Marangoni instability in a liquid layer bounded by two coaxial cylinder surfaces

A liquid layer, confined between two coaxial cylinder surfaces, has either a gas-liquid interface on the inside and is heated from the outer (solid) boundary, or it has a gas-liquid interface on the outside and is heated from the inner (solid) boundary. Neglecting gravity and using a standard normal-mode approach, we analyse surface-tension driven instability (Marangoni instability) of the motionless steady state in which the temperature depends on the radial coordinate only. Numerical results for the critical Marangoni number and corresponding wave-number pair are presented for various values of the curvature of the interface. This curvature turns out to exert a significant influence on the onset of Marangoni convection flows. Further, the stability behaviour of the system is found to be quite variable, depending on whether the interface is on the inside or on the outside of the layer and whether it is well-conducting or nearly-isolated.