On the effective diffusion in the Sierpinski carpet

摘要

In this work, we use the method of volume averaging to upscale the pore-scale diffusion equation on the Sierpinski carpet. Based on the isotropy condition in the fractal structure and the fact that the ratio of length scales in the Sierpinski carpet is constant, a general expression for the effective diffusion coefficient regarding the iteration of the fractal structure is suggested. Additionally, a general expression is recommended when such a ratio is not constant. The comparison between the direct numerical simulations and the results obtained from the upscaled model suggests that using a simplified expression for the effective diffusion coefficient is an attractive option when simulating large-scale fractal systems.