The stability characteristics of an ultra-thin layer of a viscous liquid flowing down a cylindrical fibre are investigated by a linear theory. The film with the thickness lessthan 100 nm is driven by an external force and under the influence of the van der Waalsforces. The results show that, when the relative film thickness decreases, the curvature of the fibre depresses the development of the linear perturbations, whereas the van der Waals forces promote the instabilities. This competition results in a non-monotonous dependence of the growth rate on the relative film thickness. The critical curves are also obtained to describe the transition from the absolute instability to the convective instability, indicating that the van der Waals forces can enlarge the absolutely unstableregion. Furthermore, the surface tension can cause the development of the absolute instability, where as the external force has an opposite effect.
To understand the influences of nanoparticleson dewetting in ultra-thin films,both linear stability theory and numerical simulations are performed in the presentstudy,with the consideration of oscillatory structural(OS)forces.Long scale approximation is utilized to simplify thehydrodynamic and diffusion equations to a nonlinear systemfor film thickness and nanoparticle concentration.Resultsshow that the presence of nanoparticles generally suppressesthe dewetting process.Two physical mechanisms responsible for this phenomenon are addressed in the present study.When the oscillatory structural forces are relatively smaller,the essential feature of film evolution is similar to the case ofparticle-free flow.The reduction of the linear growth rate andthe postponement of film rupturing can be attributed to theincrement of the viscosity due to the presence of nanoparticles.On the other hand,when the intensity of the OS forcesbecomes stronger,the stepwise thinning of film can be observed which prevents the film from rupture.Numerical simulations indicate that this phenomenon is caused by the existence of a stable zone due to the oscillatory nature of thestructural forces.Another interesting finding is that the nonuniformity of the distribution of nanoparticle concentrationmight destabilize a spinodally stable film,and trigger the occurrence of film dewetting.
此文基于加权残数积分边界层(WRIBL,Weighted-residual Integral Boundary-layer)模型,推导出描述电场作用下的沿波纹壁面下落的二维液膜流动的演化方程,分析了电场和壁面结构对稳定性的影响以及定常流动的特性。在壁面振幅较小的情况下,毛细作用促使薄膜更稳定,而电场则使其流动的失稳,此文提出了这两种作用的平衡条件,并说明壁面结构的引入可以加剧这两方面的效应。对定常流动的分析说明了表面波相对振幅和与壁面的相位差随物理参数的变化情况,并显示电场对流场共振现象有抑制作用。
