Analytical fractal models for permeability and conductivity of open-cell metallic foams

It is demonstrated that analytical models of permeability and effective thermal conductivity for open-cell metallic foams can be developed using fractal theory, for the theory lends itself better to the problem at hand where the pore morphology of the foam is typically random. Upon determining the average tortuosity based on selected representative flow streamlines in a representative structure (RS) of the foam, the permeability as a function of porosity, average tortuosity and pore size ratio is analytically obtained, with no empirical or fitting parameter needed. Similarly, the analytical fractal model of effective thermal conductivity does not include any empirical or fitting parameter. Good agreement with experimental data verifies both models, squarely justifying the applicability of using fractal theory to characterize open-cell metallic foams. It is also demonstrated that the present fractal models can better characterize the randomness of pore distributions than previous permeability and conductivity models built upon simplified geometries including periodically distributed unit cells.