Linear instability analysis of thermocapillary convection in a bilayer system

Abstract

a b s t r a c tThe linear instability analysis of thermocapillary conve ction in a bila yer system consisting of silicon oil 10cS and fluorinert FC70 liquids was discussed in this paper. The bilayer system was bound below by a rigid plate and above by a free surface with a passive gas. The two immiscible liquids were separated by an interface. A constant horizontal temperature gradient was imposed along the interfaces. Two typical cases were studied: (i) streamwise homogeneou s disturbances (the streamwise disturbance wave number a = 0); (ii) spanwis e homogeneou s disturbances (the spanwis e disturbance wave number b = 0). When a = 0, it was found that convection in the two layers may occur in the form of stationary mode or oscillatory mode. The oscillatory mode takes the form of traveling wave, which propagates in either spanwis e direction. When b = 0, convection in the two layers occurs in the form of oscillatory mode, which takes the form of traveling wave propagating in the same direction as base flow. The three dimensional analysis suggested that disturbance in the spanwis e direction was the major cause of destabilization in the system. The influences of Biot number Bi and the depth ratio h on the unstable modes in the bilayer system were discussed.

Linear-stability analysis of thermocapillary-buoyancy convection in annular two-layer system with a radial temperature gradient

“…It was certified that a strong damping of the melt flow can be obtained by using an encapsulant liquid layer that has the appropriate viscosity, heat conductivity and/or thickness. Afterward, Ding and Liu [10] performed a linear instability analysis of the thermocapillary convection in a bilayer system consisting of silicone oil 10cSt and fluorinert FC-70 liquids with a constant horizontal temperature gradient. The results show that convection in the two layers may occur in the form of a stationary mode or an oscillatory mode, and the disturbance in the spanwise direction is the major cause of destabilization.…”