Post-nucleation conversion of an air bubble to clathrate air-hydrate crystal in ice

We present an attempt to model the process of conversion of an air bubble, trapped in ice, to clathrate air-hydrate crystal after its nucleation on the air-ice interface. Both counterparts of the transformation are considered: diffusion of interstitial water and air molecules through the growing hydrate layer that coats the bubble surface, and compressive deformation of the three-phase lair-hydrate-ice) system at a given temperature and load pressure. The mathematical model is constrained by laboratory experiments covering a wide range of thermodynamic conditions. Computational tests show that either diffusion or bubble compression can be the rate-limiting step in the post-nucleation growth of air-hydrate crystal. As a plastic material, air-hydrate appears to be, at least, one order harder than ice. The mass transfer coefficient for the diffusion of air and water molecules in air-hydrate is estimated to be 0.6-1.3 mm(2)/yr at 263 K with the activation energy not higher, than 30-50 kJ/mol. The mass flux of air, although small in comparison with that of water, plays an important role in the conversion. Special attention is paid to the case of air-hydrate growth in air bubbles in polar ice sheets. (C) 1998 Elsevier Science B.V. All rights reserved.