邊界效應對多孔膠體粒子擴散泳之影響

Abstract

本論文探討電解質溶液中各種邊界效應對多孔膠體粒子擴散泳現象之影響。為了描述多孔粒子系統，我們利用雙球座標系統進行多區聯解系統的非線性電場及流場方程式，再利用牛頓-拉福生疊代法求得系統之穩態解。並進一步探討加入平面邊界條件後，極化效應、電雙層重疊效應對多孔膠體粒子擴散泳動度之影響。 研究結果發現，隨著電荷密度變大，化學泳的驅動力會增加，並使多孔粒子的擴散泳動度加快；而當電解質溶液裡的陰陽離子擴散係數不同時，電泳項的驅動力就會出現，當多孔粒子帶正電時，電泳項的驅動力方向會與化學泳項相反，且略大於化學泳項，讓多孔粒子會往負的方向移動，此時的擴散泳動度為此兩項競爭的結果。而電雙層厚度也會影響擴散泳動度，在電雙層厚度約等於粒子半徑時，受流動項的極化效應影響會使擴散泳動度降低最多。而當多孔粒子的摩擦係數愈高時，也會導致擴散泳動度愈慢。 當多孔粒子碰到平面邊界條件如金屬導體平板或是氣液交界面時，多孔粒子的電雙層皆會受到影響，在電雙層還未與平面接觸時，平面邊界條件會擠壓電雙層，使其濃度梯度增加，並讓化學泳項的驅動力變大。而當電雙層接觸到平面邊界條件之後，平板與氣液交界面兩種情形下濃度梯度造成的化學泳項驅動力才會有差異，導致擴散泳動度也會不同。在平板時，由於受到不可滑動的流力邊界條件影響，離子會被限制住在平板以及粒子之間，所以濃度梯度會變得較大，化學泳驅動力以及擴散泳動度便會增加；氣液交界面時，離子在平面上並無受限，可自由移動，因此並無平板時的擠壓作用，當電雙層觸碰到氣液交界面後，會被平面干擾導致濃度梯度無法像單一粒子時完整建立，導致擴散泳動度因此下降。

Diffusiophoretic behavior of porous colloidal particles subject to a electrolyte concentration gradient is investigated theoretically for arbitrary double layer thickness and surface potential. The governing general electrokinetic equations are put in terms of 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. We find that the fixed charge density of the porous particle will increase the chemiphoresis and diffusiophoresis. 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. When the fixed charge density is positive, the direction of electrophoresis will have opposite pattern with chemiphoresis. The competition between chemiphoresis and electrophoresis will result in diffusiophoresis. In 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 porous particle will exhibit significance differences between planar metal surface and air-water interface. In the condition of planar metal surface, there will be an increase in chemiphoresis and demonstrates an decrease in the state of air-water interface