Analytical Solution of a Gas Release Problem considering Permeation with Time-Dependent Boundary Conditions

Abstract

Abstract In preparation for determining material properties such as Sieverts’ constant (solubility) and diffusivity (transport rate) we give a detailed discussion on a model describing some gas release experiment. Aiming to simulate the time-dependent hydrogen fluxes and concentration profiles efficiently, we provide an analytical solution for the diffusion equations on a cylindrical specimen and a cylindrical container for three boundary conditions (B.C.). These (B.C.) occur in three phases – loading phase, evacuation phase and gas release phase. In the loading phase the specimen is charged with hydrogen assuring a constant partial pressure of hydrogen. The gas will be quickly removed in the second phase, in the third phase, the hydrogen is released from the specimen to the gaseous phase. The diffusion equation in each phase is a simple homogeneous equation. Due to the complex time-dependent (B.C.), we transform the homogeneous equations to the non-homogeneous ones with a zero Dirichlet (B.C.). Compared with the time consuming numerical methods our analytical approach has an advantage that the flux of desorbed hydrogen can be explicitly given and therefore can be evaluated efficiently. Our analytical solution also assures that the (B.C.) are exactly satisfied. The interaction between specimen and container is taken into account.