- 學位論文
纖維狀多孔介質中於徑向之暫態電滲透流動
Transient electroosmosis in the transverse direction of a fibrous porous medium
摘要
本論文探討一充滿於許多個平行且均勻排列之帶電圓柱所構成的纖維狀多孔介質中之電解質溶液，突然受到一徑向方向固定外加電場作用下的暫態電滲透流動。吾人假設圓柱周圍電雙層的厚度遠小於圓柱半徑和兩相鄰圓柱的間距，但是會考慮到此薄電雙層內部的電滲透流動隨時間的演變。透過使用單元小室模型，對於各包覆單一圓柱之虛擬同心圓柱形小室，以非穩態的流體動量守恆方程式求解出在電雙層外部的流速。求解的過程會使用拉普拉斯轉換，而整個流體之暫態電滲透速度是纖維狀介質孔隙度及圓柱電動力半徑的函數，並隨在小室虛擬表面上兩種不同邊界條件可得到兩種定量上略為不同的解。分析結果顯示，對於較低孔隙度之介質，其電滲透流動隨時間的成長明顯較快，而流體之暫態電滲透速度會隨著圓柱電動力半徑的增加而上升。
並列摘要
The transient electroosmotic response in the porous medium constituted by a homogeneous array of parallel, charged, circular cylindrical fibers filled with an electrolyte solution to the step application of an electric field in the transverse direction is analytically studied. The thickness of the electric double layers surrounding the dielectric cylinders is assumed to be small relative to the radius of the cylinders and the gap width between two adjacent cylinders, but the effect of time-evolving electroosmosis within the thin but finite double layers is incorporated. Through the use of a unit cell model, the transient equation of conservation of the fluid momentum outside the double layer is solved for each cell, in which a single cylinder is enveloped by a coaxial shell of the ionic fluid. Explicit expressions for the transient electroosmotic velocity of the bulk fluid in the Laplace transform as functions of the porosity of the fibrous medium and the electrokinetic radius of the constitutive cylinders are obtained for two different conditions at the virtual boundary of the cell. Our results indicate that the time scale for the growth of electroosmosis is significantly smaller for a fiber matrix with a lower porosity and the electroosmotic velocity increases with a decrease in the double-layer thickness relative to the cylinder radius.
參考文獻
延伸閱讀
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