Surface Tension Effect on Nonlinear Waves in a Thin Micropolar Liquid Film Flow down along a Vertical Cylinder

微極液膜表面張力效應之直立外圓柱流的非線性液動穩定性分析

鄭博仁(Po-Jen Cheng) ； 劉國基(Kuo-Chi Liu) ； 龔傑(Chieh Kung)

《先進工程學刊》 4卷1期 (2009/01) Pp. 33-42

https://doi.org/10.29948/JAE.200901.0005

摘要

本文利用長波微擾解所得到之廣義自由面運動方程式，探討直立圓柱面上微極流體薄膜流表面張力效應所表現之穩定性。首先以正模分析法來探討液膜的線性穩定性，進而得出線性中立穩定曲線、線性振幅增長率及線性波速。其次應用時間和空間之多重尺度法研究液膜的弱非線性穩定性質。研究結果顯示，當考慮表面張力時，流場將會產生亞臨界不穩定及超臨界穩定狀況。再者，微極流體之表面張力在穩定流場中具有消散擾動能量功能，因而減少對流之流動和表面波之波峰及波谷間的波動，即干擾後之振幅受到表面張力之影響而較易減少。而在流場不穩定時，表面張力增加擾動能量，故振幅增加更快。

關鍵字

穩定性分析 ； 表面張力

並列摘要

The influence of surface tension effect on the nonlinear hydrodynamics stability of a thin micropolar liquid film flowing down along a vertical cylinder is investigated. A long-wave perturbation method is employed to solve generalized nonlinear kinematic equations at free film interface. The normal mode approach is first used to compute the linear stability solution for the film flow. The method of multiple scales is then used to obtain the weak nonlinear dynamics of the film flow for stability analysis. Results indicate that both subcritical instability and supercritical stability conditions possibly to occur in a micropolar film flow system with surface tension effect. It is shown that the flow stability in the stable states increases as surface tension value increases. However, the flow becomes somewhat unstable in unstable states as surface tension value increases.

並列關鍵字

stability analysis ； surface tension