New SFB 1313 publication, published in the scientific journal Advances in Water Resources. The work has been developed in the context of the SFB 1313 research projects A02, A05, and C02.
"A phase-field approach to model evaporation from porous media: Modeling and upscaling"
Authors
- Tufan Ghosh (University of Stuttgart, research project A05)
- Carina Bringedal (Western Norway University of Applied Sciences, Bergen, research project A05)
- Christian Rohde (University of Stuttgart, research project A05, B03, and C02)
- Rainer Helmig (University of Stuttgart, research projects A02, A05, and C02)
Abstract
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.