Microgravity Science and Technology

, Volume 31, Issue 3, pp 293–304 | Cite as

Linear-Stability Analysis of Thermocapillary-Buoyancy Convection in an Annular Two-Layer System with Upper Rigid Wall Subjected to a Radial Temperature Gradient

  • Dong-Ming Mo
  • Deng-Fang RuanEmail author
Original Article


This paper presented a linear-stability analysis on thermocapillary-buoyancy convection in radially heated annular pool filled in 5cSt silicone oil / HT-70 two-layer fluids. The influences of the aspect ratio, radius ratio and thickness ratio on the flow stability were discussed. Results indicate that the system is most unstable when the thickness ratio is close to 0.375. Flow bifurcation appears when the thickness ratio varies from 0.625 to 0.875. Three corresponding destabilization mechanisms were revealed. Effect of buoyancy convection and the upper boundary condition on the flow stability were also analyzed. The upper rigid wall can enhance the flow stability in the annular two-layer system, especially when the thickness ratio is near 0.75. Furthermore, the buoyancy can greatly reduce the flow stability comparing with that under the microgravity condition.


Thermocapillary-buoyancy convection Two-layer system Linear-stability analysis Annular pool 



Complex matrix


Complex matrix


Unit vector


Depth, m


Dimensionless depth


Wave number


Marangoni number


Dimensionless pressure


Prandtl number


Radius, m


Dimensionless radius


Temperature, K


Dimensionless radial velocity


dimensionless azimuthal velocity


Dimensionless velocity vector


Dimensionless vertical velocity


Axial coordinate, m


Dimensionless axial coordinate

Greek Symbols


Thermal diffusivity, m2/s


Thermal expansion coefficient, 1/K


Surface tension coefficient, N/(m.K)


Thickness ratio, ε = h1/h


Aspect ratio, η = h/(ro-ri)


Dimensionless temperature, Θ = (T-Tc)/(Th-Tc)


Azimuthal coordinate, rad


Thermal conductivity, W/(m.K)




Dynamic viscosity, kg/(m.s)


Kinematic viscosity, m2/s


Density, kg/m3


Dimensionless time


Radius ratio, Γ = ri/ro


Temperature perturbation


Propagation angle of the hydrothermal wave, °


Dimensionless stream function


Phase velocity





Critical point






Liquid layer, the lower layer (j = 1) and upper layer(j = 2)





This work is supported by Chongqing Research Program of Basic Research and Frontier Technology (Grant No. cstc2018jcyjAX0597) and Science and Technology Research Program of Chongqing Municipal Education Commission of China (Grant No. KJQN201803201).


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Copyright information

© Springer Nature B.V. 2019

Authors and Affiliations

  1. 1.State Key Laboratory of Mechanical TransmissionChongqing UniversityChongqingChina
  2. 2.Department of Mechanical EngineeringChongqing Industry Polytechnic CollegeChongqingChina
  3. 3.College of Automotive EngineeringChongqing UniversityChongqingChina

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