Pattern formation of freezing infiltration in porous media

Gravity-driven flow of water into unsaturated porous media can form preferential pathways due to the gravity fingering instability. Here, we consider this process in a subfreezing porous medium using numerical simulations. We find that the macroscopic infiltration rate can be well predicted by the freezing Damk\"ohler number. In contrast to the classical instability, the introduction of freezing in this problem gives rise to a new flow regime in which secondary flow pathways form in between the initial channels. This secondary instability homogenizes the otherwise channelized flow field and decreases the effective infiltration velocity.