Diffusiophoresis of Colloidal Particles in an Electrolyte Solution

本論文探討電解質溶液中各種膠體系統之擴散泳現象。在此我們利用正交配位法求解系統的非線性電場及流場方程式，突破過去低表面電位與極薄電雙層厚度的假設，進一步探討極化效應、電雙層重疊效應、以及平面邊界效應對膠體粒子擴散泳動度的影響。究結果發現，隨著膠體粒子的表面電位逐漸提高，粒子的擴散泳動度隨著粒子表面電位的增加會產生一局部極值。尤其當陰陽離子的擴散速度不相等的時候，在高濃度區域與低濃度區域之間會產生一誘發電場，此誘發電場將在帶電粒子周圍產生一電滲透流，給予粒子加速或是減速的效果。同時，我們發現隨著粒子的體積分率越大，粒子的擴散泳動度越慢。另外，粒子表面若具有可解離的官能基，粒子的表面電位將不再是一個固定的常數，使得粒子的擴散泳動度也跟著改變。在液滴的擴散泳現象裡，當液滴內外流體的黏度十分接近時，液滴內部流體的流動現象會對液滴的擴散泳動度有顯著的影響。一方面，我們發現當粒子受外加濃度梯度朝一平面運動時，平面邊界會擠壓電雙層的分佈而產生一局部濃度梯度，尤其當粒子周圍的電雙層恰好接觸到平面的時候粒子有最大速度，但是隨著粒子越接近平面，平面的流體拖曳力效應反而越明顯。除此之外，比較金屬導體平板、非導體平板、液氣交界面三種不同平面邊界，我們發現不同種類的平面邊界會使粒子受到不同大小的流力與電力，造成粒子的擴散泳動動在這三種情形裡有所差異。鍵字：擴散泳現象、電動力學現象、膠體、液滴、邊界效應。Diffusiophoretic behavior of colloidal particles subject to a uniform electrolyte concentration gradient is investigated theoretically for arbitrary double layer thickness and surface potential. The governing general electrokinetic equations are put in terms of spherical coordinates and bipolar spherical coordinates, and solved numerically with a pseudo-spectral method based on Chebyshev polynomial. Without any assumption about particle surface potential or double layer thickness, the effects of key factors are examined such as the effect of double layer polarization, double layer overlapping, and boundary effect. t is found, among other things, that the diffusiophoretic mobility exhibits a local maximum as well as a local minimum with varying particle surface potential. In contrast to the case of identical diffusivity of cations and anions, a local electric field is induced in the present case due to an unbalanced charge distribution between higher and lower concentration regions. Depending upon the direction of this induced electric field, the diffusiophoretic mobility can be larger or smaller than that for the case of identical diffusivity. The effect of volume fraction ratio of colloids is also examined. The higher the ratio is, the lower the mobility. Furthermore, if the surface pf a particle contains dissociable functional groups, the dissociation of which yields a variation of particle surface potential. The diffusiophoretic mobility of the particle will change accordingly. Besides, it is found that the internal flow of a liquid drop, characterized by their viscosity, has the most significant impact on the diffusiophoretic motion of a liquid drop when the viscosity ratio is approach 1.0. n the study of a spherical colloidal particle normal to a planar boundary, it is found, among other things, that the presence of a planar boundary results in a local concentration gradient, provided that the double layer does not touch the planar boundary. If it does, however, the diffusiophoretic mobility of the particle will exhibit a maximum as the double layer just touches the planar boundary, thanks to the competitive force of hydrodynamic drag. Distinctive features pertinent to a planar metal surface, a non-conducting plane, and an air-water interface are also examined in particular. It is concluded that the planar boundary poses not only as a conventional hydrodynamic retarding force, but may lead to different electrostatic interaction hence alter the polarization situation, which has profound electrostatic impact on the motion of the particle when it is close to the plane.eywords: diffusiophoresis, Electrokinetics, colloids, liquid drop, boundary effect.目錄人著作目錄 I要 IIIbstract V錄 VII表目錄 IX一章 導論 1.1 擴散現象與濃度梯度 1.2 膠體粒子的擴散泳現象 3.3 膠體粒子擴散泳現象的相關應用 7.4 各種膠體系統擴散泳之文獻回顧 11二章 理論分析 23.1 電動力學主控方程式 23.2 平衡系統與擾動系統 30.3 硬球密集懸浮系統 38.4 液滴密集懸浮系統 50.5 球對平面系統 61.6 表面調節邊界條件 75.7 擴散泳動度之計算 78三章 數值方法 85.1 正交配位法 86.2 微分矩陣表示式 89.3 空間映射 91.4 牛頓-拉福生疊代法 95.5 兩區聯解問題之處理 99四章 結果與討論 102.1 密集膠體懸浮系統之擴散泳現象 113.2 密集液滴懸浮系統之擴散泳現象 176.3 球對平面之擴散泳現象 207.4 表面調節現象對擴散泳動度的影響 253五章 結論 261號說明 265考文獻 269錄A 流場主控方程式的推導 286錄B 擴散泳相關邊界條件的推導 291錄C 雙球座標簡介 301錄D 平面介電常數的影響 30