多孔球膠體粒子之電動力學現象探討

Abstract

本研究以假性光譜法數值模擬多孔粒子在懸浮液中之電動力學行為，其中包含了電泳與擴散泳。為了適當描述此系統，我們採用Brinkman所提出的多孔物質模型，並在此物理空間中求解相互耦合的電動力學方程組。多孔粒子具有可供流體穿透的特性，因此能夠更貼切描述生物粒子或聚電解質聚合物，比硬球模型更適合用來描述此類膠體。 現存多孔粒子相關的電動力學理論，大多假設粒子帶電量必須極低，這個假設使他們的結果無法表現出粒子帶電量非線性的影響。此外，在本身帶電量足夠高時，離子雲的極化效應也會浮現，而使粒子帶電量對泳動度的影響更加複雜，本論文突破了粒子帶電量的限制，分別探討多孔膠體粒子懸浮溶液中的電泳與擴散泳現象。由於電泳與擴散泳皆隸屬於電動力學現象，我們將擇其相通的部份，在第二章理論分析一併介紹；第三章詳述本論文所採用的數值方法與計算流程。在內容上，我們將分為三個章節討論，其中第四章討論密集多孔粒子在無鹽溶液中的電泳現象，第五章為密集多孔粒子在電解質溶液中電泳現象，並在第六章討論單一多孔粒子在電解質溶液中的擴散泳現象。 我們發現多孔粒子固定電荷密度越高時，離子雲的變形越為嚴重，會大幅降低泳動度。整體而言，多孔粒子的摩擦係數越高，泳動速度越低，並會逐漸趨於定值；然而當多孔粒子摩擦係數極低時，粒子內部對流造成的極化效應可能取代流體阻力而成為主要的阻力來源。隨著電雙層厚度的變化，可以觀察到解析所無法預測到的局部極值；隨著電雙層厚度持續變薄，多孔粒子的電位越低，泳動度會趨於一定值；在電雙層厚度等同於粒子半徑時，極化效應最為顯著。密集度會提供額外的流體阻力，會降低泳動速度。此外，當電雙層互相重疊時，極化效應的影響會消失。

The electrokinetic behavior including electrophoresis and diffusiophoresis in either dilute or concentrated suspensions of charged porous particles is investigated. Brinkman model is adopted to simulate the porous structure. A pseudo-spectral method based on Chebyshev polynomials is used to solve the resulted general electrokinetic equations. Instead of the classic hard sphere model, porous particle model may be a better choice in describing bio-particles and polyelectrolytes, which are usually permeable to ions and fluid. We found, among other things, that the polarization effect due to the convection flow within the porous sphere is a crucial factor in determining its electrophoretic behavior. An induced electric field opposite to the applied electric field is generated, which deters the particle motion significantly when the particle is highly permeable. Approximate analytical prediction for dilute suspensions neglecting convection flow can overestimate the mobility severely in this situation. The approximate analytical prediction is satisfactory when the permeability of particle is low, though. Counterion condensation happens at high fixed charge density which decreases the mobility drastically and the mobility approaches a constant value asymptotically. The mobility profile of the particles with increasing volume fraction can exhibit local minimum if the corresponding dimensionless parameter Qfix/(λa)2 is high, where Qfix and λa are respectively the fixed charge density and the friction coefficient of the porous particles in dimensionless form. This is due to the overlapping of counterion clouds surrounding particles, which offsets the polarization effect, becomes significant as the suspension gets concentrated. No such phenomenon for low Qfix/(λa)2, where the mobility profile decreases monotonously with increasing volume fraction. Comparison with experimental data available in the literature for polyelectrolyte suspensions is excellent, indicating the reliability of this analysis, as well as the success of using charged porous sphere to model a polyelectrolyte system.