Stability of bubbles in a linear elastic medium: Implications for bubble growth in marine sediments

Methane bubbles in muddy fine-grained sediments grow initially through a process of elastic expansion, punctuated by discrete fracture events (LEFM-growth). The ability of the surrounding sediments to support a stress and actively resist expansion can, under conditions of low gas production or high sediment toughness, result in the cessation of growth and the presence of stable bubbles. Thus, it is possible for a bubble to stop growing despite the presence of a source in the sediments that continues to produce gas. This contrasts with growth of bubbles in a fluid medium, which cannot support a stress and so will continue to grow as long as a surrounding source provides gas. This "no-growth" condition is the result of the coupling between gas supply (methane production or supersaturation) and the sediment mechanics. Here we quantify this condition and present a criterion for the switch between no-growth and the LEFM growth regimes. We apply this theory to the sediments of Eckernforde Bay, in the Kiel Bight, Germany, and despite the absence of measurements for the key sediment mechanical properties, we can provide a qualitative explanation for the sizes and shapes of the observed bubble population with depth in the sediment. We also show how the release of hydrostatic pressure can stimulate growth, by pushing otherwise stable bubbles into the LEFM growth regime. This could provide a mechanism for the release of bubbles during periods of low water, such as during low tide or wave events.