On convection driven by surface tension caused by transient heat conduction

The onset of convection caused by surface tension (ST) during transient coo ling of a thin layer of liquid is investigated. This study shows that it ca n be predicted by a newly defined transient Marangoni number Ma, which inco rporates the mode and rate of cooling, where a non-linear temperature profi le develops continuously until instability sets in. The spatio-temporal dev elopment of local hydrodynamic equilibrium can thus be traced to the point of instability. The onset of convection for evaporative-cooling can be pred icted from the maximum transient Ma whose values are the same as those prev iously obtained by linear stability analysis for Blot number = 0. The criti cal times and critical depths for stable heat conduction in liquids (before convection) can thus be determined accurately. Agreement with observed val ues from the literature is very good. The critical transient Marangoni numb ers and the sizes of convection cells have also been predicted with reasona ble accuracy. A theoretical limiting depth that demarcates between surface tension and buoyancy controlled convection is proposed. There exists theore tical and laboratory evidence to support that surface tension dominates in fluid depth less than 5 mm and buoyancy predominates over 10 mm. (C) 1999 E lsevier Science Ltd. All rights reserved.