帶電軟質粒子在表面帶電孔洞中之沉降運動

Abstract

本文探討一個球形軟質粒子在一個充滿對稱電解質溶液的球形孔洞內之沉降運動，軟質粒子由一個未帶電的球形硬核和一個包覆在外帶電的均勻多孔層組成。在假設系統些微偏離平衡狀態的情況下，利用常規微擾法，以多孔層的空間電荷密度和孔洞的表面電荷密度為微小參數，將主導流場、電位和電化學位能分布的非線性的電動力方程式簡化成為線性化方程式，並結合適當的邊界條件，求解了線性化電動力方程式後，再利用重力、流體阻力和電力的合力平衡，求解出軟質粒子沉降速度的表示式。本研究發現孔洞表面帶電可以增加軟質粒子的沉降速度，主要是由於沉降電位梯度造成的孔洞內電滲透使流體循環流動加強。除此之外，多孔層中的空間電荷和孔洞表面電荷電性相同時，粒子速度大致上會因孔洞的影響而增加。當此二固定電荷電性相反時，孔洞表面電荷密度相對於多孔層空間電荷密度足夠多時，則會增加粒子速度。孔洞表面電荷對軟質粒子沉降速度的影響會因為硬核與粒子半徑比、粒子與孔洞半徑比和粒子半徑與流體於多孔層內滲透長度的比值減小而增加，但此影響不是粒子半徑與電雙層厚度的比值的單調變化函數。

The sedimentation of a soft particle composed of an uncharged hard sphere core and a charged porous surface layer inside a concentric charged spherical cavity full of a symmetric electrolyte solution is analyzed in quasi-steady state. By using a regular perturbation method with small fixed charge densities of the soft sphere and cavity wall, a set of linearized electrokinetic equations relevant to the fluid velocity field, electrical potential profile, and ionic electrochemical potential energy distributions are solved. A closed-form formula for the sedimentation velocity of the soft sphere 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. The existence of the surface charge on the cavity wall increases the settling velocity of the charged soft sphere, principally because of the electroosmotic enhancement of fluid recirculation within the cavity induced by the sedimentation potential gradient. When the porous layer space charge and cavity wall surface charge have the same sign, the particle velocity is generally enhanced by the presence of the cavity. When these fixed charges have opposite signs, the particle velocity will be enhanced or reduced by the presence of the cavity if the wall surface charge density is sufficiently large or small relative to the porous layer space charge density in magnitude. The effect of the wall surface charge on the sedimentation of the soft sphere increases with decreases in the ratios of core-to-particle radii, particle-to-cavity radii, and particle radius to porous layer permeation length, but is not a monotonic function of the ratio of particle radius to Debye length.