Nonuniform collective dissolution of bubbles in regular pore networks

We present the development of a mathematical model that describes the collective dissolution of gas bubbles in two-dimensional regular pore networks. The model is solved numerically by considering lattices with up to 169 bubbles and by evaluating the role of pore network connectivity, the presence of vacant sites and the initial bubble size distribution. In dense lattices, diffusive shielding prolongs the dissolution time of bubbles located in the centre of the lattice. The presence of the pore network enhances this effect, its strength depending on the network connectivity. For dense lattices, the extension of the final dissolution time relative to the unbounded (bulk) case can be approximated by the power-law function, B^k/l, where the constant l is the inter-bubble spacing, B is the number of bubbles and the exponent k depends on the network connectivity. Sparse bubble lattices experience decreased collective effect, as bubbles are further apart from each other. The results reveal that the evolution of the solute concentration field is both a consequence and a factor affecting bubble dissolution or growth. In fact, the geometry of the pore network perturbs the inward propagation of the dissolution front and generates vacant sites within the bubble lattice. This effect is enhanced by increasing the lattice size and decreasing the network connectivity, yielding strongly non-uniform solute concentration fields. The presence of an initial bubble size distribution leads to increasingly non-uniform dissolution time of the lattice, as a result of a solute concentration field that is nonuniform from the outset.