Onset of marangoni convection in a horizontal fluid layer experiencing evaporative cooling

The onset of Marangoni convection in an initially isothermal, quiescent fluid layer experiencing evaporative cooling from above is analyzed theoretically. For this system, the stability analysis on regular cell modes is conducted, based on the linear stability theory, the energy method, and their modifications. The stability equations are derived and the critical time to mark the onset of convection (tau(c)) is obtained, as a function of the Marangoni number (Ma) and the Prandtl number (Pr). The linear stability theory predicts more-stable conditions than the energy method. The present results show that tau(c) decreases as Pr increases for a given Ma value. The present predictions are compared with the available experimental data of propanol.