论文标题
Marangoni在粘弹性二进制膜中具有交叉效果的不稳定
Marangoni instability in a viscoelastic binary film with cross-diffusive effect
论文作者
论文摘要
粘弹性流体通常是聚合物溶质和牛顿溶剂的混合物。在存在温度梯度的情况下，这些溶质的分层可以通过坏效应进行。在这里，考虑到流体的这一二进制方面，我们研究了经典的Marangoni不稳定性问题。该薄膜以可变形的自由表面为界面，受到固体基板的加热。线性稳定性分析对有限波长（短波扰动）的扰动进行了数值，这表明在该系统中可以出现单调和振荡性不稳定性。发现在存在SORET扩散的情况下，热毛细血管和溶质毛细血管之间的相互作用会引起两种不同的振荡不稳定性，即即使对于牛顿二进制混合物，以前也忽略了一种模式。作为这项工作的主要结果，我们根据模型参数值提供了对不同不稳定模式的敏感性的完整图片。最后，在长波分析的框架下开发了一个近似模型，该模型可以定性地描述系统的稳定性行为而无需数字解决问题。
The viscoelastic fluids are usually the blends of a polymeric solute and a Newtonian solvent. In the presence of a temperature gradient, stratification of these solutes can take place via the Soret effect. Here, we investigate the classical Marangoni instability problem for a thin viscoelastic film considering this binary aspect of the fluid. The film, bounded above by a deformable free surface, is subjected to heating from below by a solid substrate. Linear stability analysis performed numerically for perturbations of finite wavelength (short-wave perturbations) reveals that both monotonic and oscillatory instabilities can emerge in this system. The interaction between the thermocapillary and solutocapillary forces in the presence of Soret diffusion is found to give rise to two different oscillatory instabilities, of which one mode was overlooked previously, even for the Newtonian binary mixtures. As a principal result of this work, we provide a complete picture of the susceptibility to different instability modes based on the model parameter values. Finally, an approximate model is developed under the framework of long-wave analysis, which can qualitatively depict the stability behaviour of the system without numerically solving the problem.
