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Description:
The dynamic behavior of a free gas--liquid phase boundary is often influenced by evaporation or condensation to an extend that may not be neglected. In this paper, we derive a general model for the dynamics of a two phase flow with evaporation, starting from the balance of mass, energy, and momentum. The model takes into account that the gas phase might consist of a mixture of vapor and inert gas. It is based on the incompressible Navier--Stokes equations in the bulk of the liquid and the gas phase, convection--diffusion equations for heat and vapor, and appropriate conditions for the transfer of mass, momentum, and energy through the phase boundary. As a simplification, the flow field in the liquid and gaseous phase can be decoupled, if the stress from the gas phase on the free surface is neglected. The special case of a gas phase containing only pure vapor is considered, which allows one to neglect the gas phase completely, leading to a single phase flow problem with a free boundary.