剛性橢球在任意軸向位置於球形孔洞中之擴散泳行為

Abstract

本論文是以有限元素法探討帶有任意表面電位以及任意電雙層厚度的生物膠體任意形狀橢球粒子在不帶電球形孔洞中軸向任意位置之擴散泳行為，而橢球粒子的邊界效應被我們理論解析。我們的研究藉由無因次表面電位、橢球形狀因子、電雙層鬆弛效應、化學滲透或擴散滲透流以及兩種競爭的電雙層極化效應來展現成果。我們假設相較於由粒子或邊界所建立的電場或者濃度場，外加濃度場較弱，故原來相互耦合的電場、流場以及離子濃度場方程式可以線性化，並以微擾理論與疊加原理來求解。 無因次擴散泳速度在一般的例子中，速度大小排序為長橢球＞圓球＞扁橢球。無因次擴散泳速度以無因次表面電位、電雙層厚度、軸偏移率、或者孔洞大小為橫軸做圖，在某些條件下甚至導致膠體粒子泳動方向改變或者擴散泳速度產生局部極值。而此極值產生的原因為電力以及流體阻力兩者競爭的結果決定膠體粒子泳動之方向。本論文所獲得的結果提供擴散泳設計與操作具參考價值的資訊。

The boundary effect on the diffusiophoretic behavior of a spheroid is analyzed theoretically by considering the diffusiophoresis of a charged spheroid under arbitrary surface potential and double-layer thickness at an arbitrary position in an uncharged spherical cavity. We demonstrate that the phenomenon under consideration is governed by scaled surface potential, the aspect ratio of a spheroid, double-layer relaxation, chemiosmotic/diffusioosmotic flow, and two types of the competing double-layer polarization. Based on the assumption that the applied concentration gradient is weaker than the electric field and concentration field established by the particle and/or the boundary, we solve this phenomenon by virtue of the perturbation theory and the superposition principle. The scaled diffusiophoretic velocity are examined rank as prolate >sphere>oblate in general cases. The diffusiophoretic velocity as a function of the scaled surface potential, or the thickness of EDL, or the axial deviation, or the cavity size may exhibit a local maximum just because the competition of electric force and hydrodynamic drag determines the moving direction of the particle. These contributed to valuable information for the design and implementation of an diffusiophoresis operation.