本文是對於非牛頓流體的薄膜穩定性進行的一些研究。針對動態物體表面的薄膜流動進行分析，使用長波微擾法得到廣義自由面運動方程式，對於流體薄膜的線性穩定性分析，忽略其非線性項之後應用正模分析法計算其中立穩定曲線從而分析結果，對於非線性穩定性，則使用多重尺度法來探討液膜的弱非線性穩定性。通過探討Ginzburg-Landau方程式中特殊項的值來判斷流體薄膜的狀態，從而將流體的流態定性為無條件穩定、亞臨界不穩定、超臨界穩定和超臨界爆炸解的狀態。
首先研究的對象是在直立平板沿著垂直方向運動上的冪律薄膜流。著重分析了平板的垂直運動以及流動指標對於薄膜穩定性的影響。在線性穩定性分析中，中立穩定曲線明顯受到平板垂直運動和流動指標影響，當平板向下運動越強烈，流動指標數值越大時，流體薄膜越穩定。在非線性穩定性分析中，亞臨界不穩定區域和絕對穩定區域會隨著平板向下運動增強以及流動指標增加時擴大，同時超臨界穩定區域和超臨界不穩定區域被壓縮，反之則會出現相反的結果。亞臨界不穩定區域的臨界振幅在較高的無因次波數下會隨著平板向上的移動速度增加以及流動指標變小而降低，從而顯示出穩定性變弱的結果。在超臨界穩定區域的臨界振幅在較低的無因次波數下會因為平板向下移動速度增加或者流動指標變大而增強，此時的波速也會相應的降低，從而使流體薄膜的穩定性條件變的更寬鬆。其中在平板向上運動的時候，流動指標對薄膜穩定性的影響更加顯著，而在平板向下運動的時候流動指標的變化對薄膜穩定性的影響相對不那麼顯著。
分析在磁場影響下的導電黏彈性流體薄膜沿旋轉垂直圓柱外側流下的流體穩定性。重點分析了磁場，旋轉，黏彈性以及圓柱半徑對薄膜流體的穩定性影響。增加更強的磁場，降低旋轉和降低流體的黏彈性能提高薄膜的線性穩定性。在非線性穩定性分析中，當亞臨界不穩定區遇到增強磁場，降低旋轉和降低流體黏彈性的變化時，區域範圍會增加，相應的超臨界不穩定區域會減少。亞臨界穩定區和超臨界穩定區會受到磁場，旋轉和黏彈性的變化而產生變化，總體區域面積變化不大，但是相對於雷諾數和無因次波數的範圍有整體移動。在有條件穩定區域內，增強磁場，降低旋轉以及黏彈性會讓穩定性條件變得更加寬鬆。以上這些結論都需要在無因次半徑在相對較小時成立。圓柱的半徑較小時，薄膜系統的穩定性主要受到磁場，旋轉和黏彈性影響較大，當無因次半徑變得更大之後，會更強烈的影響薄膜系統，使之變得不穩定，其影響將主導薄膜穩定性，同時其他參數的影響相對而言明顯減弱。

This thesis analyses the stability of non-Newtonian film flow on moving surfaces.
The generalized kinematic equation of free film interface is obtained by using the long wave perturbation method. Linear perturbation equation is solved by normal mode approach method for the linear stability. The multiple scales method is used to solve the nonlinear perturbation equation. The nonlinear stability is discussed by the Ginzburg-Landau equation. There are four types of the states of the nonlinear stability such as subcritical instability, subcritical stability (absolute stability), supercritical stability and supercritical instability (supercritical explosive state).
The first model is a thin power law fluid flowing down a moving plane in a vertical direction. The result of linear and nonlinear stability shows the downward speed increases and the power law index increases enhance the stability of film flow.
The second model is a thin electrically-conductive viscoelastic fluid film flow along the side of a rotating vertical cylinder with the effect of magnetic field. The general result of linear and nonlinear stability shows the increasing of magnetic and radius of the cylinder enhance the stability of film flow, the increasing of rotational velocity and effect of viscoelastic reduce the stability of film flow. Meanwhile, increasing radius under large Rossby number can lead to losing stability easier, such as the dimensionless radius is more than 50. It is worth noting that this phenomenon is leaded by the radius, and the influence is stronger than other parameters.

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