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研究生:凃博閔
研究生(外文):Bo-min Tu
論文名稱:外加場下肥皂膜的能量耗散
論文名稱(外文):Energy Dissipations in Soap Films under External Fields
指導教授:陳培亮陳培亮引用關係
指導教授(外文):Peilong Chen
學位類別:碩士
校院名稱:國立中央大學
系所名稱:物理研究所
學門:自然科學學門
學類:物理學類
論文種類:學術論文
論文出版年:2004
畢業學年度:92
語文別:英文
論文頁數:41
中文關鍵詞:肥皂膜能量耗散
外文關鍵詞:Soap FilmEnergy Dissipation
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藉由不同形式的電磁力作用下,肥皂膜產生各種不同的流場,而這些流場可利用粒子追蹤技術來測量之。在圓形流場下,空氣的速度分佈能以Navier-Stokes 方程式描述,此時我們僅考慮方位角上的速度分量。利用此方程式與雙層膜的實驗,我們能測量出肥皂膜與空氣的速度佈。除此之外,我們利用共振的方式求得每張肥皂膜的厚度。藉由肥皂膜與空氣的速度分佈及膜厚度的測得,能量耗散於肥皂膜與空氣之間的比例得以估計出。其中影響能量耗散的重要因素為〝流場尺度〞與〝頻率響應〞。經由實驗證明,調整此兩因素下,空氣阻力於此實驗系統中仍是有意義的能量耗散現象。
Several kinds of flows in the soap film is created by different electromagnetic forcing and measured by particle tracking. In circle flow the velocity of air is described well by Navier-Stokes equation with only azimuthal velocity component. Using the equation and double films experiment, the velocity in soap film and air are
measured. Besides, film's thickness is measured by resonance method. The ratio of energy dissipation rate in air and soap film is found. The important factors of the effect rate are "injection scale" and "frequency response". Comparison of these rates demonstrates that the air friction is a significant energy dissipation mechanism in the system.
1.Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1
2 Viscous Dissipation of Energy . . . . . . . . . . . . . . . . . . . . . .8
2.1 Navier-Stokes equations .. . . . . . . . . . .. . . . . . . . . . . . 8
2.1.1 Time-independent Navier-Stokes equations . . .. . . . . . . . . . . .8
2.1.2 Time-dependent Navier-Stokes equations . . . . . . . . . . . . . . . 9
2.2 Double Films experiment . . . . . . . . . . . . . . . . . . . . . . . 11
2.3 Energy dissipation rate . . . . . . . . . . . . . . . . . . . . . . . 13
3 Apparatus and Measurement. . . . . . . . . . . . . . . . . . . . . . . 15
3.1 Experimental Setup and Steps . . . . . . . . . . . . . . . . . . . . .15
3.2 Film Thickness Measurement . . . . . . . . . . . . . . . . . . . . . .18
3.3 Velocity Measurement and Fit . . . . . . . . . . . . . . . . . . . . .19
4 Result and Analysis . . . . . . . . . . . . . . . . . . . . . .. . . . .22
4.1 Injection scale and Frequency response . . . . . . . . . . . . . . . .22
4.2 Velocity Variation in Two Films by Varying Thickness . . . . . . . . .27
4.3 Single Film's Characters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
4.4 Hysteresis between (ALF) to (AVF) state . . . . . . . . . . . . . . . 33
4.5 The ratio of energy dissipation rate . . . . . . . . . . . . . . . . 37
5 Conclusion . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 38
References . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . 40
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