Paper VT-MoA9
Modeling of Diffusion Processes in Vacuum Technology with Finite Element Method

Monday, October 20, 2008, 4:40 pm, Room 205

Diffusion of gasses is a frequent phenomenon in vacuum technology. Examples are: permeation of atmospheric gasses through parts of chamber wall (elastomeric seals and plastics), diffusion of dissolved hydrogen gas in a chamber wall and its evolution into vacuum, and permeation of gasses through membranes in permeation leak elements. The process can be mathematically represented with a diffusion equation, which is a second order partial differential equation. Its solutions depend on the geometry of the system and on initial and boundary conditions. Solutions can be found in analytical form for simple geometries and selected simple initial and boundary conditions only. Diffusion equation can be solved also numerically with finite element method (FEM). Numerical calculations can be applied for arbitrary initial and boundary conditions. In the presentation we will discuss a simple one dimensional case, which can be applied when the problem can be approximated with planar geometry. Numerical calculation of a time dependency of the concentration profile within the sample can be easily performed in a widely use spreadsheet program Excel. The reliability of FEM calculations was checked for a special case of initial and boundary conditions, when the analytical solution is known also. We will also present a practical example of FEM modeling of He gas flow into a vacuum system through a Viton gasket after short-time exposure to He at atmospheric side. Such problem is often observed when He leak detection is performed.