Modeling the effective conductivity of the solid and the pore phase in granular materials using resistor networks

To model the effective conductivity of the solid and the pore phase of a lithium-ion battery (UB) we make use of the resistor network method (RN). We recall the scheme on how resistor networks can generally be set up and numerically solved. Furthermore, we explain how this general method can be applied to an assembly of spherical particles where for the individual resistances between touching particles an analytical formula is being used. As a new feature, we use the same scheme to setup resistor networks for the pore phase of an assembly of spherical particles where we propose a simple geometric approach for the calculation of the individual resistances of pore throats. For the validation of this method we created several random particle structures with different size distributions and calculated effective conductivities with both the RN and the finite element method (FEM). On the one hand, the comparison between RN and FEM shows a very good performance of the RN because the mean error lies within 4%. On the other hand, the RN results always lie within the well-known theoretical bounds for the effective conductivity in porous media. As an important aspect, the RN has proven to be highly efficient concerning the computation time and the resource costs. (C) 2019 Published by Elsevier B.V.