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研究生:宋鴻明
研究生(外文):Hung-Ming Sung
論文名稱:非牛頓流體薄膜流的非線性液動穩定性分析
論文名稱(外文):Nonlinear Hydrodynamic Stability Analysis of Non-Newtonian Liquid Film Flows
指導教授:陳朝光陳朝光引用關係賴新一
指導教授(外文):Chao-Kuang ChenHsin-Yi Lai
學位類別:博士
校院名稱:國立成功大學
系所名稱:機械工程學系碩博士班
學門:工程學門
學類:機械工程學類
論文種類:學術論文
論文出版年:2004
畢業學年度:92
語文別:中文
論文頁數:178
中文關鍵詞:正模分析法長波微擾法穩定性分析薄膜流多重尺度法非線性破裂凡得瓦爾勢能
外文關鍵詞:normal mode analysismethod of multiple scalesvan der Waals potentiallong-wave perturbationnonlinear rupturethin film flowstability analysis
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  本文針對黏彈性流體及微極流體等薄膜流,探討沿垂直方向移動的直立平板與圓柱表面流下的薄膜流之線性及弱非線性液動穩定性問題,並分析附著在直立圓柱表面的微極流體薄膜的破裂過程。首先使用長波微擾法推導薄膜的自由面方程式,在探討薄膜流場的穩定性問題上,主要分析平板及圓柱的移動效應對系統穩定性的影響。在線性穩定性分析中,應用正模分析法求出線性振幅的增長率、線性波速和中立穩定狀態等的通式,並可判定線性之穩定與不穩定狀態。其次在液膜弱非線性穩定性分析上,以時間和空間之多重尺度展開法推導得Ginzburg-Landau方程式,定出超臨界爆炸、超臨界穩定、亞臨界不穩定及無條件穩定等狀態,並分析亞臨界不穩定區域之臨界振幅值及超臨界穩定波之平衡振幅及波速。在探討附著在垂直圓柱表面的微極流體薄膜的破裂問題上,使用數值方法來求解非線性薄膜厚度方程式。在非線性破裂理論分析上,針對微極流體之微極參數 對薄膜破裂機制的影響,以及凡得瓦爾勢能、表面張力和圓柱半徑的大小等影響破裂過程的因素,做深入的探討與分析。
  本文所獲得的結果,綜合敘述如下:
(一)平板及圓柱移動的方向與速率對系統穩定性的影響
  直立平板及圓柱垂直往下移動會使薄膜流的穩定性增加,隨移動速度增加,薄膜流愈穩定,且黏彈參數 與微極參數 對流場穩定性的影響降低。平板及圓柱垂直往上移動會使薄膜流的穩定性降低,隨移動速度增加,薄膜流愈不穩定,且黏彈參數 與微極參數 對流場穩定性的影響增加。
(二)圓柱半徑大小對系統穩定性的影響
  不論圓柱垂直往上或往下移動,隨圓柱半徑增加,流場呈現相對穩定狀態。圓柱半徑 對流場穩定性的影響,隨圓柱往下移動的速度增加而降低。相反的,圓柱半徑 對流場穩定性的影響,隨圓柱往上移動的速度增加而增加。
(三)附著在直立圓柱表面的微極流體薄膜破裂分析
  微極流體薄膜發生破裂的時間隨 值的增加而延長。此外,增加圓柱的半徑或增加流體的表面張力,均會延遲薄膜發生破裂的時間;凡得瓦爾勢能效應增加,將加速薄膜的破裂。
  This paper presents a stability analysis of thin viscoelastic and micropolar liquid films flowing down a plate or cylinder moving in a vertical direction. The nonlinear rupture problem of thin micropolar liquid films on a cylinder is also investigated. The long-wave perturbation method is employed to derive the generalized nonlinear kinematic equations for a free film interface. The current thin liquid film stability analysis provides a valuable input to investigations into the influence of the style of motion of the vertical plate or cylinder on the stability behavior of the thin film flow. The normal mode method is employed to solve the linear solutions of the film flow, and the threshold conditions and linear growth rate of the amplitudes are obtained to analyze the linear stability behavior. This study utilizes the multiple scales method and derives the corresponding Ginzburg-Landau equation to characterize the nonlinear behavior of the flow. The subcritical stability, subcritical instability, supercritical stability, and supercritical instability states are obtained from the nonlinear stability analysis. The present rupture analysis of a thin liquid film on a cylinder supports investigations into the onset of film rupture and permits an understanding of the relative influences of factors such as micropolar parameter, cylinder radius, van der Waals potential, and surface tension on the rupture process.
  The following conclusions can be drawn from the current numerical modeling results:
(1)Influence of style of motion of vertical plate or cylinder on stability behavior of thin film flow:
  A downward direction motion of the vertical plate or cylinder tends to enhance the stability of the downward-traveling film flow on the plate or cylinder. The film flow system becomes more stable as the downward direction velocity of the plate or cylinder increases. The effects of the viscoelastic parameter, , and the micropolar parameter, , on the stability of the thin film flow are diminished as the downward direction velocity of the plate or cylinder increases. Conversely, an upward direction motion of the plate or cylinder tends to reduce the stability of the down-traveling film flow. The film flow system becomes more unstable as the upward direction velocity of the plate or cylinder increases. The effects of the viscoelastic parameter, , and the micropolar parameter, , on the stability of the thin film flow become more pronounced as the upward direction velocity of the plate or cylinder increases.
(2)Influence of cylinder radius on stability behavior of thin film flow:
  The film flow becomes more stable by increasing the radius of the cylinder as the cylinder moves either upward or downward. The effect of the cylinder radius on the stability of the thin film flow becomes less significant as the downward direction velocity of the cylinder increases. Conversely, the radius effect becomes more pronounced as the upward direction velocity of the cylinder increases.
(3)Rupture analysis of thin liquid film on cylinder:
  The occurrence of film rupture is delayed as the value of the micropolar parameter, , is increased. Furthermore, the rupture time of the film flow decreases as the van der Waals potential effect increases. Conversely, increasing the surface tension or the cylinder radius delays the onset of the rupture process.
中文摘要………………………………………………………………………I
英文摘要……………………………………………………………………III
誌謝…………………………………………………………………………VI
目錄………………………………………………………………………VII
表目錄………………………………………………………………………X
圖目錄………………………………………………………………………XI
符號說明………………………………………………………………XXVI
第一章 緒論…………………………………………………………………1
1-1研究目的及背景……………………………………………………1
1-2研究方法……………………………………………………………2
1-3 文獻回顧……………………………………………………………4
1-4 本文架構…………………………………………………………12

第二章 薄膜穩定性分析理論……………………………………………16
2-1 廣義自由面方程式………………………………………………16
2-2 線性液膜穩定性分析……………………………………………17
2-3非線性液膜穩定性分析…………………………………………17
第三章 沿垂直方向移動之直立平板表面流下的黏彈性流體薄膜流
之線性及非線性穩定分析………………………………………24
3-1 統御方程式與邊界條件…………………………………………24
3-2 黏彈性流體薄膜流之長波微擾解………………………………29
3-3 線性與非線性薄膜流穩定性分析………………………………32
第四章 沿垂直方向移動之直立圓柱表面流下的黏彈性流體薄膜流
之線性及非線性穩定分析………………………………………58
4-1 統御方程式與邊界條件…………………………………………58
4-2 黏彈性流體薄膜流之長波微擾解………………………………62
4-3 線性與非線性薄膜流穩定性分析………………………………66
第五章 沿垂直方向移動之直立圓柱表面流下的微極流體薄膜流
之線性及非線性穩定分析………………………………………103
5-1 統御方程式與邊界條件…………………………………………103
5-2 微極流體薄膜流之長波微擾解…………………………………107
5-3 線性與非線性薄膜流穩定性分析………………………………113
第六章 附著在直立圓柱表面的微極流體薄膜之非線性破裂分析……149
6-1 統御方程式與邊界條件…………………………………………150
6-2 微極流體薄膜之長波微擾解……………………………………154
6-3 破裂理論分析……………………………………………………156
6-4 結果與討論………………………………………………………159
第七章 總結與展望………………………………………………………164
7-1 綜合結論…………………………………………………………164
7-2 建議及展望………………………………………………………165
參考文獻…………………………………………………………………167
自述………………………………………………………………………176
歷年發表著作……………………………………………………………177
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