具電荷調整性質之纖維狀多孔介質之擴散滲透

Abstract

本論文解析研究電解質溶液在由一群相互平行排列且具電荷調整表面之帶電圓柱體所組成的纖維狀多孔介質中的擴散滲透現象。其所施加的濃度梯度為定值，且方向垂直於圓柱體的軸線，而當圓柱體表面的官能基發生結合或解離反應時，所產生的電荷調整機制使表面電荷密度與表面電位線性相關。吾人使用容許相鄰圓柱體的電雙層相互重疊之小室模型進行分析，每個小室含有一個圓柱體及其鄰近的電解質。假設此擴散滲透系統只有些微偏離平衡狀態，因此主導離子濃度分布、電位分布、流場分布的電動力方程式可進行線性化處理。使用正規微擾法，將圓柱體的表面電位當作微小的擾動參數，吾人即可求得線性化電動力方程式之解析解，並透過力平衡來求得到擾動參數二階之流體擴散滲透速度，將其表示為纖維狀介質之孔隙度及其他特徵參數之函數。結果顯示，結合或解離反應之平衡常數或電荷決定離子之濃度等電荷調整參數會對表面電荷密度、表面電位及擴散滲透速度有顯著的影響，但在非常厚或非常薄電雙層的極限狀況下，擴散滲透速度則不受電荷調整機制之影響。

The diffusioosmotic flow of an electrolyte solution in the fibrous porous medium constructed by a homogeneous array of parallel charge-regulating circular cylinders with arbitrary electric double layers is analytically studied. The imposed electrolyte concentration gradient is constant and normal to the axes of the cylinders. 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. A unit cell model which allows for the overlap of the double layers of adjacent cylinders is employed. The electrokinetic equations that govern the ionic concentration distributions, the electrostatic potential profile, and the fluid flow field in the electrolyte solution surrounding the charge-regulating cylinder in a unit cell are linearized assuming that the system is only slightly distorted from equilibrium. Through the use of a regular perturbation method, these linearized equations are solved with the zeta potential of the cylinder as the small perturbation parameter. An analytical expression for the diffusioosmotic velocity of the electrolyte solution as a function of the porosity of the ordered array of cylinders correct to the second order of their zeta potential is obtained from a balance between the electrostatic and the hydrodynamic forces exerted on each cylinder. Our results indicate that the charge regulation characteristics such as the equilibrium constants of the reactions occurring at the cylinder surfaces and the bulk concentration of the charge-determining ions influence the surface charge density and potential and diffusioosmotic mobility substantially. For the limiting cases of a very thin or very thick electric double layer, the diffusioosmotic mobility is independent of the charge regulation parameter.