柱状纤维上超薄液膜的线性稳定性分析

Linear Instability of Ultra-Thin Liquid Films Flowing Down a Cylindrical Fibre

运用线性理论分析了粘性超薄液膜沿柱状纤维垂直下落的稳定性特征,研究了厚度低于100 nm的薄膜在外力驱动下的流动以及van der Waals力的影响.结果表明随着薄膜相对厚度的下降,纤维表面的曲率将使得线性扰动的发展得到抑制,而van der Waals力促进扰动的增长,这一竞争机制导致了增长率随薄膜相对厚度非单调的变化.还得到了流动的绝对和对流不稳定分区.结果表明van der Waals力扩大绝对不稳定流动区域,表面张力也会有利于绝对不稳定的发展,而外驱动力正好起到相反的作用.

The stability characteristics of an ultra-thin layer of viscous liquid flowing down a cylindrical fibre were investigated by linear theory.The film with a thickness less than 100 nm was driven by an external force,and under the influence of van der Waals forces.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 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 absolute to convective instability,which demonstrates that the van der Waals forces have the role of enlarging the absolutely unstable region.Furthermore,the surface tension is benefitial for the development of the absolute instability,whereas the external force plays an opposite effect.