具有葉片的圓管縱向電滲流解析

Abstract

本論文主要是從尋找解析解探討微流體在電滲效應下的流體行為，並探討在具有葉片狀的圓管微流道中之各項物理性質，所使用的物理模型包括Poisson-Boltzmann equation(PB)、Navier-Stokes equation和霍姆霍茲方程式（Helmholtz equation）等方程組。 電滲流的流動，主要是依靠壁面電位勢，及外加電場所產生的電位勢的交互作用所致。在本論文中將使用Poisson-Boltzmann equation和霍姆霍茲方程式（Helmholtz equation）來探討具有葉片狀圓管微流道中的電滲流，並藉由改變不同參數R(外徑)值和K值來進行分析。其中K為流道的半徑和德拜長度的比值。 流體假設在穩態時，藉由以上之參數，來分析流場內流速分布情形、流量大小和流況發展趨勢。探討微流道內不同葉片數時，流場的流速分佈圖及流量大小，並觀察其上述物理性質的變化。 由數值計算的結果可得知，在不同葉片數時，R值或K值較小時，流速分布較為鬆散且流量較小，但是當R值或K值變大時，流速分布較為密集且流量較大。

In this study, we focus on the analytical solution of electro-osmotic flow, and discusses the physical properties in the circular tube with a vaned core . We use Poisson-Boltzmann equations (PB) , Navier-Stokes equation ,and Helmholtz equation to solve the questions . The electro-osmotic flow is mainly due to the interaction of wall electric potential and applied electric field . In this study, we use Poisson-Boltzmann equations (PB) and Helmholtz equations to analyze electro-osmosis flow in the circular tube with a vaned core by changing the different parameters R and K, where R is the outer radius ,K is the ratio of the radius of the micro-flow channels to the Debye length .We assume the flow is steady state, and we use these parameters to analyze the velocity distribution in the flow field, volume flow rate, and the flow field development trend. We discuss different vaned cores in the flow channels, the figure of flow field velocity and volume flow rate, then observe the physical properties. In conclusion, we can know that if R and K are smaller, the velocity and volume flow rate are small in any condition. But if R and Kare bigger, the velocity is concentrated and volume flow rate is bigger.