纖維狀多孔性介質之暫態電動力流動

Abstract

本論文使用單元小室模型，進行分析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勻纖維狀多孔性介質中的暫態電動力流動現象，所施加的均勻電場與壓力梯度，其方向皆平行於這些圓柱體的軸線。藉由求解Poisson-Boltzmann方程式和包含靜電作用力修正過後的Navier-Stokes方程式，吾人可以求得在任意電雙層厚度及表面電位時流體相的電位分佈和暫態流速分佈。由暫態流速的結果可以獲得和時間以及纖維狀介質之孔隙度有關的流體電滲透速度和有效導電度的表示式。從結果得知，圓柱體半徑與電雙層厚度比值、孔隙度、時間以及表面電位大小等相關參數對初期的暫態電動力流動現象有顯著且有趣的影響。而對孔隙度較小的纖維狀介質而言，流體速度以及電流密度達到一定程度接近穩定狀態時所需要的時間較短。

The transient response of ionic solutions in the porous medium constructed by a homogeneous assemblage of parallel charged circular cylinders to the step application of an electric field and a pressure gradient in the axial direction is analyzed through the use of a unit cell model. By solving the Poisson-Boltzmann equation and modified Navier-Stokes equation applicable to the system, the electric potential distribution and time-evolving velocity profile in the fluid phase are determined for arbitrary electric double layer thickness and zeta potential associated with the dielectric cylinders. Results for the flow rate, electroosmotic velocity, and effective electric conductivity of the fluid are obtained as functions of the elapsed time and the porosity of the fibrous medium. The effects of the relevant parameters on the transient starting electrokinetic flow in the fiber array are significant and interesting. For a fibrous medium with smaller porosity, a much shorter elapsed time is needed for the fluid velocity and electric current density to be within a certain percentage of their steady-state values.