Pikina E S, Shishkin M A, Kolegov K S, Ostrovskii B I, Pikin S A
Landau Institute for Theoretical Physics of the RAS, 142432, Chernogolovka, Moscow region, Russia.
Institute of Solid State Physics of the RAS, 142432 Chernogolovka, Moscow region, Russia.
Phys Rev E. 2022 Nov;106(5-2):055105. doi: 10.1103/PhysRevE.106.055105.
We present a theoretical study and numerical simulation of Marangoni convection within ellipsoidal isotropic droplets embedded in free-standing smectic films (FSSFs). 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 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 are derived analytically. The temperature distribution in the ellipsoidal drop and the surrounding air is determined in the frame of the perturbation theory. As a result, the analytical solutions for the stationary thermocapillary convection are obtained 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 drops are made. Both 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 exists. Thus, the thermocapillary convection within the ellipsoidal droplets in overheated FSSF is possible for the arbitrarily small Marangoni numbers. Possible experimental observations enabling the checking of our predictions are proposed.
我们对嵌入自支撑近晶薄膜（FSSFs）中的各向同性椭球形液滴内的马兰戈尼对流进行了理论研究和数值模拟。对在高于本体近晶 - 各向同性转变温度的FSSF中自发形成的各向同性液滴以及沉积在近晶薄膜表面的油透镜的热毛细流动进行了分析。详细考虑了一个实际模型，其中液滴上界面没有近晶层，而在液滴下表面近晶层仍然存在。对于各向同性液滴和油透镜，这有效地导致了流体运动在与近晶壳边界处的停滞。当薄膜上侧温度高于下侧温度时，上述不对称构型在实验中得以实现。通过解析推导得到了描述椭球形液滴内马兰戈尼对流流动的斯托克斯流函数的全套定常解。在微扰理论框架内确定了椭球形液滴和周围空气中的温度分布。结果，针对不同的液滴椭圆率比以及液晶和空气的热导率，获得了定常热毛细对流的解析解。同时，对液滴内热毛细运动进行了数值流体动力学计算。解析和数值模拟均预测了由液滴自由表面上的马兰戈尼效应决定的轴对称循环对流运动。由于液滴界面的曲率，沿其自由表面总是存在温度梯度。因此，对于任意小的马兰戈尼数，过热FSSF中椭球形液滴内的热毛细对流都是可能的。提出了能够检验我们预测的可能实验观测方法。
