An Idealized Model of Buoyant Gas Spreading and Silt Release beneath Rough Cave Ceilings

Sandy Hardian Susanto Herho , Dasapta Erwin Irawan, Rusmawan Suwarman, Deny Juanda Puradimaja

Gas exhaled by open-circuit divers collects under the ceilings of submerged caves, migrates along the rock, and dislodges loose silt that then falls through the passage, a process that cave divers call percolation. This study develops an idealized model of the process. Buoyant gas under a self-affine rough ceiling is treated as a quasi-static sequence of pools that fill to their spill points, release gas that climbs to the next high point, and merge where their levels meet. Moving contact lines strip silt from the rock, and the released silt settles as a spectrum of grain sizes that reduces the distance at which a diver can see. The computation agrees exactly with an independent depression-filling algorithm, conserves gas volume to round-off, and reproduces the known exponents of invasion percolation in its capillary limit. A balance between the relief of the ceiling and its dip defines a pool scale that organizes where gas collects, and the area covered by gas from a single source grows more slowly than the volume supplied, as predicted by the self-affine geometry. The cutoff at the pool scale is soft, so large pools persist on steeper ceilings than the scale alone would suggest. In a reference passage, the lead diver of a team releases far more silt than the diver behind, and a team releases far less than the sum of its members acting alone, because the lead diver fills the pools and strips the paths that later divers reuse. This ordering holds across every detachment efficiency and ceiling geometry tested. Visibility toward the exit at eye level continues to decline for an hour or more after a team has passed, as fine silt descends from a nearly opaque layer beneath the ceiling. Absolute silt masses and sighting ranges depend on quantities that have not been measured in caves, and the results are best read as scaling relations and comparisons between scenarios.