New formulas for the tortuosity factor of electrochemically conducting channels

Abstract

Abstract Porous composite mediums consisting of multiple interpenetrating percolating phases are widely used in electrochemical cells and batteries. The electrochemical species, for example electrons, ions, and gaseous molecules, are confined to transport within the specific conducting phase networks. Our ability to understand physical and chemical processes within these tortuous networks is often limited by the lack of suitable mathematical representation of their tortuosity factor. Thus, the quantitative formulation of tortuosity factor is urgently needed in this regard. From purely geometric perspectives, this work has proposed new formulas to calculate the tortuosity factor for a single conducting channel and a bundle of channels, using the coordinates of the channel central line and the channel radius distribution along the channel central line. The formulas are easy to use and statistically identical to the ideal value of tortuosity factor. The new formulas can serve as a practical tool for analysis and rational design of the three-dimensional conducting networks.