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研究生： 王御蓁
Yu-Chen Wang
論文名稱： 肥皂膜上的能量耗散
Energy dissipation in soap film
指導教授： 陳培亮
Peilong Chen
口試委員:
學位類別： 碩士
Master
系所名稱： 理學院 - 物理學系
Department of Physics
畢業學年度： 90
語文別： 英文
論文頁數： 37
中文關鍵詞： 空氣阻力 、肥皂膜
外文關鍵詞： air drag, soap film
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    • 摘要
    受力於電磁場下的肥皂膜，其能量主要耗散於與空氣
    分子的作用以及流體內部的黏滯力。此論文說明如何
    透過實驗找出空氣阻力與黏滯力之間的比值。驅動一
    穩定電流通過磁場下的薄膜，使薄膜上的流場達到穩
    定狀態。利用追蹤薄膜上的微粒，測得穩定流場的旋
    轉週期。再以不同頻率垂直震盪薄膜，使之達到穩定
    駐波，並取得此時的共振頻率以供推算薄膜厚度。從
    膜的厚度與旋賺週期的關係可知越厚的膜，阻力係數
    越大，使得旋轉週期越長。由於空氣阻力始終存在，
    若膜的厚度趨於零，則旋轉週期必定是正值。我們由
    此一關係可得到空氣阻力與黏滯力的比值並由每一張
    膜的厚度值所決定。

    Abstract
    We study energy dissipation rates on soap lms driven by electromagnetic forces. The relative
    amplitude between air- uid friction and uid viscosity has been determined. The ow eld in
    the soap lm is maintained in steady state by driven a steady current across the soap lm.
    Therefore, the energy dissipation rates must exactly balance the energy injection rate. In
    experimental process, rotational periods are obtained by particle tracking, and the thickness
    of the soap lm are measured by resonant frequency. These results are used to calculated the
    e ect of air friction and uid''s viscosity. When the lm is thicker, the uid''s drag is greater,
    leading to longer rotating period. When the lm thickness tends to zero, the rotating period
    must be a positive value, due to the air friction. As a result, we can obtain the ratio of the two
    energy dissipation rates. This ratio suggests that the e ect of air friction is greater as the lm
    is thinner. However, in conclusion our results show that the most part of energy dissipation is
    due to the uid''s viscosity.

    Contents 1 Introduction 1 2 Soap Film under Electromagnetic Field 7 2.1 Electrokinetic equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 2.2 Uniform magnetic eld . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 2.3 Nonuniform magnetic eld . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 3 Previous Estimate of Air Drag 14 3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 3.1.1 The operation of the em cell. . . . . . . . . . . . . . . . . . . . . . . . . 15 3.2 Rayleigh drag model. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 3.3 Enstrophy dissipation rates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 4 Apparatus and Measurement 19 4.1 Experimental apparatus . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 4.2 Rotating period measurement . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 4.3 Film thickness measurement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 5 Result and Analysis 28 6 Conclusion 36

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