帶電多孔粒子之暫態電泳

Abstract

本論文分析研究一均勻帶電的多孔球形粒子在任意電雙層厚度情況下突然受到外加電場作用的暫態電泳運動現象，此多孔粒子可以表示一個離子溶液可穿透之高分子電解質分子或奈米粒子凝聚體。對於帶電多孔粒子在一廣大不可壓縮牛頓流體之電解質溶液中，可以得到靜電作用力修正過後的暫態Stokes及Brinkman方程式，運用流線函數與拉普拉斯轉換求得流場分布，再利用粒子受力平衡以及拉普拉斯數值解逆轉換獲得多孔粒子電泳速度。使用多孔粒子穩態電泳速度可將多孔粒子的暫態電泳速度與加速度正規化，分別再探討它們與粒子電動力半徑κa、粒子內流體滲透度參數λa、粒子與流體密度比ρp / ρ、以及無因次時間νt / a^2的關係。 本研究結果顯示正規化電泳速度會隨著無因次時間νt / a^2增加而增加。在固定滲透度參數λa以及密度比ρp / ρ的情況下，正規化電泳速度會隨著電動力半徑κa增加而增加。在固定λa以及κa的情況下，正規化電泳速度會隨著ρp / ρ增加而遞減。在固定κa以及ρp / ρ時，正規化電泳速度會先隨著λa增加而遞增，到一定值λa之後會再隨著λa增加而遞減。而正規化電泳加速度會隨著無因次時間νt / a^2增加而減少，且隨著λa的增加而增加。

The starting electrophoretic motion of a porous, uniformly charged, spherical particle, which models a solvent-permeable and ion-penetrable polyelectrolyte coil or floc of nanoparticles, in an arbitrary electrolyte solution due to the sudden application of an electric field is studied for the first time. The unsteady Stokes/Brinkman equations with the electric force term governing the fluid velocity fields are solved by means of the Laplace transform. An analytical formula for the electrophoretic mobility of the porous sphere is obtained as a function of the dimensionless parameters κa, λa, ρp / ρ,and νt / a^2, where a is the radius of the particle, κ is the Debye screening parameter, λ is the reciprocal of the square root of the fluid permeability in the particle, ρp and ρ are the mass densities of the particle and fluid, respectively, νis the kinematic viscosity of the fluid, and t is the time. The electrophoretic mobility normalized by its steady-state value increases monotonically with increases in νt / a^2 and κa, but decreases monotonically with an increase in ρp / ρ, keeping the other parameters unchanged. A porous particle with a high fluid permeability in general trails behind an identical porous particle with a lower permeability and a corresponding hard particle in the growth of the normalized electrophoretic mobility, although typically this mobility first increases with an increase in λa from zero at λa = 0 to a maximum at some value of λa and then decreases with a further increase in λa to a constant as λa → ∞ for fixed values of κa, ρp / ρ, and νt / a^2 . The normalized electrophoretic acceleration of the porous sphere decreases monotonically with an increase in the time and in general increases with an increase in λa from zero at λa = 0.