Fig. 11: The schematic representation of the 1D spherical IK model, where bubbles are assumed to be uniformly distributed within the matrix.

The blue sphere (\({\Omega }_{{\rm{b}}}\)) represents the 1D bubble, while the grey region (\({\Omega }_{{\rm{s}}}\)) represents the diffusion domain. The boundaries \(\partial {\Omega }_{{\rm{b}}}\) and \(\partial {\Omega }_{{\rm{s}}}\) correspond to the bubble surface and the simulation domain boundary, respectively. \({{\rm{R}}}_{{\rm{b}}}\) and \({{\rm{R}}}_{{\rm{f}}}\) denote the average bubble radius and half of the average distance between bubbles, respectively.