The determination of relative path length as a measure for tortuosity in compacts using image analysis

Tortuosity is defined as the ratio of the actual path length from start to goal through the pores to the Euclidean distance (shortest linear distance). However, traditional methods to calculate tortuosity, such as the calculation of tortuosity out of the results from dissolution experiments, do not determine path length directly. In this paper we describe the application of image analysis for direct measurement of path length in order to obtain quantitative information on tortuosity. Several planes in cubic sodium chloride compacts, made by uni-axial compression, were imaged using scanning electron microscopy (SEM). In these images the average path length from top-to-bottom and from left-to-right was calculated, using the gray-weighted distance transform (GDT). As the direct, straight forward path was defined as having a length of unity, the relative path length could be taken as a quantitative measure for the tortuosity. The relative path length through the pores was found to be 1.4-1.6 and the relative path length over the grains was significantly lower (1.0-1.2). In most cases, the relative path length through the pores was significantly higher for the compacts containing small particles than for the compacts made of large particles. The relative path length was also dependent on the direction of the measurement, i.e. in the direction of compression of the compact or perpendicular to it. This indicates anisotropy in structure with the pores preferentially oriented in the direction of compression. It was concluded that this method is a valuable tool for the determination of path length in compacts as a direct measure for tortuosity. It can also be used to evaluate the anisotropy in structure.