Fractionation of soil gases by diffusion of water vapor, gravitational settling, and thermal diffusion

Abstract

Air sampled from the moist unsaturated zone in a sand dune exhibits depletion in the heavy isotopes of N 2 and O 2. We propose that the depletion is caused by a diffusive flux of water vapor out of the dune, which sweeps out the other gases, forcing them to diffuse back into the dune. The heavy isotopes of N 2 and O 2 diffuse back more slowly, resulting in a steady-state depletion of the heavy isotopes in the dune interior. We predict the effect's magnitude with molecular diffusion theory and reproduce it in a laboratory simulation, finding good agreement between field, theory, and lab. The magnitude of the effect is governed by the ratio of the binary diffusivities against water vapor of a pair of gases, and increases ~linearly with the difference between the water vapor mole fraction of the site and the advectively mixed reservoir with which it is in diffusive contact (in most cases the atmosphere). The steady-state effect is given by δ i = [ i / j i o / j o − 1 ] 10 3 ‰ ≅ [ ( 1 − x H 2 O 1 − x H 2 O 0 ) ( D j − H 2 O / D i − H 2 O ) − 1 − 1 ] 10 3 ‰ , where δ i is the fractional deviation in permil of the gas i/gas j ratio from the advectively mixed reservoir, x H 2O and x H 2O 0 are respectively the mole fractions of water vapor at the site and in the advectively mixed reservoir, and D i−H 2O is the binary diffusion coefficient of gas i with water vapor. The effect is independent of scale at steady state, but approaches steady state with the time constant of diffusion set by the length scale. Exploiting the mechanism, we make an experimental estimate of the relative diffusivities of O 2 and N 2 against water vapor, finding that O 2 diffuses 3.6 ± 0.3% faster than N 2 despite its greater mass. We also confirm in the study dune the presence of two additional known processes: gravitational fractionation, heretofore seen only in the unconsolidated firn of polar ice sheets, and thermal diffusion, well described in laboratory studies but not seen previously in nature. We predict that soil gases in general will exhibit the three effects described here, the water vapor flux fractionation effect, gravitational fractionation, and thermal diffusion. However, our analysis neglects Knudsen diffusion and thus may be inapplicable to fine-grained soils.