懸浮液中表面可調整電荷膠體粒子之擴散泳

Diffusiophoresis in a Suspension of Charge-Regulating Colloidal Spheres

李育龍(Yu-Lung Li)

指導教授 ： 葛煥彰

國立臺灣大學/工學院/化學工程學研究所/碩士(2006年)

https://doi.org/10.6342/NTU.2006.01480

摘要

本文以理論解析具有表面電荷可調整特性的膠體粒子於任意電雙層厚度下均勻懸浮在具有濃度梯度的對稱電解質溶液中之擴散泳。粒子表面所發生的電荷調整現象採用線性化的邊界條件來描述，此線性化的邊界條件說明了表面電荷密度與表面電位之間的關係。本文使用單元小室模型，考慮粒子之間的交互作用且允許相鄰帶電粒子周圍的電雙層重疊。主導對稱電解質溶液中的電位分布、離子濃度分布及流場分布的電動力方程式可以藉由假設相對於平衡狀態，系統只有受到微小的擾動來線性化。這些線性化的方程式可以用正規微擾法以表面電荷密度（或zeta電位）為微小擾動變數來求得解析解，進而求得具表面可調整電荷粒子的擴散泳速度準確到表面電荷密度（或zeta電位）的第二階。結果顯示，表面可調整電荷對擴散泳速度的影響，對於表面電荷於小室模型的外邊界條件非常敏感。在非常稀薄的懸浮液及電雙層為非常薄或非常厚這些極限的情況，粒子的速度與電荷可調整的變數無關。

關鍵字

擴散泳 ； 表面可調整電荷

並列摘要

An analytical study of diffusiophoresis in a homogeneous suspension of identical spherical charge-regulating particles with an arbitrary thickness of the electric double layers in a solution of a symmetrically charged electrolyte with a uniform prescribed concentration gradient is presented. The charge regulation due to association/dissociation reactions of ionogenic functional groups on the particle surface is approximated by a linearized regulation model, which specifies a linear relationship between the surface charge density and the surface potential. The effects of particle interactions are taken into account by employing a unit cell model, and the overlap of the double layers of adjacent particles is allowed. The electrokinetic equations that govern the electric potential profile, the ionic concentration distributions, and the fluid flow field in the electrolyte solution surrounding the particle in a unit cell are linearized assuming that the system is only slightly distorted from equilibrium. Using a regular perturbation method, these linearized equations are solved with the equilibrium surface charge density (or zeta potential) of the particle as the small perturbation parameter. Closed-form formulas for the diffusiophoretic velocity of the charge-regulating sphere correct to the second order of its surface charge density or zeta potential are derived. Our results indicate that the charge regulation effect on the diffusiophoretic mobility is quite sensitive to the boundary condition for the electric potential specified at the outer surface of the unit cell. For the limiting cases of a very dilute suspension and a very thin or very thick electric double layer, the particle velocity is independent of the charge regulation parameter.

並列關鍵字

Diffusiophoresis ； Charge-Regulating

參考文獻

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