Hydromagnetic Stability of a General Viscous Fluid Film With Weakly Nonlinear Effects on a Rotating Vertical Cylinder

廣義型黏滯流體薄膜具弱非線性效應於旋轉垂直圓柱穩定性分析

林銘哲(Ming-Che Lin) ； 鄭博仁(Po-Jen Cheng)

《中國機械工程學刊》 42卷1期 (2021/02) Pp. 33-41

摘要

This paper examines the hydromagnetic stability of a general viscous fluid film with weakly nonlinear effects on a rotating vertical cylinder. The power-law fluid model under an applied uniform magnetic field is used to provide a mathematical description instead of the rheology of polymer resist films. Long-wave perturbation techniques are used to derive the dimensionless generalized nonlinear kinematic equation to represent the physical coating flow. The Ginzburg-Landau equation is applied to numerically calculate pattern formation and illustrate necessary threshold conditions of the critical flow states. The influences of polymer resist films with hydromagnetic stability are studied in terms of the Hartmann constant, m, Rossby number, Ro and flow index, n on weakly nonlinear stability with a small Reynolds number. Moreover, The enhanced magnetic effects are found to the material flows as a dilatant fluid is more stable than a pseudo plastic fluid with the same coating flow.

關鍵字

hydromagnetic stability ； Hartmann number ； general viscous fluid

並列摘要

本文檢驗廣義型黏滯流體薄膜具弱非線性效應於旋轉垂直圓柱之液磁穩定性，數學建模選用冪次律模型流體做為在外加均勻磁場作用下分析高分子光阻劑流變行為，並利用長波擾動技巧得到該流體系統之無因次廣義自由面運動方程式。Ginzburg-Landau方程式用來數值解析並圖示各種流動狀態之臨界條件，並探討漢特曼數（Hartmann constant）、羅斯比數（Rossby number）及流動指數（flow index）在小雷諾數流動下對高分子光阻劑磁液動穩定性之影響。再者，當相同塗層流動條件下，增加磁場效應，研究結果指出脹流性流體（dilatant fluid）比擬塑性流體（pseudo plastic fluid）較具穩定作用。