震盪式電滲透流與壓力驅動流對質傳與溶質分離的影響

Mass Transport and Separation of Species due to Oscillatory Electroosmotic and Pressure-Driven Flows

黃俊菖(Jyun-Chang Huang)

指導教授 ： 賴君亮

國立臺灣大學/工學院/機械工程學研究所/碩士(2007年)

https://doi.org/10.6342/NTU.2007.10017

摘要

本文探討在二維矩形微流道中，結合震盪式電場以及壓力場，並藉著泰勒擴散（Taylor dispersion）效應，對溶於電解液的非電解質溶質進行質量傳輸以及分離。在假設稀薄溶液，沒有電雙層的重疊效應，Zeta電位不大，以及流體在流動時視為不可壓縮的完全發展流情況下，可以將電場，速度場，以及濃度場方程式線性化，並求得解析解；同時在固定平均振幅的條件下，計算出溶質的傳輸率。主要的四個無因次參數分別為沃默斯利數（Womersley number），施密特數（Schmidt number），無因次德拜長度（Debye length），以及無因次平均震盪幅度。
　　分析結果顯示，震盪式電滲透流會隨著沃默斯利數，施密特數，無因次平均震盪幅度的增加以及無因次德拜長度的減少，而有較好的無因次平均質量傳輸率；壓力震盪流也會隨著沃默斯利數，施密特數以及平均震盪幅度的增加而有較好的質量傳輸效果，但隨著沃默斯利數以及施密特數增加，無因次平均質量傳輸率的增加速度趨緩。整體來說，同一種溶液裡，壓力震盪流在低的沃默斯利數有較好的平均質量傳輸率，而在高的沃默斯利數之下，震盪式電滲透流的平均質量傳輸率會比較高。
　　當兩種溶質溶於電解溶液時，隨著電場以及壓力場的震盪會產生不同的質量傳輸率。在震盪頻率很小的時候，擴散係數大的溶質平均質量傳輸率比擴散係數小的來得快；隨著震盪頻率的增加，由於擴散係數較大的溶質會有較小的施密特數，而使得平均質量傳輸率變得較慢；但是當震盪頻率大到某個值以後，擴散係數大的質量傳輸率又會有較大的平均質量傳輸率，形成交叉現象（cross-over phenomenon）；藉此探討溶質分離的現象。

關鍵字

泰勒擴散 ； Zeta電位 ； 電雙層,震盪式電滲透流,壓力震盪流,交叉現象,溶質分離.

並列摘要

The mass transport and solute separation by combined oscillatory electroosmotic and pressure-driven flows are theoretically studied. With the assumptions of dilute solution, non-overlapping of electrical double layers, small Zeta potential, and fully-developed imcompressible flow, the governing equations for the electrical, velocity, and concentration fields are linearized and solved analytically. The dimensionless mass flow rate is then calculated under the condition of constant tidal displacement. The four primary dimensionless parameters are Womersley number, Schmidt number, dimensionless Debye length, and averaged tidal displacement.
The results indicate that the dimensionless mass flow rate due to the oscillatory electroosmotic flow increases with Womersley number, Schmidt number, averaged tidal displacement, and decreases with dimensionless Debye length while the dimensionless mass flow rate due to the oscillatory pressure-driven flow increase only with Womersley number, Schmidt number, averaged tidal displacement, and remains the same with dimensionless Debye length. Moreover, the oscillatory pressure-driven flow possesses better dimensionless mass flow rate than the oscillatory electroosmotic flow for small values of Womersley number. With large values of Womersley number, the situation is reversed.
The mass transport rate varies, in general, with solutes even in the same solvent and with the same oscillation frequency. For low frequency, the solute with large diffusivity possesses large dimensionless mass flow rate. As the oscillation frequency increases, the transport of the solute with larger diffusivity, and thus smaller Schmidt number, becomes mild while if increases rapidly again when frequency keeps increasing, resulting in the so called cross-over phenomenon. Consequently, the solute separation becomes possible.

並列關鍵字

Taylor dispersion ； electrical double layer ； oscillatory electroosmotic flow ； oscillatory pressure-driven flow ； cross-over phenomena ； solute separation.

參考文獻

Blackshear, P.J., “Implantable drug-delivery systems.” Sci. Am., vol.241, pp. 66–73, 1979.

Burgreen, D., Nakache, F. R., “Electrokinetic Flow in Ultrafine Capillary Slits.” The Journal of Physical Chemistry vol. 68, pp. 1084-1091, 1964

Barragan, V. M., Bauza, C. R., “Electroosmosis through a Cation-Exchange Membrane: Effect of an ac Perturbation on the Electroosmotic Flow.” Journal of Colloid and Interface Science 230, pp. 359–366, 2000.

Bhatteacharyya, A., Masliyah. J.H., Yang, J., “Oscillating laminar electrokinetic flow in infinitely extended circular microchannels.” J. Colloid Interface Sci. vol. 261, pp. 12-20, 2003.

Chen, C.H., Santiago, J.G., “A Planar Electroosomtic Micropump.” J. Microelectromechanical System vol. 116, pp. 72-683, 2002.