Processes governing meltwater penetration into cold firn remain poorly constrained. Here, in situ experiments are used to develop a grain-scale model to investigate physical limitations on meltwater infiltration in firn. At two sites in Greenland, drilling pumped water into cold firn to >75 m depth, and the thermo-hydrologic evolution of the firn column was measured. Rather than filling all available pore space, the water formed perched aquifers with downward penetration halted by thermal and density conditions. The two sites formed deep aquifers at ~40 m depth and at densities considerably less than the air pore close-off density (~725 kg m−3 at −18°C, and ~750 kg m−3 at −14°C), demonstrating that some pore space at depth remains inaccessible. A geometric grain-scale model of firn is constructed to quantify the limits of a descending fully saturated wetting front in cold firn. Agreement between the model and field data implies the model includes the first-order effects of water and heat flow in a firn lattice. The model constrains the relative importance of firn density, temperature and grain/pore size in inhibiting wetting front migration. Results imply that deep infiltration, including that which leads to firn aquifer formation, does not have access to all available firn pore space.