  We propose a modified Invasion Percolation (IP) model to simulate the
infiltration of glue into a porous medium under gravity in 2D. Initially, the
medium is saturated with air and then invaded by a fluid that has a hardening
effect taking place from the interface towards the interior by contact with the
air. To take into account that interfacial hardening, we use an IP model where
capillary pressures of the growth sites are increased with time. In our model,
if a site stays for a certain time at interface, it becomes a hard site and
cannot be invaded anymore. That represents the glue interface becoming hard due
to exposition with the air. Buoyancy forces are included in this system through
the Bond number which represents the competition between the hydrostatic and
capillary forces. We then compare our results with results from literature of
non-hardening fluids in each regime of Bond number. We see that the invasion
patterns change strongly with hardening while the non-hardening behavior
remains basically not affected.
