the Electrophoresis of a Porous Particle

鄭文立(Wen-Li Cheng)

指導教授 ： 李克強

國立臺灣大學/工學院/化學工程學研究所/博士(2010年)

https://doi.org/10.6342/NTU.2010.03553

摘要

本研究主要以假性光譜法對多孔膠體粒子在邊界附近的電泳現象進行數值模擬，其中包含導電平板以及圓柱形開管兩大類型的邊界。多孔粒子具有流體可穿透的特性，與傳統硬球粒子不同，需考慮粒子內部的電荷分布及流體流動情形。為了適當描述系統，吾人使用雙球座標與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。
研究結果發現，當多孔粒子所帶的固定電荷密度愈高，極化效應愈明顯，也愈容易呈現出反離子凝聚的效果。伴隨著電解質濃度增加，多孔粒子的整體電位值會逐漸降低，電泳動度的量值和趨勢會回歸至低電位假設下的解析式。傳統以固定表面電位來描述電動力學現象的方式不再適用，為其與硬球粒子間最明顯的差異。而多孔粒子的摩擦係數影響較為單純，所對應的電泳動度與其值呈現簡單的比例關係：其值愈大，對應的電泳動度愈小。
而邊界效應所帶來之主要影響是降低多孔粒子電泳的速度，且其程度會隨著電雙層厚度的縮小而遞減，主要原因在於電雙層的存在會侷限多孔粒子周圍流體的流動。此外，邊界的存在會對多孔粒子本身的電雙層造成擠壓，使得流體中的離子濃度重新分布，造成極化效應和反離子凝聚現象的程度發生改變，尤其當邊界為圓柱開管時，因為邊界平行於多孔粒子的運動方向，極化效應會更加地明顯。
另一方面，如圓柱管壁帶有電位，其表面也會形成電雙層，並在外加電場作用下產生電滲透流，其強度會隨著電解質濃度提高上升到一個正比於管壁電位的固定值，可視為一個背景的流動。若管壁電位與多孔粒子電位異號，會加快多孔粒子電泳的速度；反之則會降低。當管壁電位夠高時，甚至能使多孔粒子往反方向移動。此特殊的現象可應用於在微流體通道中控制、分離不同種類的多孔粒子。

關鍵字

電泳現象 ； 多孔粒子 ； 雙球座標 ； 極化效應 ； 反離子凝聚 ； 電雙層 ； 邊界效應 ； 電滲透

並列摘要

Electrophoresis of a porous particle normal to a well conducting plane and along the centerline of a cylindrical pore are investigated theoretically 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.
We find that the polarization effect and the counterion condensation are more apparent as the fixed charge density of the porous particle increases. The presence of the solid boundary retards the particle motion in general, and is more significant when the electric double layer surrounding the particle is thick. The degree of polarization effect and counterion condensation would vary due to the deformation of electric double layer. Moreover, for the case of a charged pore, an electric double layer will occur near the pore surface, and an electroosmotic flow will take place upon the external electric field. The flow can either enhance the particle motion or deter it, depending on the potential sign on the pore. The direction of particle motion may even change when the pore is highly charged.

並列關鍵字

electrophoresis ； porous particle ； bipolar coordinate ； polarization ； counterion condensation ； electric double layer ； boundary effect ； electroosmotic flow

參考文獻

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