Analytical solution for dynamic evaporation of liquid in isothermal condition

An analytical solution based on a diffuse-interface model is presented for an isothermal evaporation problem at subsaturated vapor pressure. The macroscopic equations are derived from the free-energy formulation widely used in the lattice Boltzmann literature, distinguishing our approach from conventional evaporation models that rely on jump conditions or purely kinetic theory. The interface behavior is fully described by differential equations, eliminating the need for assumptions such as local thermodynamic equilibrium at the interface. We derive an exact analytical solution for the inviscid case and propose an approximate solution that accounts for viscous effects. Our model reveals a relationship between evaporation rate and viscosity within the diffuse-interface framework. The analytical results are validated against numerical simulations using the open-source parallel library openlb, demonstrating excellent agreement within the framework of diffuse-interface methods.