Nonequilibrium Moisture Transport
When equilibrium between liquid and vapor phases cannot be assumed, the liquid saturation and vapor mass fraction are not related, therefore, both the water conservation equations for the liquid phase and vapor phase must be solved separately.
Unlike the equilibrium assumption, the evaporation source is taken into account for the mass conservation equations, and not only for the heat source it generates in the heat transfer equation. Just like the liquid saturation and vapor mass fraction are not related, so are the mass sources Gl and Gv.
The following material properties, fields, and source are defined:
•
 ϕw (dimensionless) is the relative humidity.
•
 ρg (SI unit: kg/m3) is the moist air density, defined from the dry air and vapor densities, in function of the amount of vapor.
•
 ug (SI unit: m/s) is the moist air velocity field, that should be interpreted as the Darcy velocity, that is, the volume flow rate per unit cross sectional area.
•
 ωv (dimensionless) is the vapor mass fraction in moist air, defined as
•
 Μv (SI unit: kg/mol) is the molar mass of water vapor.
•
 csat (SI unit: mol/m3) is the vapor saturation concentration.
•
 T (SI unit: K) is the temperature.
•
 gw is the moisture diffusive flux is defined as:
•
 Deff (SI unit: m2/s) is the effective vapor diffusion coefficient in the porous medium, computed from the diffusion coefficient in a free medium, and accounting for the porosity and tortuosity of the porous medium.
•
 ul (SI unit: m/s) is the liquid water velocity field, defined from the absolute pressure gradient by the Darcy’s law as:
•
 κrl (dimensionless) is the relative liquid water permeability, that may be defined as a function of the liquid saturation.
•
 κ (SI unit: m2) is the porous medium permeability.
•
 pA (SI unit: Pa) is the absolute pressure.
•
 ρl (SI unit: kg/m3) is the liquid water density, defined as a function of the temperature.
•
 glc is the liquid water capillary flux, defined either from the capillary pressure gradient by a Darcy’s law:
or by a diffusion equation using the relative humidity:
•
 Dw (SI unit: m2/s) is the moisture diffusivity.
•
 pc (SI unit: Pa) is the capillary pressure, that can be related to the liquid saturation through different models, see Capillary Pressure Models.
•
 G (SI unit: kg/(m3⋅s)) is a moisture source (or sink). See the Moisture Source node.
The moisture source due to evaporation is calculated as a deviation form the equilibrium state:
where Kevap is the evaporation rate (SI unit: 1/s) which gives the speed with which the system comes back to equilibrium after a disturbance, R (SI unit: J/(mol⋅K) is the universal gas constant, pv,eq (SI unit: Pa) is the equilibrium vapor pressure, and pv (SI unit: Pa) is the partial pressure of water vapor.
In turn, the equilibrium vapor pressure can be given as a function of water activity aw (dimensionless) and vapor saturation pressure psat (SI unit: Pa):
The evaporation source is added as a mass source in the fluid flow equations solved for the computation of the moist air velocity field, ug.
The corresponding latent heat source is defined as:
where Lv is the latent heat of evaporation.
For a steady-state problem, the liquid water saturation, and vapor mass fraction do not change with time and the first term in both moisture transport equations disappears.