Fracture-Driven Single Bubble Grows and Migration Model in Aquatic Muds

Methane (CH$_4$) is the most prevalent hydrocarbon and a significant greenhouse gas found in the atmosphere. Buoyancy-driven CH$_4$ bubble growth and migration within muddy aquatic sediments are closely associated with sediment fracturing. This paper presents a model of buoyancy-driven CH$_4$ single bubble growth in fine-grained cohesive (muddy) aquatic sediment. * Solid mechanics model component simulates bubble elastic expansion caused by solute supply from the surrounding mud, followed by differential fracturing of the mud by the evolving bubble front, a process governed by the principles of Linear Elastic Fracture Mechanics (LEFM). This differential fracturing controls the evolving shape and size of the bubble. * The model integrates the LEFM with the dynamics of solute exchange between the bubble and the surrounding mud, alongside the conservation of CH$_4$ gas within the bubble. * An advanced meshing strategy allows balancing between the geometry resolution and the amount of mesh elements, thereby optimizing for both solution accuracy and computational efficiency. This model is intended to be a foundational tool for proper upscaling of single bubble characteristics to effective gassy medium theories. This will enhance the accuracy of the acoustic applications and could contribute to evaluation of overall CH$_4$ emission from the aquatic muds.