A fractal model for gas permeation through porous membranes

Macro and micro porous membranes have been used in many industrial areas. The disordered nature of pore structures in these membranes suggests the existence of a fractal structure formed by the pores. Fractal theory is employed to build the permeation model through these porous membranes. The fractal dimensions for surface pore area and tortuosity of membrane is obtained by box-counting method. Contrary to previous studies which consider only the Poiseulle flow in pores, in this research, the model reflects two gas diffusion mechanisms simultaneously: when the Knudsen number is less than 0.01, the Poiseulle flow is dominant; while when the Knudsen number is greater than 10, the Knudsen flow is dominant; and when the Knudsen number is from 0.01 to 10, the two mechanisms coexist. Contact gas permeation experiments with three porous hydrophobic PVDF membranes are conducted to validate the model. Comparisons between the current model and those from references are made.