Abstract
The onset of convection caused by surface tension (ST) during transient cooling of a thin layer of liquid is investigated. This study shows that it can be predicted by a newly defined transient Marangoni number
Ma, which incorporates the mode and rate of cooling, where a non-linear temperature profile develops continuously until instability sets in. The spatio-temporal development of local hydrodynamic equilibrium can thus be traced to the point of instability. The onset of convection for evaporative-cooling can be predicted from the maximum transient
Ma whose values are the same as those previously obtained by linear stability analysis for Biot number=0. The critical times and critical depths for stable heat conduction in liquids (before convection) can thus be determined accurately. Agreement with observed values from the literature is very good. The critical transient Marangoni numbers and the sizes of convection cells have also been predicted with reasonable accuracy. A theoretical limiting depth that demarcates between surface tension and buoyancy controlled convection is proposed. There exists theoretical and laboratory evidence to support that surface tension dominates in fluid depth less than 5
mm and buoyancy predominates over 10
mm.