The motion of long bubbles in a network of tubes

The motion and interaction of discrete bubbles in porous materials is studi ed numerically using a network model. The goal is to extend analytical resu lts for the motion of bubbles through a single straight tube to a more 'rea listic' geometry for porous materials, modeled here as a planar network of straight tubes of different radii. The problem is characterized by two dime nsionless parameters, the capillary number (Ca) and the volume fraction of bubbles (phi); results are characterized by determining the effective perme ability of the network and the mean residence time of bubbles in the materi al. The simulations indicate that at low volume fraction most of the bubble s follow a limited number of high-flow pathways through the network. In thi s case the predictions of our simulations can be approximated by a simple a nalytical model. Bubbles interact with each other because their presence ch anges the local resistance to flow in individual tubes. As phi increases, i nteractions between individual bubbles become important resulting in a wide r range of residence times in the porous material.