Non-monotonic trapping of air clusters during imbibition into dry granular media

Imbibition of wetting fluids displacing nonwetting fluids through granular media yields complex patterns with entrapment of the nonwetting phase, yet how pore-space geometry modulated by grain packing controls this retention remains insufficiently understood. This study combines Hele-Shaw experiments, pore-scale theory, and simulations to investigate air trapping during imbibition of viscous liquids into a dry monolayer of monodisperse beads. Capillary-controlled invasion exhibits an irregular non-monotonic variation in trapped-air content across packing densities from loose (φ = 0.75) to dense (φ = 0.85), peaking unexpectedly at the intermediate packing of φ = 0.80 with maximal cluster fragmentation. This non-monotonicity arises from a packing-dependent competition in the dominant pore-scale trapping mechanisms: loose packings favor by-passing of larger pore bodies, whereas dense packings promote the snapped-off blob formation within the limited pore geometry. Mapping our theoretical thresholds (hydrodynamic capillary number Cabyp, Casnp, and geometric channel-radius ratio k, pore-throat aspect ratio λsnp) onto the experimental packing conditions identifies a cooperative window near φ ≈ 0.80 in which both trapping mechanisms are concurrently active, consistent with simulations of the elementary interfacial events including preferential channel outpacing, corner-film swell, and pinch-off—these results elucidate the critical role of grain packing in regulating fluid retention in porous media applications.