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.

结果表明，可以使用分形理论开发开孔金属泡沫的渗透率和有效热导率的分析模型，因为该理论更适合于手头的问题，其中泡沫的孔隙形态通常是随机的。在基于泡沫的代表性结构 (RS) 中选定的代表性流动流线确定平均弯曲度后，通过分析获得作为孔隙率、平均弯曲度和孔径比的函数的渗透率，无需经验或拟合参数。同样，有效热导率的分析分形模型不包括任何经验或拟合参数。与实验数据的良好一致性验证了两种模型，正好证明了使用分形理论来表征开孔金属泡沫的适用性。还表明，与以前建立在简化几何结构（包括周期性分布的晶胞）上的渗透率和电导率模型相比，当前的分形模型可以更好地表征孔隙分布的随机性。