Pore structure and conductivity modelled by bidisperse ballistic deposition with relaxation

A complex pore structure, as found in natural materials, can be generated by a simple algorithm which 'deposits' grains of two different sizes on a cubic lattice. A relaxation process allows the grains to be rearranged in a more stable configuration. The proportion in which the two different types of grains are mixed determines the pore structure. In this work we calculate the conductivity of the porous material when a conducting fluid fills the pore space and the solid matrix is insulating. We find that in the relaxed bidisperse ballistic deposition model the porosity and conductivity vary non-monotonically with the fraction of small-sized grains. Both properties show maxima, which moreover do not coincide. An explanation is offered from the analysis of the details of the pore geometry, such as the backbone mass and the chord length distribution.