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 less than 100 nm is driven by an external force and under the influence of the van der Waals forces. 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 unstable region. Furthermore, the surface tension can cause the development of the absolute instability, whereas the external force has an opposite effect.
To understand the influences of nanoparticles on dewetting in ultra-thin films, both linear stability the- ory and numerical simulations are performed in the present study, with the consideration of oscillatory structural （OS） forces. Long scale approximation is utilized to simplify the hydrodynamic and diffusion equations to a nonlinear system for film thickness and nanoparticle concentration. Results show that the presence of nanoparticles generally suppresses the dewetting process. Two physical mechanisms responsi- ble 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 of particle-free flow. The reduction of the linear growth rate and the postponement of film rupturing can be attributed to the increment of the viscosity due to the presence of nanoparti- cles. On the other hand, when the intensity of the OS forces becomes stronger, the stepwise thinning of film can be ob- served which prevents the film from rupture. Numerical sim- ulations indicate that this phenomenon is caused by the ex- istence of a stable zone due to the oscillatory nature of the structural forces. Another interesting finding is that the non- uniformity of the distribution of nanoparticle concentration might destabilize a spinodally stable film, and trigger the oc- currence 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。
