  We develop a phase-field model for evaporation from a porous medium by
explicitly considering a vapor component together with the liquid and gas
phases in the system. The phase-field model consists of the conservation of
mass (for phases and vapor component), momentum, and energy. In addition, the
evolution of the phase field is described by the Allen-Cahn equation. In the
limit of vanishing interface width, matched asymptotic expansions reveal that
the phase-field model reduces to the sharp-interface model with all the
relevant transmission conditions on the moving interface. An energy estimate is
derived, which suggests that for the diffusion-dominated regime, energy always
decreases with time. However, this is not trivial in the case of other regimes.
Through numerical examples, we analyze the efficiency of the developed
phase-field formulation in modeling the evaporation process. We observe that
our formulation is able to capture shrinking liquid droplet, in other words
evaporation. Further, the phase-field model is upscaled to the Darcy scale
using periodic homogenization for the diffusion-dominated regime. The effective
parameters at the Darcy scale are connected to the pore scale through
corresponding cell problems.
