Marangoni convection in a finite-size cylinder

This paper considers a liquid in a finite-size cylinder in which Marangoni instability occurs. The upper boundary of the liquid is free and deformable. The problem of the occurrence of convection in a cylindrical container is solved using the method of separation of variables. A homogeneous differential equation of the sixth order with constant coefficients and complex boundary conditions is obtained. In the case of monotonic perturbations, an analytical expression for critical Marangoni numbers is derived. The case of a weightless liquid in the cylinder is considered.