帶電軟質粒子無鹽懸浮液中之電泳與電導

Electrophoresis and Electric Conduction in Salt-Free Suspensions of Charged Soft Particles

林維晟(Wei-Cheng Lin)

指導教授 ： 葛煥彰

國立臺灣大學/工學院/化學工程學研究所/碩士(2021年)

https://doi.org/10.6342/NTU202101947

摘要

本論文使用單元小室模型分析於一無鹽懸浮液中，球形帶電軟質粒子(每個粒子中心為一球形固體硬核，於其表面吸附一層帶有固定電荷密度之多孔聚電解質)之電泳運動與懸浮液之電傳導。在一單元小室內，僅有一種異性離子存在於一帶電軟質粒子周圍之無鹽溶液中，藉由適用於此系統之線性化Poisson-Boltzmann方程式以及Laplace方程式分別求解平衡電位分布以及由外加電場所引起之擾動電位分布，並透過離子的連續方程式及修正後的Stokes方程式分別求得電化學位能分布以及流體流速分布。求解上述物理量分布後，再藉由力平衡以及平均電流密度即可獲得軟質粒子電泳可動度和懸浮液有效電導度的解析解公式，結果顯示粒子之間的交互作用對於電泳可動度與有效電導度有著顯著的影響。與電解質溶液懸浮系統相同，在無鹽溶液懸浮系統中於其他參數不變的情況下，電泳可動度會隨著粒子固定電荷密度的增加而增加，並隨著硬核與粒子半徑比、粒子半徑與多孔層滲透長度比、以及粒子體積分率的增加而下降。無鹽懸浮液之正規化有效電導度也會隨著固定電荷密度的增加及硬核與粒子半徑比的下降而增加，但是正規化有效電導度並不是粒子體積分率的單調函數。

關鍵字

電泳 ； 無鹽溶液 ； 有效導電度 ； 軟質粒子 ； 單元小室模型

並列摘要

The electrophoresis and electric conduction of a concentrated suspension of spherical charged soft particles (each is a hard core coated with a polyelectrolyte layer) in a salt-free solution are analyzed by using a unit cell model. The linearized Poisson-Boltzmann equation and Laplace equation applicable to a unit cell are solved for the equilibrium electric potential profile and its perturbation induced by the imposed electric field, respectively, in the fluid containing the counterions only around the particle, and the counterionic continuity equation and modified Stokes/Brinkman equations are solved for the ionic electrochemical potential energy and fluid flow fields, respectively. Explicit analytical formulas for the electrophoretic mobility of the particles and effective electric conductivity of the suspension are obtained, and the particle interaction effects on these transport properties are significant and interesting. Same as the case in a suspension containing added electrolytes, the scaled electrophoretic mobility in a salt-free suspension is an increasing function of the fixed charge density of the particles and decreases with increases in the core-to-particle radius ratio, ratio of the particle radius to the permeation length, and particle volume fraction, keeping the other parameters unchanged. The normalized effective electric conductivity of the salt-free suspension also increases with an increase in the fixed charge density and with a decrease in the core-to-particle radius ratio, but is not a monotonic function of the particle volume fraction.

並列關鍵字

Electrophoresis ； Salt-free solution ； Effective electric conductivity ； Soft sphere ； Unit cell model

參考文獻

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