任意電雙層厚度圓柱形粒子之暫態電泳

Abstract

本論文探討一具有任意厚度電雙層之圓柱形帶電粒子置於一廣大不可壓縮牛頓流體之電解質溶液中，受到外加電場作用之暫態電泳運動現象。假設系統只受到微小擾動而偏離平衡狀態的情況下，可將流體運動主導方程式（靜電作用力修正過後的暫態Stokes方程式）線性化，以解析方法解得流場分布及粒子暫態電泳速度。研究結果顯示，在固定粒子與流體之密度比值下，粒子電泳速度隨時間之增加情形會隨著粒子表面電雙層厚度愈薄而愈快，而在相同電雙層厚度下，相對密度愈重的粒子的電泳速度隨時間之增加情形比較輕的粒子為慢。而圓柱形粒子達到一定程度接近穩定狀態時所需要的時間比球形粒子較長。

A theoretical study is presented for the dynamic electrophoretic response of a circular cylindrical particle to a step change in the applied electric field. The electric double layer surrounding the particle may have an arbitrary thickness relative to the particle radius. The transient Stokes equation modified with the electrostatic effect which govern the fluid velocity field is linearized by assuming that the system is only slightly distorted from equilibrium. Semi-analytical results for the transient electrophoretic mobility of the particle are obtained as a function of relevant parameters. The results demonstrate that the electrophoretic mobility of a particle with a constant relative mass density at a specified dimensionless time normalized by its steady-state quantity decreases monotonically with a decrease in . For a given value of , a heavier particle lags behind a lighter one in the development of the electrophoretic mobility. For the case of large , our result reduces to the corresponding analytical solution. The growth of the electrophoretic mobility with the elapsed time for a cylindrical particle is substantially slower than for a spherical particle.