Thermocapillary convection in an annular cylindrical container

The liquid–gas interface of a liquid in an annular container is subjected to a temperature gradient. Since shear stress on the free liquid surface depends on the temperature it shall create a variable shear stress on the surface which in turn yields by viscous traction a thermocapillary convection in the bulk of the liquid. For constant temperature T ₂ > T ₁ on the outer cylindrical wall and T ₁ on the inner wall a steady convection shall emerge. The morphology of the ensuing flow is investigated as a function of the diameter ratio and the liquid height ratio and exhibits the growth of bottom rim vortex rings, which unite to single vortex rings of opposite flow direction to the original single strong vortex ring above it. The results also show how such a system depends on the magnitude of the diameter ratio and the liquid height ratio. The evaluation of the results exhibits the evolution of vortex rings.