纖維狀多孔性介質中橫向之電滲透可動度及導電度

Abstract

本論文利用解析方法，研究電解質溶液在由一群相互平行且表面帶電的圓柱體所組成的均質多孔性纖維狀介質中之穩定的電滲透流及電流傳導，所施加的均勻電場，其方向垂直於圓柱體的軸線，而每個不導電的圓柱體表面之電雙層，相對於圓柱半徑可以有任意的厚度。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。假設系統只有稍微偏離平衡狀態，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以線性化處理。藉由正規擾動法，將圓柱的表面電荷密度(或表面電位)當作微小的擾動參數，可以得到這些線性化後方程式的解析解，並獲得電解質溶液的電滲透流速和有效導電度，表示為纖維狀介質的孔隙度及其他特徵參數的函數。吾人求解時，在小室外層邊界，使用了不同的邊界條件，進而比較其結果。在相同的條件下，由相互平行之圓柱組成的多孔性介質中，其垂直軸線方向的有效導電度小於由球形粒子組成的懸浮溶液中的導電度。在適當的情況下，圓柱間或球形粒子間的交互作用對有效導電度有相當大的影響。

The steady electroosmosis and electric conduction in the fibrous medium constructed by a homogeneous array of parallel, identical, charged, circular cylinders filled with an electrolyte solution is analytically examined. The imposed electric field is constant and normal to the axes of the cylinders. The electric double layer surrounding each dielectric cylinder may have an arbitrary thickness relative to the radius of the cylinder. 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 charged cylinder in a cylindrical 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 surface charge density (or zeta potential) of the cylinder as the small perturbation parameter. Analytical expressions for the electroosmotic velocity of the fluid solution and the effective electric conductivity in the array of cylinders are obtained in closed forms as functions of the porosity of the fiber matrix and other characteristics of the porous system. Comparisons of the results of the cell model with different conditions at the outer boundary of the cell are made. The cell model predicts that, under an otherwise identical condition, the electric conductivity in a porous medium composed of an array of parallel cylinders in the transverse direction in general is smaller than that of a suspension of spheres, but there exist some exceptions. The effect of interactions among the cylinders or spheres on the effective conductivity can be significant under appropriate conditions.