Two-dimensional network simulation of diffusion-driven coarsening of foam inside a porous medium

摘要

A two-dimensional network simulation has been created that predicts the behavior of foam in a porous medium by physically specifying the locations of all the lamellae in the system and by solving the complete set of Young-Laplace and diffusion equations. A singularity arises in the system of differential algebraic equations due to the curvature of the pore walls. Newton-Raphson iteration is used along with Keller's method of arc-length continuation and a new jump resolution technique to locate and resolve bifurcations in the system of coupled lamellae. As gas is released from these bubbles during diffusion, the pressure of gas bubbles in the pore bodies increases. One dimensionless group describes the ease with which gas can diffuse through a lamella, the second represents the amount of gas encapsulated within the pore throats initially. Given this scaling, the resulting plots of pressure versus time and normalized lamellae positions versus time are universal for all system sizes and characteristics. This is true as long as the initial lamella distribution is the same in each case.