Journal of Materials Science

, Volume 53, Issue 12, pp 9076–9090 | Cite as

Water vapour permeation through high barrier materials: numerical simulation and comparison with experiments

  • A. Batard
  • E. Planes
  • T. Duforestel
  • L. Flandin
  • B. Yrieix


The long-term thermal performance of vacuum insulation panels (VIP) is brought by the capacity of their barrier envelope to maintain the core material under vacuum. This study is focused on the detailed modelling of gas transfer through the defects of aluminium-coated polymer films used for VIPs’ envelopes. The 3D simulations were performed with monolayer and multilayer metal-coated polymer films. They have been carried out in dynamic conditions with the SYRTHES® software developed by EDF R&D. The results show that the water vapour and air permeations through a monolayer film slightly depend on the polymer substrate thickness, diffusivity and solubility, but primarily, on the defects geometry and arrangement. Regarding multilayer films, the permeation can be deduced from the ideal laminate theory. We are now able to provide and operate a numerical model, which can calculate the permeance of monolayer or multilayer metallized polymer films as a function of the coating quality and the geometry of the layers. Even if calculated permeances are ten times higher than measurements, this study improves our understanding of gas transports through VIPs’ barrier envelope and allows to manage more efficiently the relations between the films microstructures and their overall permeability. This paper is split into 6 parts: physical phenomena, methodology and modelling tools, simulation results, experiments and model validation and then, discussion and conclusion.

List of symbols

Greek letters

\(\lambda \)

Thermal conductivity (\(\hbox {W}\,\hbox {m}^{-1}\,\hbox {K}^{-1}\))

\(\phi _i\)

Mass flux density of gas i (\(\hbox {kg}\,\hbox {s}^{-1}\))

\(\Pi _i\)

Permeance to the gas i (\(\hbox {kg}\,\hbox {m}^{-2}\,\hbox {s}^{-1}\,\hbox {Pa}^{-1}\))

\(\rho \)

Density (\(\hbox {kg}\,\hbox {m}^{-3}\))

Other symbols

\(\emptyset \)

Defect diameter (m)

Physical constants


Boltzmann’s constant (\(1.381\times 10^{-23}\,\hbox {J}\,\hbox {K}^{-1}\))


Specific gas constant of gas i (\(\hbox {J}\,\hbox {kg}^{-1}\,\hbox {K}^{-1}\))

Roman letters


Concentration of a gas i (\(\hbox {kg}\,\hbox {m}^{-3}\))


Specific heat capacity (\(\hbox {J}\,\hbox {kg}^{-1}\,\hbox {K}^{-1}\))


Knudsen coefficient (\(\hbox {m}^2\,\hbox {s}^{-1}\))


Diffusion coefficient of gas i in material j (\(\hbox {m}^2\,\hbox {s}^{-1}\))


Polymer thickness (m)


Surface fraction of defects (%)


Scale factor (–)


Distance between defects (m)


Barrier complex’s thickness (m)


Molecular mass of gas i (kg)


Partial pressure of gas i (Pa)


Solubility coefficient of gas i in material j (\(\hbox {kg}\,\hbox {m}^{-3}\,\hbox {Pa}^{-1}\))


Temperature (K)



The authors gratefully acknowledge the collaborators of the Project EMMA-PIV (No. ANR 12-VBDU-0004-01) that includes this research and also the National Research Agency (ANR) for his financial support. Thanks also to the “Consortium des Moyens Technologiques Communs” (CMTC, 38, France) for his contribution to the SEM observations. This work is performed within the framework of the Centre of Excellence of Multifunctional Architectured Materials “CEMAM” No. AN-10-LABX-44-01.


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© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.EDF R&D, ENERBATEDF Lab Les RenardièresMoret-Loing-et-OrvanneFrance
  2. 2.LEPMI, LMOPSUniversité de SavoieLe Bourget-du-LacFrance
  3. 3.EDF R&D, MMCEDF Lab Les RenardièresMoret-Loing-et-OrvanneFrance

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