Abstract
In this work, we focus on the experiments of permeation in order to characterise the transport coefficients and how they depend on the gas concentration. First, a physical and mathematical modelling approach is presented. Two models are used in order to describe the diffusion of gases in polymers. The mathematical modelling leads thereafter to the construction of an unusual optimisation problem. A work complementary to this approach relates to the study of parameter sensitivity, which characterises the coefficient of diffusion and the maximum gas concentration, unknown in the permeation tests. This method of optimisation does not depend on the initialisation of the parameters and makes it possible to determine a unique set of parameters.
Highlights
The understanding of the mechanisms of damage in polymer sheaths during gas decompression passes by the knowledge of the gas transport phenomena in polymers, by the study of the influence of gas absorption on material properties, and by modelling the material behaviour during a decompression
When the interactions between the polymer chains and the gas molecules are strong, for example, during the diffusion of carbon dioxide (CO2) in fluoride polymers, the diffusion coefficient depends on the gas concentration inside the material
The optimal values, which minimise the difference between the experimental values of the quantity of gas crossing the polymer and the corresponding numerical results, are presented
Summary
The understanding of the mechanisms of damage in polymer sheaths during gas decompression passes by the knowledge of the gas transport phenomena in polymers, by the study of the influence of gas absorption on material properties, and by modelling the material behaviour during a decompression. The mathematical theory of diffusion (Crank, 1968) in an isotropic system is based on the assumption of proportionality between the diffusing flow of molecules (that is the quantity of species that cross a membrane by unit of time and surface) and the concentration gradient between both faces of the membrane. It is Fick’s first law: J = −D ∂C ∂x (1). In the case of a polymer-gas system, Relation (3) links the coefficient of diffusion to thermodynamical variables of the system:
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