密集帶電液滴之沉降行為暨聚電解質粒子 在不含鹽類溶液中之電泳行為

Sedimentation in a Concentrated Suspension of Charged Liquid Drops and Electrophoresis of Polyelectrolytes in a Salt-Free Medium

江嘉評(Chia-Ping Chiang)

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(2008年)

https://doi.org/10.6342/NTU.2008.10516

摘要

本論文的研究主要以假性光譜法對帶電液滴以及聚電解質（polyelectrolytes）硬球粒子之電動力學現象進行數值模擬，其中包含密集帶電液滴在電解質溶液（electrolyte solution）中之沉降行為、聚電解質粒子在不含鹽類溶液（salt-free solution）的密集懸浮系統中以及在球形孔洞中之電泳行為。不含鹽類溶液中的離子來自聚電解質粒子表面的官能基解離而釋放出的反離子。我們分別以1959年Kuwabara所提出的單位晶格模型（unit cell model）以及1995年Zydney所提出的孔洞模型來描述這些系統，求解耦合的電動力學方程組。

密集帶電液滴之沉降行為的研究結果發現，液滴之沉降速度隨液滴黏度愈大（液滴受到的拖曳力愈大）、密集度愈大（相鄰液滴間的障礙效應愈大）以及表面電位愈高（電雙層的極化效應愈強）而愈小，並隨著電雙層厚度的變化而存在一個局部極小值（電雙層極化效應與內電場相互競爭的結果）；沉降電位則是隨著液滴黏度愈小而愈大。當帶電粒子的表面電位很低時，無因次沉降電位與其無因次電泳動度間的關係只為密集度的函數。密集聚電解質硬球粒子之電泳行為的研究結果發現，當粒子的密集度與帶電量都很小時，其電泳動度隨著帶電量的增加而線性增加，此特徵隨著體積分率愈大而愈不明顯；當帶電量超過某個臨界帶電量時，由於反離子凝聚現象（counterion condensation）發生，電泳動度隨著帶電量的增加不再有明顯的變化。此外，電泳動度隨著密集度愈大、反離子的價電數愈大或electric Peclet數愈大（即擴散係數愈小）而愈小。關於聚電解質粒子在球形孔洞中電泳行為的研究，其結果在定性上與在密集懸浮系統中的情形相當類似，在定量上，由於孔洞邊界為一實體邊界，粒子的電泳速度在孔洞中比起在密集懸浮系統中要來得慢。

關鍵字

帶電液滴 ； 沉降速度 ； 沉降電位 ； 聚電解質 ； 不含鹽類溶液 ； 電泳動度 ； 反離子凝聚現象

並列摘要

In this study, we investigate numerically the electrokinetic phenomena of charged liquid drops and polyelectrolytes in solutions based on the pseudo-spectral method. These phenomena include the sedimentation of a concentrated suspension of charged liquid drops in an electrolyte solution, the electrophoresis of a concentrated suspension of polyelectrolytes in a salt-free solution, and the electrophoresis of a spherical polyelectrolyte in a salt-free solution within a spherical cavity. A salt-free solution indicates that the liquid phase contains only counterions which come from the dissociation of the functional groups of polyelectrolytes. We adopt respectively the Kuwabara’s unit cell model and the cavity model suggested by Zydney to describe these systems, and solve the coupled electrokinetic equations those govern the electric field, the ionic concentration field and the flow field in these problems.
In the first study, we found that, the larger the viscosity of a liquid drop, the larger the volume fraction, or the higher the zeta potential, the smaller the sedimentation velocity. The sedimentation velocity has a local minimum with the change of the electric double-layer thickness. The lower the viscosity of a liquid drop is, the larger the sedimentation potential is. In the second study, we found that, if both the volume fraction and surface charge of the polyelectroyte are sufficiently small, the electrophoretic mobility increases with the surface charge linearly; however, when the surface charge exceeds a certain critical value, counterion condensation occurs, and the electrophoretic mobility will not change with the increase in surface charge any more. In addition, the larger the volume fraction, the larger the valence of the counterion, or the larger the electric Peclet number (the smaller the diffusivity of the counterion), the smaller the electrophoretic mobility. In the third study, the numerical results are qualitatively similar to those obtained in a concentrated suspension; however, owing to the boundary effect, the electrophoretic mobility of a polyelectrolyte in a cavity is smaller than that in a concentrated suspension.

並列關鍵字

charged liquid drops ； polyelectrolytes ； salt-free solution ； sedimentation ； electrophoresis, counterion condensation phenomenon

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