Theoretical Analysis of Flow Passing a Single Sphere Moving in a Micro-Tube

• Main Authors: Sy-Bor Wen, 溫斯博
• Other Authors: Chun-Liang Lai
• Format: Others
• Language: zh-TW
• Published: 1999
• Online Access: http://ndltd.ncl.edu.tw/handle/74392829513484380082

碩士 === 國立臺灣大學 === 機械工程學研究所 === 87 === This thesis is aimed at investigating theoretically the flow characteristics in a long micro-tube with a sphere moving along or parallel to the centerline. The Knudsen number of the flow studied ranges from about 0.01 to 0.1. So that the mathematical model to be investigated is Navier-Stokes equation with slip boundary conditions. However, under the conditions that e=(b/l)<<O(1), and Re<O(1), and e*Re/(Ma^2)<O(1), the flow can be treated as steady and incompressible. Analytic solutions can then be obtained. For flow with a sphere moving along the centerline, the stream function method is applied to solve the flow field analytically. When a sphere is moving along a line parallel to the tube axis, the reflection method is used to obtain the approximate solution of the flow field in analytic way. The results indicated that, with slip boundary conditions, the shear stress on the wall is reduced. As a result, the pressure drop due to the existence of the sphere decreases. However, the mass flow rate and the terminal velocity of the sphere increase consequently. When the sphere is moving along a line parallel to the tube axis, the flow field is asymmetric. A net torque on the sphere is thereby induced, which decreases as Kn increases. Nevertheless, there exists no side force due to the neglect of the inertia effect. The extension of the present analysis to a compressible flow under certain conditions seems plausible.