任意電雙層厚度之帶電粒子在表面帶電孔洞中之 擴散泳運動

Abstract

本論文以理論探討一個帶電之球形粒子在一個充滿具有濃度梯度之對稱電解質溶液的帶電球形孔洞中所進行之擴散泳運動，此帶電球形粒子以及帶電球形孔洞之表面電荷皆為均勻分布。主導電解質溶液中的電位分佈、離子濃度分佈和流場分佈的電動力方程式可以藉由假設相對於平衡狀態時，系統只有受到微小的擾動來線性化。藉由正規擾動法，這些被線性化的電動力方程式以帶電球形粒子之無因次表面電位和帶電球形孔洞之無因次表面電位做為二個微小擾動參數，並搭配上適當的邊界條件，可以求得電解質溶液中的電位分佈、流速分佈、壓力分佈以及電化學位能分佈的解析解。求解上述四個物理量分佈後，再藉由處於擬穩態下，作用於帶電球形粒子的電力和流體阻力之合力為零，可以得到帶電球形粒子之擴散泳正規化速度的解析解，其表示式準確到帶電球形粒子之表面電位和帶電球形孔洞之表面電位的第二階。結果顯示：帶電球形孔洞所造成之邊界效應對於帶電球形粒子之擴散泳速度影響相當顯著，且電解質溶液沿著帶電孔洞之孔壁所產生之擴散滲透流動對於粒子之速度也有相當程度的影響。大致上粒子之擴散泳速度會隨著粒子之電雙層厚度愈來愈薄呈現增加的趨勢，而隨著球形粒子相對於孔洞愈來愈大，粒子之擴散泳速度會呈現下降之趨勢。

An analytical study is presented for the diffusiophoretic motion of a charged colloidal sphere located at the center of a charged spherical cavity filled with an electrolyte solution at the quasisteady state for the case of arbitrary electric double layers. The electrokinetic equations governing the ionic concentration, electric potential, and velocity distributions in the fluid phase are linearized by assuming that the system is only slightly distorted from equilibrium. These linearized equations are solved by using a perturbation method with the zeta potentials of the particle and cavity as the small perturbation parameters. An explicit formula for the diffusiophoretic velocity of the particle as a combination of the electrophoretic and chemiphoretic contributions valid for arbitrary values of and is obtained from a balance between the electrostatic and hydrodynamic forces acting on it, where is the Debye screening parameter, is the radius of the particle, and is the radius of the cavity. The effect of the charged cavity wall on the diffusiophoresis of the particle is interesting and can be significant. The contributions from the diffusioosmotic (electroosmotic and chemiosmotic) flow occurring along the cavity wall and from the wall-corrected diffusiophoretic driving force to the particle velocity are equivalently important, and this diffusioosmotic flow can reverse the direction of the particle velocity, which in general increases with an increase in and decreases with an increase in , but exceptions exist.