具電荷調節多孔球粒子對平板之擴散泳行為

Abstract

本研究對於可電荷調節的多孔粒子垂直於平板邊界的擴散泳動行為進行數值方法的模擬。為同時描述多孔粒子與平板邊界，本研究使用雙球座標系統進行電動力學方程組的多區聯解，並用牛頓-拉福生迭代法求系統穩態解。本研究針對電解質離子濃度(κac)、解離常數(B)、溶液pH值、穿透度(λa)與粒子到平板距離(h*)的變化討論對於擴散泳動行為的影響，研究結果發現電解質離子濃度較小時，粒子帶電量均會較高，同時擴散電場效應也會較明顯，因此粒子傾向負方向的運動，且泳動度普遍較大；另一方面，當電解質離子濃度較大時，反離子凝聚效果顯著，粒子電量較低，且電雙層極化效應主導泳動，因此泳動度有較低的趨勢。而在粒子接近平板時，與一般硬球電泳的情況相差甚遠，除了粒子電量會因為電雙層遭平板擠壓重新分布而增加外，泳動度也會產生往高濃度或低濃度方向加速的效果，這也是因為粒子周圍離子濃度重新分布造成的效果。另外，在不同pH值環境時，由於不同效應主導泳動導致粒子泳動方向不同，因此接近平板時會導致加速或減速甚至反轉的效果。

Diffusiophoresis of a charge-regulating porous particle normal to a conducting plane is investigated theoretically in this study. Due to the configuration envolving spherical particle and planar boundary, the system characterized by bipolar coordinates. The coupled electrokinetic equations are solved linearly with a pseudo-spectral method based on Chebyshev polynomials. Also, Newton-Ralphson iteration scheme are adopted here for solution. Electrolyte concentration, dissociation constant, pH, particle transmittance and the distance between particle and plane are discussed as variables in the study. We find that the charge density of the porous particle will increase as the electrolyte concentration and counterion condensation increases. However, while the electrolyte concentration is low, effect of the diffusion potential dominants which leads particle to negative direction. Otherwise, the polarization effect will take place and goes to positive direction. We also find that the presence of solid plane will increase the particle charge density as well as particle mobility. The plane will deform the electric double layer and redistribute the electrolye ions, which builds an induced electric field toward positive or negative direction, depends on the electrolyte concentration and pH.