Thermal Marangoni Convection of a Fluid Film Coating a Deformable Membrane

Abstract

The thermal Marangoni instability of a fluid film coating a deformable membrane has been investigated by taking into account the deformation of the fluid free surface. Numerical calculations for different thermal boundary conditions are presented. The prestressed membrane is supposed to be very thin and therefore its behavior is similar to that of an isothermal fluid free surface with a surface tension but with a different mechanical boundary condition; that is, the fluid should stick on its surface and thus the fluid velocity is zero. An important assumption is that the membrane has no temperature dependence and therefore that only one Marangoni number exists for the free surface of the fluid. Numerical results are presented for stationary and oscillatory thermocapillary instability in both the sinuous and the varicose modes. It is shown that membrane deformation has important implications on the Marangoni instability of the fluid layer for positive and negative Marangoni numbers.