Invasion Percolation with a Hardening Interface under Gravity

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 15 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 17 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 19 site and can not 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 21 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 23 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. 25