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

David Cohen, T. W. Patzek, Clayton Radke*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

23 Scopus citations


In order to use foams in subsurface applications, it is necessary to understand their stability in porous media. Diffusion-driven coarsening of a stationary or nonflowing foam in a porous medium results in changing gas pressures and a coarsening of the foam texture. 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. An hourglass approximates the shape of the pores, and the pore walls are considered to be highly water wet. A singularity arises in the system of differential algebraic equations due to the curvature of the pore walls. This singularity is a signal that the system must undergo oscillations or sudden lamellar rearrangements before the diffusion process can continue. 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. Gas bubbles in pore throats are regions of encapsulated pressure. As gas is released from these bubbles during diffusion, the pressure of the bubbles in the pore bodies increases. When the pressure increase is scaled by the characteristic Young-Laplace pressure, the equilibrium time for the diffusion process is scaled by the ratio of the square of the characteristic length to the gas diffusivity and two dimensionless groups. One describes the ease with which gas can diffuse through a lamella, and 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.

Original languageEnglish (US)
Pages (from-to)357-373
Number of pages17
JournalJournal of colloid and interface science
Issue number2
StatePublished - May 10 1996

Bibliographical note

Funding Information:
This work was partially funded by the Assistant Secretary for Fossil Energy, Office of Oil, Gas, and Shale Technologies of the U.S. Department of Energy under Contract DE-AC03-76SF00098 to Lawrence Berkeley National Laboratory. Additional funding was provided by the U.S. Bureau of Mines through a fellowship received by David Cohen from the California Mining and Mineral Resources Research Institute, Grant G1114106.


  • diffusion
  • foam
  • network simulation
  • porous media

ASJC Scopus subject areas

  • Electronic, Optical and Magnetic Materials
  • Biomaterials
  • Surfaces, Coatings and Films
  • Colloid and Surface Chemistry


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