Modeling has become an instrumental tool is the design and development of electrochemical systems. Multiple length and time scales are treated, but perhaps the most import and well developed models are macrohomogeneous physical models. These are typified by the porous electrode models advanced by Newman and others. These porous electrode models have been applied with great success to a variety of batteries, fuel cells, and double layer capacitors. The detailed geometry isn’t used, but instead effective transport properties account for the reduction in the magnitudes of diffusivities and conductivities. These effective transport properties are measured experimentally or often estimated using the Bruggeman relationship.

It has been well documented that the Bruggeman relationship is far from universal. These limitations are not unexpected considering the basis for the relationship between porosity and tortuosity. It should be clear that a simple relationship is not adequate. Consider, for instance shape changes in the electrode of battery undergoing cycling. The porosity may be unchanged, but effective transport properties vary. The Bruggeman relationship cannot explain this behavior.

Although the community generally agrees upon the concept of tortuosity, the ratio of effective path length to thickness of material through which transport occurs, multiple mathematical definitions exist. These descriptions are explored here. From the detailed geometry, the reverse problem can be solved, namely calculate and effective transport property and then calculate tortuosity from .

More recently, computation tools and methods to image electrode have improved dramatically. There are still many challenges, but more and more detailed geometries of electrodes are becoming available. Focused-ion-beam techniques combined with scanning electron microscopy (FIB/SEM) is such an example. Resolution on the order of tens of nanometers is routine. These developments allow us to begin to answer questions such as how to bridge length-scales between molecular dynamic and macroscopic models? Can we calculate a property of the porous media akin to a tortuosity that is both well-defined and relevant to the effective transport properties that we seek for the macroscopic models? These questions are explored through an example of the corrosion of the cathode of a PEM fuel cell.