  In this paper we develop a model to describe the diffusion process in a
porous medium. For the observed decrease in current yield, we propose other
causes than difference in diffusivity, which we consider unaltered by the
porous medium. The physical situation we try to model consists of systems of
reduced dimensions (~0.001-1.0 cm^3) with pores of sub micrometric dimension.
This is particularly suitable to represent organic structures or special cells
in electrochemical devices. We try to explore two basic contributions as an
answer for diffusion fading in porous medium, namely, the effect of the void
geometry and a dissipative process as well. This dissipative process is in the
kernel of our analysis and it is related to the heterogeneous fluctuations of
the flux lines occurring at the border among pores. To mimic biophysical and
electrochemical conditions we also include in our model a reactive process,
such migration of species do not need, necessarily, a pressure gradient because
of the reaction diffusion process. As usual, the mathematical description of
the phenomenon is introduced through the prescription of boundary and initial
conditions for a transport equation, however here we decouple the geometry from
the reaction-diffusion-convection problem examining a unitary conduct, in which
the fluid flows and that, replicated in the space, is able to generate the
entire system. We estimate the current transient provided by our model and
compare it to the one obtained by the process of controlled growth of metallic
inverse opals prepared by electrochemical crystallization of matter, so the
theoretical results can be compared with experimental data.
