论文标题
循环的marangoni在近膜片中的液滴中流动
Circulating Marangoni flows within droplets in smectic films
论文作者
论文摘要
我们介绍了嵌入自由常规近晶膜(FSSF)中的椭圆形各向同性液滴中Marangoni对流的理论研究和数值模拟。分析了对在大块近晶状体 - 异位透明过渡上过热的FSSF中自发形成的两个各向同性液滴分析的热毛细血管,并沉积在近晶膜表面上的油镜片。上滴界面不含近晶层的现实模型,而在下滴表面上,近晶层仍然持续存在详细考虑。对于各向同性的液滴和油镜,这有效地导致了带有近晶壳在边界的流体运动。当膜的上侧的温度高于下部时,上述不对称构型将在实验中实现。分析得出了描述椭圆形下降中Marangoni对流流的Stokes流函数的完整固定解决方案。椭圆形下降和周围空气中的温度分布在扰动理论的框架中确定。结果,针对不同的液滴椭圆率和液晶和空气的热电导率得出了固定热毛细血管对流的分析溶液。同时,进行了液滴中热毛细血管运动的数值水动力计算。分析和数值模拟都预测了由液滴自由表面的Marangoni效应确定的轴对称循环对流运动。由于液滴界面的曲率,沿其自由表面的温度梯度始终持续。因此,对于任意小的Marangoni数字,可能会在过热的FSSF中椭圆形液滴中的热毛细血管对流。
We present theoretical study and numerical simulation of Marangoni convection within ellipsoidal isotropic droplets embedded in free standing smectic films (FSSF). The thermocapillary flows are analyzed for both isotropic droplets spontaneously formed in FSSF overheated above the bulk smectic-isotropic transition, and oil lenses deposited on the surface of the smectic film. The realistic model, for which the upper drop interface is free from the smectic layers, while at the lower drop surface the smectic layering still persists is considered in detail. For isotropic droplets and oil lenses this leads effectively to a sticking of fluid motion at the border with a smectic shell. The above mentioned asymmetric configuration is realized experimentally when the temperature of the upper side of the film is higher than at the lower one. The full set of stationary solutions for Stokes stream functions describing the Marangoni convection flows within the ellipsoidal drops were derived analytically. The temperature distribution in the ellipsoidal drop and the surrounding air was determined in the frames of the perturbation theory. As a result the analytical solutions for the stationary thermocapillary convection were derived for different droplet ellipticity ratios and the heat conductivity of the liquid crystal and air. In parallel, the numerical hydrodynamic calculations of the thermocapillary motion in the drops were performed. Both the analytical and numerical simulations predict the axially-symmetric circulatory convection motion determined by the Marangoni effect at the droplet free surface. Due to a curvature of the drop interface a temperature gradient along its free surface always persists. Thus, the thermocapillary convection within the ellipsoidal droplets in overheated FSSF is possible for the arbitrarily small Marangoni numbers.