摘 要
微氣泡在流場中流動的現象，在微機電系統中應用相當廣泛，具有深入探討的空間，而微尺度下，表面張力對流場的影響明顯，使用實驗設備來觀察微氣泡並不容易，需要非常純淨的水質以及昂貴的器材，以數值模擬的方式除了可避免上述問題，亦有良好的理論基礎，物理現象易於明瞭，模擬與實驗兩者互相印證，則能更深入的解釋微氣泡流動的行為。
本文研究方式，是以適當的數值方法搭配物理條件，模擬微氣泡在圓柱容器中自由浮升之流場，由自由液面上跨相之壓力差獲得曲率，再利用曲率反求微氣泡形狀，同時得到浮升之終端速度。研究結果也發現，跨相壓力差與浮力，對曲率具有一定程度的影響，並在自由液面上構成力的平衡。經由流場收斂所獲得的曲率，可以判斷微氣泡形狀為扁橢圓且前後不對稱，前方受形狀阻力擠壓，曲率較小而外形稍扁；後方受黏滯力拉扯因此形狀較圓，但整體仍以扁橢圓展現。

參考文獻
[1]Duineveld, P. C., 1995, “The Rise Velocity and Shape of
Bubbles in Pure Water at High Reynolds Number,” J.
Fluid Mechanics, 292, pp. 325-332.
[2]Wu, M., and Gharib, M., 2002, “Experimental Studies on
the Shape and Path of Small Air Bubble Rising in Clean
Water,” Physics of Fluids, 14, pp. L49-L52.
[3]Ortiz-Villafuerte, J., Hassan, Y.A., and Schmidl, W. D.,
2001, “Rocking Motion, Trajectory and Shape of Bubbles
Rising in Small Diameter Pipes,”Experimental Thermal
and Fluid Science, 25, pp. 43-53.
[4]Zun., I., 1980, “The Transverse Migration of Bubbles
Influenced by Wall in Vertical Bubble Flow,” Int. J.
Multiphase Flow, 6, pp. 583-588.
[5]Takemura, F., Takagi, S., Magnaudet, J., and Matsumoto,
Y., 2002, “Drag and Lift Forces on a Bubble Rising
near a Vertical Wall in a Viscous Liquid,” J. Fluid
Mechanics, 461, pp. 277-300.
[6]Krishna, R., Urseanu, M.I., Von Baten, J.M., and
Ellenberger, 1999, “Wall Effects on the Rise of Single
Gas Bubbles in Liquids,” Int. Comm. Heat Mass Transfer,
26, pp. 781-790.
[7]De Tezanos Pinto., M., Abraham., M. A., and Cerro., R.
L., 1997, “How To Bubbles Enter A Capillary” Chemical
Engineering Science, 52, No. 11, pp. 1685-1700.
[8]Hirt, C. W., and Nichols, B. D., 1981, “Volume of Fluid
(VOF) Method for the Dynamics of free Boundaries,”
Journal of Computational Physics, 39, pp. 201-225.
[9]Lee, S. L., and Sheu,S. R., 2001, “A New Numerical
Formulation for Incompressible Viscous Free Surface Flow
without Smearing the Free Surface,” Int. J. Heat Mass
Transfer, 44, pp. 1837-1848.
[10]Shirani, E., Ashgriz, N., and Mostaghimi, J., 2005,
“Interface
Pressure Calculation Based on Conservation of Momentum
for Front
Capturing methods” Journal of Computational Physics,
203, pp. 154-175.
[11]Magnaudet, J.,Rivero, M., and Fabre, J., 1995,
“Accelerated Flows
Past A Rigid Spherical Bubble. Part 1. Steady
Straining Flow,”
Journal of Fluid Mechanics, 284, pp. 97-135.
[12]Moore, D. W., 1963, “The Boundary Layer on a Spherical
Gas Bubble,” Journal of Fluid Mechanics, 16, pp. 161-
176.
[13]張元榕, 2005,微氣泡於垂直方管內上升之研究,國立清華大學
碩士論文,新竹,台灣。
[14]Sarpkaya, T., 1996, “Vorticity Free Surface and
Surfactants,” Annual Review of Fluid Mechanics, 28,
pp. 83-128.
[15]Tsai, W. T., and Yue, D. K. P., 1996, “Computation of
Nonlinear Free-Surface Flows,”Annual Review of Fluid
Mechanics,28, pp. 249-278.
[16]Lee, S. L., 1989, “Weighting Function Scheme and Its
Application
on Multidimensional Conservation,” Int. J. Heat Mass
Transfer, 32, pp. 2065-2073.
[17]Lee, S. L., and Sheu, S. R., 2003, “Filling Process in
an Open Tank,”ASME J. of Fluids Engineering, 125, pp.
1016-1021
[18]Lee, S. L., and Tzong, R. Y., 1992, “Artificial
Pressure for Pressure-Linked Equation,” Int. J. Heat
Mass Transfer, 35, pp.
2705-2716.
[19]Lee, S. L., 1989, “A Strongly-Implicit Solver for Two-
Dimensional Elliptic Differential Equations,”
Numerical Heat Transfer, 16,pp. 161-178.
[20]Lee, S. L., and Lee, H. D., 2007, “Evolution of Liquid
Meniscus Shape in a Capillary Tube,” ASME J. Fluids
Engineering, 129, pp. 957-965
[21]Hadamard, J., 1911, “Mouvement Permanent Lent d’une
Sphere Liquide Visqueuse dansun Liquid Visqueux,” C.,
R., Acad. Sci. Paris Ser. A-B, 152, pp. 1735-1739.
[22]Hua, J., Stene, J. F., and Lin, P., 2008, “Numerical
Simulation of 3D Bubbles Rising in Viscous Liquids
Using A Front Tracking Method,” Journal of
Computational Physics, 227, pp. 3358-3382.
[23]Unverdi, S., and Tryggvason, G., 1992, “A Front-
Tracking Method for Viscous Incompressible Multifluid
Flows,” Journal of Computational Physics, 100, pp. 25-
37.
[24]Tomiyama, A., Celata, G. P., Hosokawa, S., and Yoshida,
S., 2002, “Terminal Velocity of Single Bubbles in
Surface Tension Force Dominant Regime,” Int. J.
Multiphase Flow, 28, pp. 1497-1519.
[25]王信雄, 2006,微小氣泡於軸對稱圓管內上升運動之研究,國立
清華大學碩士論文,新竹,台灣。
[26]賴盈宏, 2007,微氣泡於垂直圓管內浮升之形狀變化研究,國立
清華大學碩士論文,新竹,台灣。
[27]Blackmore, D., and Ting, L., 1985, “Surface Integral
of Its Mean Curvature Vector,” Society for Industrial
and Applied Mathematics, 27, No. 4, pp. 569-572.
[28]Ye, T., Shyy, W., and Cheng, J. N., 2001, “A Fixed-
Grid, Sharp-Interface Method for Bubble Dynamics and
Phase Change,” Journal of Computational Physics, 174,
pp. 781-815.
[29]Celata, G. P., Cumo, M., D’Annibale, F., Marco, D. P.,
Tomiyama, A., and Zovini, C., 2006, ” Experimental
Thermal and Fluid Science, 31, pp. 37-53.