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Triphasic Model of Heat and Moisture Transport with Internal Mass Exchange in Paperboard

Alexandersson, Marcus LU ; Askfelt, Henrik LU and Ristinmaa, Matti LU (2016) In Transport in Porous Media 112(2). p.381-408
Abstract
Mixture theory is used to derive a triphasic model to describe processes in paperboard consisting of solid fiber, bound water and gas. The gas is viewed as a miscible mix of the two constituents dry air and water vapor. The governing equations are mass conservation laws for bound water, dry air, water vapor, and mixture energy balance. Constitutive relations are found by exploiting the macroscale dissipation inequality. Resulting constitutive equations include Fickian diffusion of water vapor and dry air, Darcian flow for gas and Fourier heat conduction for the mixture. Mass exchange between bound water, and water vapor due to adsorption/desorption is driven by the difference in chemical potential. The interaction function is based on... (More)
Mixture theory is used to derive a triphasic model to describe processes in paperboard consisting of solid fiber, bound water and gas. The gas is viewed as a miscible mix of the two constituents dry air and water vapor. The governing equations are mass conservation laws for bound water, dry air, water vapor, and mixture energy balance. Constitutive relations are found by exploiting the macroscale dissipation inequality. Resulting constitutive equations include Fickian diffusion of water vapor and dry air, Darcian flow for gas and Fourier heat conduction for the mixture. Mass exchange between bound water, and water vapor due to adsorption/desorption is driven by the difference in chemical potential. The interaction function is based on equilibrium considerations for the bound water–water vapor system. From the description of the sorption isotherm, expressions for net isosteric heat and free energy related to water–fiber interaction are derived. The resulting thermodynamically consistent model is used to simulate moisture and heat dynamics for paperboard rolls. Simulation results are presented for a paperboard roll with anisotropic material properties subjected to a change in ambient relative humidity from 50 to 80 %. (Less)
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author
organization
publishing date
type
Contribution to journal
publication status
published
subject
in
Transport in Porous Media
volume
112
issue
2
pages
28 pages
publisher
Kluwer
external identifiers
  • scopus:84961203069
  • wos:000372878500004
ISSN
0169-3913
DOI
10.1007/s11242-016-0651-9
language
English
LU publication?
yes
id
1559ea90-d91e-45c0-a691-ad9b5c717f6a
date added to LUP
2016-05-16 13:38:09
date last changed
2017-03-05 04:33:56
@article{1559ea90-d91e-45c0-a691-ad9b5c717f6a,
  abstract     = {Mixture theory is used to derive a triphasic model to describe processes in paperboard consisting of solid fiber, bound water and gas. The gas is viewed as a miscible mix of the two constituents dry air and water vapor. The governing equations are mass conservation laws for bound water, dry air, water vapor, and mixture energy balance. Constitutive relations are found by exploiting the macroscale dissipation inequality. Resulting constitutive equations include Fickian diffusion of water vapor and dry air, Darcian flow for gas and Fourier heat conduction for the mixture. Mass exchange between bound water, and water vapor due to adsorption/desorption is driven by the difference in chemical potential. The interaction function is based on equilibrium considerations for the bound water–water vapor system. From the description of the sorption isotherm, expressions for net isosteric heat and free energy related to water–fiber interaction are derived. The resulting thermodynamically consistent model is used to simulate moisture and heat dynamics for paperboard rolls. Simulation results are presented for a paperboard roll with anisotropic material properties subjected to a change in ambient relative humidity from 50 to 80 %.},
  author       = {Alexandersson, Marcus and Askfelt, Henrik and Ristinmaa, Matti},
  issn         = {0169-3913},
  language     = {eng},
  number       = {2},
  pages        = {381--408},
  publisher    = {Kluwer},
  series       = {Transport in Porous Media},
  title        = {Triphasic Model of Heat and Moisture Transport with Internal Mass Exchange in Paperboard},
  url          = {http://dx.doi.org/10.1007/s11242-016-0651-9},
  volume       = {112},
  year         = {2016},
}