Summary
A mechanistic description and quantitative mathematical expressions are developed for the net migration rate through wood of water in the bound and vapor phases. Diffusion of bound water is driven by the gradient in the chemical potential of the bound water molecules while water vapor diffusion is driven, by the gradient in the mole fraction of water in the gas phase. Vapor and bound water are assumed always to be in local thermodynamic equilibrium. An original mathematical derivation grounded on fundamental thermodynamic relationships is applied to the bound water chemical potential in order to express the rate of bound water diffusion in terms of only the local temperature and water vapor pressure. Published experiments on nonisothermal moisture migration rates in wood are compared to the solutions of this equation and also others which have been recently proposed in the literature. Results from the equation developed in this paper are in closest agreement with the reported experimental data. This success may be attributed both to the thermodynamically correct expression derived for bound water chemical potential and to recognition of the important contribution of gas phase diffusion to total moisture migration rates.
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Abbreviations
- CP :
-
heat capacity, J/mole-K
- c:
-
molar density, moles/m3
- Db :
-
thermal diffusion coefficient, %db/K
- Dv :
-
vapor diffusion coefficient, kg/m-s-Pa
- D eff :
-
effective gas diffusivity, m2/s
- D b (1) :
-
bound water diffusion coefficient, kg/s-m3
- D b (2) :
-
bound water diffusion coefficient, kg/s-%db
- D b (3) :
-
bound water diffusion coefficient, kg/s-%db
- D b (4) :
-
bound water diffusion coefficient, kg/s-%db
- D μ :
-
bound water diffusion coefficient, kg-s/m3
- Eb :
-
activation energy for bound water diffusion, cal/mole
- EL :
-
difference between molar heat of vaporization of bound water and that of free water, J/mole
- F:
-
flux, kg/m2-s
- fA :
-
mole fraction, dimensionless
- H:
-
molar enthalpy, J/mole
- h:
-
relative humidity, %
- J:
-
flux, kg/m2-s
- K′:
-
conductivity coefficient, kg/m-s-atm
- KM :
-
bound water conductivity coefficient, kg/m-s-%db
- K′M :
-
bound water conductivity coefficient, kg/m-s-%db
- Kμ :
-
conductivity coefficient, mole-s/m3
- M:
-
moisture content, %db
- mv :
-
molecular weight, kg/mole
- NA :
-
molar flux of component A, moles/m2-s
- NB :
-
molar flux of component B, moles/m2-s
- nb :
-
flux of bound water, kg/m2-s
- nv:
-
flux of water vapor, kg/m2-s
- P:
-
water vapor pressure, Pa
- Pt :
-
total gas pressure, Pa
- Q* :
-
thermal heat of transfer, atm
- R:
-
gas constant, J/mole-K (or cal/mole-K)
- S:
-
molar entropy, J/mole-K
- T:
-
temperature, K
- V:
-
molar volume, m3/mole
- x:
-
spatial coordinate, m
- α:
-
attenuation factor for vapor diffusivity in wood, dimensionless
- ε:
-
void fraction of wood, dimensionless
- μ:
-
chemical potential, J/mole
- μ′:
-
chemical potential, atm
- μb :
-
chemical potential, J/kg
- μv :
-
chemical potential, J/kg
- μ 01 :
-
chemical potential of water vapor at the saturated pressure at temperature T, J/mole
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Stanish, M.A. The roles of bound water chemical potential and gas phase diffusion in moisture transport through wood. Wood Sci.Technol. 20, 53–70 (1986). https://doi.org/10.1007/BF00350694
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DOI: https://doi.org/10.1007/BF00350694