Direct comparison of hydraulic tortuosity and electric tortuosity based on finite element analysis

Tortuosity is one of the key parameters to characterize the transport properties of porous media. There are many models for tortuosity estimation based on some definitions: geometric, hydraulic, electric, and diffusive definitions. However, relationships among those tortuosities remain unclear due to the lack of direct comparison on the same porous media. Here we focus on hydraulic and electric tortuosities and have conducted a series of finite element simulations with the Navier–Stokes equation and the equation for electric current to directly compare tortuosities. The results revealed that: (1) on average, hydraulic tortuosity is 15% greater than that of the electric one; (2) the proposed model based on the van Genuchten-type function successfully approximates both hydraulic and electric tortuosities; (3) tortuosities obtained from the porous media packed with circular particles and square particles show quantitatively similar trends.