Linear Stability of flows in thermocapillary-buoyant liquid pools
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Fig. 1: Cylindrical liquid pool with height d and radius R. |
The free surface is heated by a parabolic heat flux Q(r). |
The flow in cylindrical thermocapillary-buoyant liquid pools with a free surface on top is studied in the limit of infinitely large surface tension. The shape of the pool is given by the ratio R/d, where R is the Radius and d the height of the pool. The free surface is heated by a non-uniform heat flux Q(r) from above, the outer wall and the bottom of the pool is kept on constant temperature T0.
The main driving forces for the flow are the shear forces on the free surface which are due to a non-uniform surface tension distribution on the free surface, which itself is due to the non-uniform heating of the free surface. For a small driving force the flow develops an axisymmetric steady flow pattern. Increasing the driving force beyond a certain critical value gives rise to a significant qualitative change of the flow pattern. The axisymmetric steady flow pattern becomes non-axisymmetric steady or non-axisymmetric oscillatory.
The aim of our work is to understand how this transition and the necessary driving force is influenced by the shape of the liquid pool, the shape of the heat flux profile, and the effect of gravity.
Furthermore we are studying the physical mechanisms responsible for this transition form axisymmetric to non-axisymmetric flow.