Tortuosity-Porosity Relationships: Review of Empirical Data from Literature

Abstract It is generally assumed that transport resistance in porous media, which can also be expressed as tortuosity, correlates somehow with the pore volume fraction. Hence, mathematical expressions such Bruggeman relation (i.e., τ 2 = ε −1/2 ) are often used to describe tortuosity ( )—porosity relationships materials. In this chapter, validity of critically evaluated based on empirical data from literature. More than 2200 datapoints – couples) collected 69 studies media transport. When analysed separately for different material types (e.g., battery electrodes, SOFC sandstones, packed spheres etc.), resulting versus —plots do not show clear trend lines, could a expression. Instead, materials strongly scattered distributions rather ill-defined ‘characteristic’ fields. Overall, those characteristic fields overlapping, means characteristics cannot separated clearly. types, much more consistent pattern becomes apparent. observed − indicates measured values depend involved type tortuosity. A relative order then For example, direct geometric and mixed tortuosities concentrated relatively narrow band close line, typically < 2. contrast, indirect higher values, they scatter over larger range. Based analysis data, detailed very among established. The main conclusion chapter thus value specific material, dependent it its microstructure. illustrates strictly bound porosity. As decreases, scattering observed. Consequently, any expression aims provide generalized description must questioned. short section provided discussion limitations relationships. This includes rare special cases, use justified.