The Stefan problem for unsteady-state evaporation of a volatile component in the solid-liquid-gas systems: Exact analytical solution

We present a theoretical analysis of isothermal evaporation of a volatile component from a solid phase covered by a liquid layer. We consider binary systems when the covering liquid layer is produced by thermal decomposition of the solid material. It is shown that the relaxation time of the volatile concentration distribution in the liquid is much shorter than the characteristic time of motion of the dissolution interface; i.e., the instantaneous profile of volatile concentration at any time is a linear function of the spatial coordinate. A new nonlinear Stefan-type problem of evaporation in a solid-liquid-vacuum system is developed that involves two moving phase transition interfaces: an evaporating interface and a dissolving interface. Exact analytical solutions of the nonlinear Stefan-type problem under consideration are found in a parametric form. It is shown that the dissolving interface moves faster than the evaporating interface; i.e., the thickness of the liquid layer increases with time. An increase in evaporation rate coefficient leads to a steepening of the concentration gradient across the liquid layer, changing the volatile concentration at the evaporating interface, and the evaporative flux changes accordingly. The model under consideration is extended to the case when the evaporation flux becomes a weakly nonlinear function of the impurity concentration at the evaporating interface. Exact parametric solutions are found in this case too. (C) 2010 Elsevier Ltd. All rights reserved.