Mathematical modeling of interaction of the thermal, gravitational and thermocapillary convection in the domains with interfaces is very important and actual problem even without mass transfer. The presence of an unknown interface, that is not a material surface by taking into account the evaporation, brings in the modeling the additional difficulties. The principal question here is to formulate the interface conditions. The generalized kinematic, dynamic and energetic conditions are formulated in this paper in the dimensionless form on the basis of the conservation laws and strong discontinuity relations. The theoretical aspects of investigation of the problems with interfaces, hypotheses used by derivation of the interface conditions and methods of simplifications of the problem statements are discussed.

Key words: convection in a fluid, co-current gas flow, interface, evaporation through the interface, interface conditions.