Nonlinear Rupture Theory of a Thin Micropolar Liquid Film on a Cylinder under a Magnetic Field

直立圓柱表面微極流體薄膜在磁場效應影響下之非線性破裂理論

10.29548/BGYY.201103.0005

宋鴻明(Hung-Ming Sung)；徐仲亭(Chung-Ting Hsu)

微極流體 ； 磁場 ； 破裂 ； 薄膜 ； 表面張力 ； 凡得瓦爾勢能 ； micropolar ； magnetic field ； rupture ； thin film ； surface tension ； van der Waals potential

修平學報

22期（2011 / 03 / 01）

63 - 80

英文

本研究探討在磁場效應的影響下，直立圓柱表面微極流體薄膜的非線性破裂現象。首先使用長波微擾法推導薄膜的自由面方程式，利用電腦數值計算方法解薄膜的自由面方程式，研究微極流體薄膜受定值且均勻的磁場影響下，在直立圓柱表面的非線性破裂機制，分析磁場效應的大小、表面張力、凡得瓦爾勢能及圓柱半徑大小對破裂機制的影響，另外針對微極流體之微極參數K對薄膜破裂機制的影響，做深入的探討與分析。結果顯示，隨著磁場無因次參數、微極參數及圓柱半徑之增加，或減少初始擾動，將會延緩薄膜之破裂。

This paper studies the nonlinear rupture process of the thin micropolar liquid film on a cylinder under the influence of the uniform magnetic field. The long-wave perturbation method is employed to derive the generalized kinematic equations with free film surface conditions. The generalized nonlinear evolution equation is solved numerically. The effects of magnetic field, the van der Waals potential, the surface tension, the micropolar parameter, K, and the radius of the cylinder on the rupture behavior are extensively investigated. The results show that the film rupture time will be delayed by increasing the associated parameters including the Hartmann number, the micropolar parameter, and the radius of the cylinder, or to decrease the initial disturbance.

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