帶電球形軟質粒子在帶電球形孔洞中之擴散泳

Abstract

本研究分析在一個充滿對稱型電解質溶液並具有濃度梯度的同心帶電球形腔體中，由一個不帶電的硬球核心與一個均勻帶電的多孔表面層組成的球形複合軟質粒子的擬穩態擴散泳動現象。藉由對軟質粒子與腔體壁的固定電荷密度進行正規微擾法，求解與流體速度場、電位分佈以及離子濃度分佈相關的線性化電動力方程式。進而獲得了軟質粒子的擴散泳動（包含電泳及化學泳的貢獻）速度的解析結果，此速度為以下幾個無因次群的函數：實心硬核與複合粒子半徑比值（r_0/a） 、複合粒子與帶電空腔半徑比值（b/a） 、複合粒子半徑與電雙層特性厚度（Debye screening length）的比值（κa）以及複合粒子半徑與多孔層滲透長度（porous layer permeation length）的比值（λa）。 在一般狀況下，帶電的腔體壁對複合粒子的擴散泳動行為具有顯著影響。沿著腔體壁產生的擴散滲透（diffusioosmosis），包含電滲透（electroosmosis）和 化學滲透（chemiosmosis） 所造成的流體流動，會大幅改變複合粒子的擴散泳速度，甚至可能使其方向反轉。整體而言，擴散泳速度隨著實心硬核與複合粒子半徑比值、複合粒子與帶電空腔半徑比值、複合粒子半徑與多孔層滲透長度的比值增加而減小，隨著複合粒子半徑與電雙層特性厚度的比值增加而增加。

The quasi-steady diffusiophoresis of a soft particle composed of an uncharged hard sphere core and a uniformly charged porous surface layer in a concentric charged spherical cavity full of a symmetric electrolyte solution with a concentration gradient is analyzed. By using a regular perturbation method with small fixed charge densities of the soft particle and cavity wall, the linearized electrokinetic equations relevant to the fluid velocity field, electric potential profile, and ionic concentration distributions are solved. A closed-form formula for the diffusiophoretic (electrophoretic and chemiphoretic) velocity of the soft particle is obtained as a function of the ratios of core-to-particle radii, particle-to-cavity radii, particle radius to the Debye screening length, and particle radius to porous layer permeation length. In typical cases, the confining charged cavity wall significantly influences the diffusiophoresis of the soft particle. The fluid flow caused by the diffusioosmosis (electroosmosis and chemiosmosis) along the cavity wall can considerably change the diffusiophoretic velocity of the particle and even reverse its direction. In general, the diffusiohoretic velocity decreases with increasing core-to-particle radius ratio, particle-to-cavity radius ratio, and ratio of particle radius to porous layer permeation length, but increases with increasing ratio of particle radius to the Debye length.