Linear-stability Analysis of Thermocapillary Flow in an Annular Two-layer System with Upper Rigid Wall

The linear-stability analysis of thermocapillary flow in the annular immiscible two-layer system of 5cSt silicone oil and HT-70 with a radial temperature gradient was carried out. The annular two-layer system is heated at the outer cylindrical wall and cooled at the inner wall, the bottom and top surfaces are bounded by two rigid and heat-insulated walls. The influences of the liquid layer depth and radius ratio between the cold inner wall and the hot outer wall on stability are thoroughly investigated. The critical Marangoni number, critical wave number and critical phase velocity are obtained. In addition, the mode of bifurcation for the hydrothermal wave is predicted at different liquid layer depth, and the temperature disturbance pattern of hydrothermal wave at interface is also exhibited.