非平整加热斜面上液膜流动稳定性研究

Stability of liquid film flow along the uneven heated slope

针对非平整不均匀加热基底上的二维粘性流体薄膜流,研究了其非线性表面波的演化过程及流动稳定性。利用长波摄动法推导出非平整基底上非线性表面波的零阶和一阶演化方程。基于得到的演化方程,研究了平基底上以及正弦波纹基底波峰和波谷处各参数对液膜稳定性的影响,结果表明:Mn数为稳定影响因素,随Mn数的增大,液膜稳定区域增大;倾角θ为不稳定影响因素,随θ的增大,液膜稳定区域减小;相同条件下,正弦波纹基底波峰处液膜流动稳定区域最大,平基底其次,波谷处稳定区域最小,液膜在基底波谷处最易失稳。

This paper mainly studies the evolution and stability of the nonlinear surface wave of a two dimensional vis-cous liquid film along an uneven inclined non-uniformly heated wall. A long wave perturbation method is used to derive Zero-and First-order evolution equation of the nonlinear surface wave flow on uneven substrate. Based on the evolution equation, the parameters effect on the stability of liquid film at flat suhstrate and trough and crest of sinusoidal corruga-ted substrate is analyzed. The theoretical results show that Marangoni number gives a stabilizing effect, and the stable zone increases with an increase of Marangoni number, while the angle theta is unstable factors, the stable region de- creases with increase of angle theta. The stable region of liquid film is largest at crest of sinusoidal corrugated sub-strate, flat base secondly, and trough of sinusoidal corrugated substrate has the minimum stable region that liquid film is most vulnerable to instability at this location.