本文研究微流體(microfluidics)管內流動，在不同體積流率下，流體稀薄化(rarefaction)對微管內非穩態流動(unsteady)的影響。文中分析體積流率變化與壓力變化的關係，包含如下四種實例：(1)梯形活塞運動(trapezoidal piston motion)；(2)等加速度(constant acceleration)；(3)突然被啟動之流動(impulsively started flow)；(4)突然被堵住之完全發展流動(impulsively blocked fully developed flow)。藉由拉普拉斯轉換技巧(Laplace transform technique)，由管內流非穩態動量方程式推導出速度(velocity)與壓力梯度(pressure gradient)關係的解析解。分析過程我們以"肯德森數" (Knudsen number) 代表流體稀薄化程度，所得結果以圖形表示，並與連體無滑動邊界之結果相比較。得到以下結果，對於四種不同體積流率下的實例，當稀薄化效應越大，管壁的滑動現象越明顯，相對地使邊界速度也增加，在管內的速度反而減小；稀薄化效應對壓力梯度值的影響，在不同的實例中則有不同的變化。

　　In this study，the effects of rarefaction of unsteady flow through the microtubes for arbitrary volume flow rate are studied. The relationship between the change of volume flow rate and the change of pressure is analyzed under 4 different cases：(1)trapezoidal piston motion, (2)constant acceleration, (3)impulsively started flow, and(4) impulsively blocked fully-developed flow. The analytical solution of the velocity and pressure gradient of momentum equation of unsteady flow in microtube are solved by using the Laplace transform technique. During the analysis process, the Knudsen number( ) is used, to show the level of rarefaction. The results are presented graphically and compared to the results of continuum under no-slip condition. Form the results, we found that, the effects of wall-slip becomes significant with increasing the rarefaction. The boundary velocity also increases whereas the velocity of the tube will decrease with the same condition. The influence of the rarefaction for the pressure gradient is varied for different cases.

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