  Using numerical simulations and analytical approximations we study a modified
version of the two-dimensional lattice model [R. Piasecki,phys. stat. sol. (b)
209, 403 (1998)] for random pH:(1-p)L systems consisting of grains of high
(low) conductivity for H-(L-)phase, respectively. The modification reduces a
spectrum of model bond conductivities to the two pure ones and the mixed one.
The latter value explicitly depends on the average concentration gamma(p) of
the H-component per model cell. The effective conductivity as a function of
content p of the H-phase in such systems can be modelled making use of three
model parameters that are sensitive to both grain size distributions, GSD(H)
and GSD(L). However, to incorporate into the model information directly
connected with a given GSD, a computer simulation of the geometrical
arrangement of grains is necessary. By controlling the polydispersity in grain
sizes and their relative area frequencies, the effective conductivity could be
raised or decreased and correlated with gamma(p). When the phases are
interchanged, a hysteresis-loop-like behaviour of the effective conductivity,
characteristic of dual media, is found. We also show that the topological
non-equivalence of the system's microstructure accompanies some GSDs, and it
can be detected by the entropic measure of the spatial inhomogeneity of model
cells.
