B_(2)O_(3)/蓝宝石熔体浮力-热毛细对流的线性稳定性分析

Linear Stability Analysis of Buoyancy-thermal Capillary Convection of B_(2)O_(3)/Sapphire Melt

本文对水平温度梯度作用下,上部为固壁的环形双液层的浮力-热毛细对流稳定性进行了线性稳定性分析,确定了半径比Γ=0.2、深宽比η=0.1、下液层厚度与总厚度比ε=0.5时B_(2)O_(3)/蓝宝石熔体工质对的临界Marangoni数、临界波数m与临界相速度ω,预测了失稳之后液-液界面上的温度波动型态。并且,把同几何条件下B_(2)O_(3)/蓝宝石熔体与5cSt硅油/HT-70的液-液界面径向速度与温度、径向R=0.5处的径向速度与温度进行了比较,发现在B_(2)O_(3)/蓝宝石熔体中,液-液界面处的热毛细对流,比浮力对流的作用更为重要。

In this paper,the linear stability analysis of buoyancy and thermal capillary convective stability of annular double liquid layer with upper solid wall under horizontal temperature gradient is carried out.The critical Marangoni number,critical wave number m and critical phase velocityωof the working medium pair of B_(2)O_(3)/sapphire melt were determined when the radius ratioΓ=0.2,the depth to width ratioη=0.1,and the ratio of the thickness of the lower liquid layer to the total thicknessε=0.5.The temperature fluctuation pattern at the liquid-liquid interface after instability was predicted.Furthermore,the radial velocity and temperature at the liquid-liquid interface of B_(2)O_(3)/sapphire melt and 5cSt silicone oil/HT-70 are compared under the same geometrical conditions,and the radial velocity and temperature at the radial R=0.5 are compared.It is found that the thermal capillary convection at the liquid-liquid interface is more important than buoyancy convection in B_(2)O_(3)/sapphire melt.