An analytical model for gas diffusion though nanoscale and microscale fibrous media

Gas diffusion in nanofibrous and microfibrous materials is of great interest in microfluidics. In this work, an analytical model is proposed, based on fractal theory, to quantify gas diffusion across fibrous media composed of nanofibers and microfibers. The fractal model is expressed in terms of pore area and tortuosity fractal dimensions, allowing statistical quantification of the geometrical structures of fibrous media. Knudsen diffusion in nanoscale pores is considered. To validate this model, moisture vapor diffusion rate through electrospun nanofibrous webs was measured using the inverted-cup method. The diffusivities predicted from the proposed model agree well with the experimental measurements in the present investigation and those reported in the literature for effective diffusivities of gas diffusion layers in fuel cells. Based on the model, the effect of porosity, fiber radius, and the ratio between the minimum and the maximum pore sizes on the effective diffusivity is analyzed.