A fractal model for gaseous leak rates through contact surfaces under non-isothermal condition

There often exists some gas leakage from defects/micro-pores between two contacting surfaces even they are welded together, which have been shown to be usually rough and fractal. In this work, the region between two contacting surfaces is considered as a porous medium, and then a fractal model for gaseous leak rate through the contacting surfaces under non-isothermal condition is derived based on the Darcy law and diffusion theory. The proposed model for the pressure-driven gas flow flux affected by temperature is expressed as a function of porosity, the fractal dimensions and temperature. Every parameter in the proposed model has clear physical meaning. The model predictions are compared with the available experimental data, and good agreement between them is obtained.