帶電球形多孔粒子懸浮液之沉降速度與沉降電位

Abstract

本論文以理論探討帶有固定電荷的多孔球形粒子在電解質溶液中形成懸浮系統所進行之沈降運動。解析的過程中，吾人使用單元小室模型，考慮在任意電雙層厚度但低電位的條件下，透過求解Poisson-Boltzmann 方程式和修正過的Stokes 方程式，利用適當的邊界條件，以求得帶電多孔粒子在對稱性電解質溶液中之平均沈降速度以及沉降電位。由於所考慮的系統相對於平衡狀態只受到一微小擾動，可將原本交互聯立的非線性電動力微分方程式轉化為線性的問題。配合正規微擾分析法，得到小室內電解質溶液中的電位分佈與流速分佈。 再藉由平衡作用於粒子的重力、電力、和流體阻力等三種力後，可以求得帶電粒子的沈降速度以及懸浮液之沉降電位(電泳可動度)的解析形式表示式。結果顯示：粒子內部的水力摩擦環節與固定電荷的存在，對粒子的沈降速度以及懸浮液之沉降電位(電泳可動度)各有相等的影響；另外，粒子在對稱電解質溶液中的濃度變化對沈降速度以及沉降電位(電泳可動度)也有顯著影響。

The body-force-driven migration in a homogeneous suspension of polyelectrolyte molecules or charged flocs in an electrolyte solution is analyzed. The model used for the particle is a porous sphere in which the density of the hydrodynamic frictional segments, and therefore also that of the fixed charges, is constant. The effects of particle interactions are taken into account by employing a unit cell model. The overlap of the electric double layers of adjacent particles is allowed and the relaxation effect in the double layer surrounding each particle is considered. The electrokinetic equations which govern the electrostatic potential profile, the ionic concentration (or electrochemical potential energy) distributions, and the fluid velocity field inside and outside the porous particle in a unit cell are linearized by assuming that the system is only slightly distorted from equilibrium. Using a regular perturbation method, these linearized equations are solved for a symmetrically charged electrolyte with the density of the fixed charges as the small perturbation parameter.

An analytical expression for the settling velocity of the charged porous sphere is obtained from a balance among its gravitational, electrostatic, and hydrodynamic forces. A closed-form formula for the sedimentation potential in a suspension of identical charged porous spheres is also derived by using the requirement of zero net electric current. Our results indicate that the effects of the overlap of the adjacent double layers and of the relaxation of the diffuse ions are quite significant, even for the case of thin double layers.