Theory for Moisture Transport in Building Materials
By considering that building materials are in general surrounded by an environment of constant atmospheric pressure and under a certain range of temperature and moisture conditions, specific equations are proposed in Ref. 16 for moisture transport in this kind of materials.
Starting from the equation for the transport of moisture in porous media (using the diffusion model for capillary flux):
let’s make the assumption that there is no variation of the ambient total pressure (pA = 1 atm). In this case, by defining the gas and liquid velocities ug and ul as Darcy velocities, the convective fluxes for vapor and liquid water vanish:
By introducing the moisture storage capacity, ξ, defined as
the equation reads
Finally, the diffusive flux for vapor can be written as
By making the approximation that xaMa + xvMv is constant, and that moist air is an ideal gas, we have:
The vapor permeability coefficient is then defined as
The Moisture Transport in Building Materials Interface solves for the following equation derived from Ref. 16:
(4-138)
This equation models the moisture transfer as the sum of the capillary moisture flux:
and the vapor diffusion flux:
with the following material properties, fields, and source:
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 ξ (SI unit: kg/m3) is the moisture storage capacity.
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 δp (SI unit: s) is the vapor permeability tensor.
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 ϕw (dimensionless) is the relative humidity.
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 psat (SI unit: Pa) is the vapor saturation pressure.
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 T (SI unit: K) is the temperature.
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 Dw (SI unit: m2/s) is the moisture diffusivity.
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 G (SI unit: kg/m3·s) is the moisture source.
See Saturation State for the definition of saturation pressure psat as a function of temperature.