圓柱形孔道內球形帶電粒子在高分子溶液中之電泳與電滲透運動

Electrophoretic and Electroosmotic Motion of a Charged Spherical Particle within a Cylindrical Pore Filled with Polymeric Solution

黃郁棻(Yu-fen Huang)

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(2017年)

https://doi.org/10.6342/NTU201700486

摘要

在毛細管電泳及微米/奈米流體的系統中，所採用的介質除了眾所習知的凝膠與水溶液之外，高分子溶液也逐漸被廣泛應用，所採用的流體管道也愈來愈微小化。本研究探討帶電球形粒子於填充高分子溶液的圓柱形管道中之電泳與電滲透運動現象，並以Debye-Bueche-Brinkman (DBB)模型來描述高分子水溶液的流體性質。DBB模型針對線性高分子溶於均勻的溶劑系統，描述高分子溶液的流變學特性，為經過嚴謹推導的非牛頓流體模型。對應的電動力學主控方程式乃由Debye及Bueche以Chebyshev多項式為基礎，採用修正的假性光譜法來進行數值解。
根據數值模擬結果，吾人發現粒子的泳動度因電雙層極化效應而在κa等於1附近有明顯的下降，特別是在窄管道中。此乃導因於管壁產生額外的侷限效應，而使帶電粒子附近電雙層當中的反離子移動到粒子運動方向之後方，誘發反向電場而阻滯粒子運動。在高分子溶液中，粒子的泳動度低於電解質水溶液，乃因高分子流體中黏滯力對粒子運動的阻礙效應更強。此外，管壁帶電條件下，管道中的電滲透流分布呈現特別的非牛頓特性。不同於牛頓流體中呈現平推流(plug flow)的分布，在高分子溶液中可明顯觀察到電滲透流的流速分布在管壁附近出現極大值，且為軸對稱分布。此種軸向變化的速度分布可能對於靠近管壁流動的小分子提供額外的沖提分離機制。本研究突破數學上複雜性的限制，數值模擬結果對於採用高分子溶液為介質的微奈米管道電泳與電滲透現象分析提供良好的理論研究基礎。

關鍵字

電泳 ； 電滲透 ； 電動力學 ； Debye-Bueche-Brinkman高分子溶液 ； 電雙層極化效應

並列摘要

Electrophoretic and electroosmotic motion of a charged spherical particle within a cylindrical pore filled with a Debye-Bueche-Brinkman (DBB) polymeric solution is investigated theoretically, which is of high relevance in capillary electrophoresis as well as micro- and nanofluidic applications involving polymeric solutions in a micro- or nanopore. The DBB model describes rheological response of a polymeric solution with linear polymer dissolved in a homogeneous solvent. It is a well-known non-Newtonian model in liquid physics based on rigorous theoretical derivations. By Debye and Bueche, corresponding governing fundamental electrokinetic equations are solved numerically with a patched pseudo-spectral method based on Chebyshev polynomials.
We found that the double layer polarization effect reduces the particle mobility severely when the Debye parameter, κa, is around unity, especially in narrow pores. This is attributed to the extra confinement effect from the nearby wall which tends to sweep the predominant counterions within the double layer to the wake of the moving particle, resulting in a motion-deterring induced electric field. The electrophoretic mobility in a polymer solution is smaller than that in an aqueous electrolyte solution in general due to the much stronger viscous drag effect in a polymer solution. Moreover, electroosmotic flow (EOF) due to a charged pore wall is found to exhibit a highly non-Newtonian behavior. Unlike the corresponding plug-like flow for a Newtonian solution, an axisymmetric flow with a large local maximum in the velocity profile in the region near the pore wall is observed. This radial-varying velocity profile offers a potential extra separation mechanism which favors the elution of smaller particles in general.
The results obtained here provide fundamental understandings and insights of the electrophoresis and electroosmosis phenomena in a cylindrical pore filled with polymeric solution.

並列關鍵字

electrophoresis ； electroosmosis ； electrokinetics ； electric double layer polarization ； Debye-Bueche-Brinkman (DBB) polymer solution

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