Effect of surfactants on the long-wave stability of two-layer oscillatory film flow
Effect of surfactants on the long-wave stability of two-layer oscillatory film flow
复制标题
表面活性剂对两层振荡膜流长波稳定性的影响
DOI：
10.1017/jfm.2021.833
复制
发表时间：
2021-10
影响因子：
3.7
通讯作者：
Lu Xi-Yun
中科院分区：
文献类型：
--
作者：
Wang Cheng-Cheng;Huang Haibo;Gao Peng;Lu Xi-Yun
摘要研究了长波扰动下振荡平板驱动的两层薄膜流的稳定性。系统地研究了膜厚比（$n$）、粘度比（$m$）、密度比（$r$）、振荡频率（$\beta$）和不溶性表面活性剂等因素对稳定性的影响。识别出四种特殊的Floquet模式，并通过求解四阶矩阵的特征值问题得到相应的增长率。一个小的粘度比（$m\le 1$）可以稳定的流动，但它取决于厚度比。如果粘度比不是很小（$m>0.1$），在$（\beta，n）$-平面内，稳定和不稳定的曲线条纹交替出现。换句话说，在这种情况下，如果两层膜流不稳定，稍微调整上层膜的厚度可以使其稳定。特别是，如果上膜足够薄，即使在高频振荡下，流动也总是稳定的。密度比的影响是相似的，即在$（\beta，r）$-平面上有弯曲的稳定和不稳定条纹。表面表面活性剂通常稳定双层振荡膜的流动，而界面表面活性剂可能稳定或不稳定的流动，但效果是温和的。研究还发现，重力一般可以稳定的流动，因为它缩小了不稳定频率的带宽。
Abstract The stability of the two-layer film flow driven by an oscillatory plate under long-wave disturbances is studied. The influence of key factors, such as thickness ratio ($n$), viscosity ratio ($m$), density ratio ($r$), oscillatory frequency ($\beta$) and insoluble surfactants on the stability behaviours is studied systematically. Four special Floquet patterns are identified, and the corresponding growth rates are obtained by solving the eigenvalue problem of the fourth-order matrix. A small viscosity ratio ($m\le 1$) may stabilize the flow but it depends on the thickness ratio. If the viscosity ratio is not very small ($m>0.1$), in the $(\beta ,n)$-plane, stable and unstable curved stripes appear alternately. In other words, under the circumstances, if the two-layer film flow is unstable, slightly adjusting the thickness of the upper film may make it stable. In particular, if the upper film is thin enough, even under high-frequency oscillation, the flow is always stable. The influence of density ratio is similar, i.e. there are curved stable and unstable stripes in the $(\beta ,r)$-planes. Surface surfactants generally stabilize the flow of the two-layer oscillatory membrane, while interfacial surfactants may stabilize or destabilize the flow but the effect is mild. It is also found that gravity can generally stabilize the flow because it narrows the bandwidth of unstable frequencies.
登录
查看更多内容
影响因子：
3.7
作者：
M. Blyth;C. Pozrikidis
通讯作者：
M. Blyth;C. Pozrikidis
影响因子：
3.7
作者：
A. Samanta
通讯作者：
A. Samanta
影响因子：
4.6
作者：
A. Frenkel;D. Halpern
通讯作者：
A. Frenkel;D. Halpern
含有不溶性表面活性剂的振荡流体层的不稳定性
影响因子：
3.7
作者：
Gao, Peng;Lu, Xi-Yun
通讯作者：
Lu, Xi-Yun
影响因子：
3.7
作者：
Halpern, D;Frenkel, AL
通讯作者：
Frenkel, AL