Thermal transients during the evaporation of a spherical liquid drop

This work is centered upon the thermal transients taking place during the evaporation of a spherical drop of a pure liquid suspended in a gaseous environment. Based on mass and energy conservation equations, a so-called complete model is developed considering quasi-steady diffusive and Stefan convective transports in the non-isothermal gas phase, and unsteady conduction in the liquid drop. A simplified version of the complete model, the so-called quasi-homogeneous model, is developed using an asymptotic analysis in the limit of small thermal homogenization time in the drop compared to the total drop evaporation time. The models enable highlighting the role of two dimensionless numbers, R and H, characterizing the two thermal transients of the problem: the thermal relaxation transient of the drop interfacial temperature and the thermal homogenization transient of the drop. The values of these two dimensionless numbers are provided for several liquids and their dependence on the evaporation conditions is discussed. It is shown that, when an accurate evaluation of the drop evaporation time is required by the considered application, the use of a fully quasi-steady model should be restricted to systems presenting small values of R compared to one (at least an order of magnitude smaller) and H<1. For other systems, it appears necessary to use the complete model or the quasi-homogeneous model. A simple formula is proposed to evaluate the relative difference between the drop evaporation times predicted by the complete model and by the fully quasi-steady model. When an accurate evaluation of the time evolution of the drop temperature field is required by the considered application, it appears to be necessary to use the complete model, whatever the system considered in this work. Indeed, the thermal transients can generally take an important part of the drop evaporation time and large temperature gradients can develop in the drop. The use of the complete model reveals that three different types of dynamics can be observed when a drop evaporates, depending on the relative values of three temperatures: the initial drop temperature, the dew point temperature of the gas far from the drop and the established interfacial temperature (i.e. the drop interfacial temperature calculated using a fully quasi-steady model).