Toward a theory of evaporation processes in liquid-solid systems

A theoretical analysis is presented of isothermal evaporation of a volatile component from a solid covered by a liquid layer. Binary compounds are considered, with the covering liquid produced by thermal decomposition of the solid material. It is shown that the relaxation time of the volatile concentration profile is much shorter than the characteristic time of motion of the melting 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 formulated that involves two moving phase transition interfaces: an evaporating interface and a melting interface. Exact analytical solutions to the problem are found. It is shown that the melting interface moves faster than the evaporating interface; i.e., the thickness of the liquid layer increases with time, its growth rate increasing with evaporation rate coefficient. It is demonstrated that the concentration profile evolves self-similarly in the course of 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.