Theory for Moisture Transport in Solids
In a porous material, moisture may be present in either vapor or liquid water, and moisture transport may occur through convection or diffusion.
Two fundamental phenomena are employed to elucidate the transport of liquid water within the pores of porous materials:
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Adsorption: the vapor is attached to the pore walls. Equilibrium vapor pressure is reached in the pores under thermodynamic conditions markedly distinct from those required in a free medium. Altering saturation conditions produces a notable shift in relative humidity, thereby rendering it a pertinent variable in the assessment of moisture content.
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Capillarity: when the porous medium is wetted by liquid water, there is a pressure difference between the liquid and gas (moist air) phases, due to the curvature of the wetting interface. The pressure difference, referred to as capillary pressure, becomes the driving force for further pore filling. Note that in some applications, the capillary pressure is replaced by the suction.
The predominance of either of these effects, adsorption or capillarity, depends on the amount of liquid water in the porous medium, and on the size and shape of the pores. Two moisture regions can be distinguished depending on the process and materials under study:
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Hygroscopic regime, where adsorption is the predominant effect. The equilibrium moisture content is better characterized by the relative humidity through the specification of a sorption curve. For a relative humidity below 95%, the slope of the sorption curve is small, and moisture content increases almost linearly as a function of the relative humidity. Building materials are mostly modeled under this assumption.
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Capillary water region, where capillarity is the predominant effect. Above 95% relative humidity, a very small variation of humidity induces a large variation of moisture content, and the capillary pressure formulation is best suited to characterize the moisture content through the specification of a retention curve (for example, the van Genuchten or Brooks and Corey retention models, see The Richards’ Equation Interface for a description of these models).
In porous media, the relative humidity and capillary pressure are the state variables to describe the thermodynamic state of water. It is assumed that the two phases, gas and liquid, are in a state of local equilibrium and are interconnected through Kelvin’s law.
As long as equilibrium conditions are upheld, the state variables are continuous when transitioning between two porous materials (such as at the interface between two materials with differing porosities) or between a porous medium and a free medium. Kelvin’s law holds true on both sides of the interface.
Conversely, liquid saturation and moisture content depend upon the properties of the porous material and may experience discontinuities at interfaces between two media with distinct properties.
The Moisture Transport in Solids Interface is dedicated to the modeling of moisture transport in porous media. In the hygroscopic moisture regime, the total moisture content is defined by the sorption curve
where the liquid saturation, sl, describes the amount of liquid water within the pores, the moist air saturation, sm, describes the amount of moist air within the pores, and εp is the porosity.
Alternatively, in the capillary regime, it is possible to use a retention curve that establishes the relationship between the capillary pressure, pc, as a function of the liquid water saturation sl:
A single equation for the transport of the total moisture content is obtained by adding the equations for the mass conservation of liquid water and vapor, and assuming local equilibrium between the liquid and gas phases. Thereafter, the evaporation and condensation source terms cancel out, and the equation of moisture transport reads
(5-22)
The interface also solves for the transport of dry air to account for changes in the moist air pressure:
where Dalton’s law is used to relate the moist air pressure to the vapor and dry air pressures:
The quantities involved are:
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sl (dimensionless) is the liquid water saturation.
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w(ϕw) (SI unit: kg/m3) is the total moisture content.
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  ϕw (dimensionless) is the relative humidity.
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 ρv (SI unit: kg/m3) is the water vapor density.
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ρl (SI unit: kg/m3) is the liquid water density, it can be a function of the temperature.
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ρa (SI unit: kg/m3) is the dry air density.
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 Spv (SI unit: 1/Pa) is the storage coefficient for the water vapor.
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 Spa (SI unit: 1/Pa) is the storage coefficient for the dry air.
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 pv,sat (SI unit: Pa) is the vapor saturation pressure, that can be a function of the temperature only.
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pm (SI unit: Pa) is the moist air pressure.
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pl (SI unit: Pa) is the liquid water pressure.
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pa (SI unit: Pa) is the dry air pressure.
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 vl (SI unit: m/s) is the liquid water velocity, defined by Darcy’s law as
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 κrl (dimensionless) is the relative liquid water permeability, that may be a function of the liquid saturation sl.
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μl (SI unit: Pa⋅s) is the liquid water viscosity, that may be a function of the temperature.
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 κ (SI unit: m2) is the permeability of the porous medium.
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 vv (SI unit: m/s) is the water vapor velocity defined by
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vm (SI unit: m/s) is the moist air velocity, defined by Darcy’s law as
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κrm (dimensionless) is the relative moist air permeability, that may be a function of the liquid saturation sl.
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μm (SI unit: Pa⋅s) is the moist air viscosity, that may be a function of the temperature.
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vvm (SI unit: m/s) is the relative velocity of vapor in moist air.
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Γc (SI unit: kg/m2·s) is the capillary flux that can be defined either from the capillary pressure gradient or by diffusion of relative humidity.
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Γa (SI unit: kg/m2·s) is the dry air flux. It is defined as
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Γw (SI unit: kg/m2·s) is the moisture (water content) flux. It is defined as
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va (SI unit: m/s) is the dry air velocity defined by
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vam (SI unit: m/s) is the relative velocity of dry air in moist air.
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 G (SI unit: kg/(m3⋅s)) is a moisture source (or sink).