The loss of stability equilibrium between two liquids in cylinder the presence of interface

The arising convection problem in a two-layers cylindrical system was considered. To seek for it solution the method of variables separation was used. As result obtained the homogeneous differential equation of sixth order with constant coefficients of the complicated boundary conditions. For the case of weightlessness and the monotonic disturbances the analytical expression for the critical Marangoni numbers were found. It is proved that with increasing radius of the cylinder, these numbers tend to well-known Marangoni number for a system of two flat layers.