Analytical Solution for the Population-Balance Model Describing Foam Displacement

Rosmery Q. Zavala, Luis F. Lozano, Pacelli L.J. Zitha, Grigori Chapiro*

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

3 Citations (Scopus)


We investigate and classify possible analytical solutions for a simplified version of the foam bubble population model, by varying injection conditions and kinetic foam generation parameter. We prove that the behavior of the analytical solutions changes at the transition between two regions, similar to rarefaction-shock solutions for the Buckley-Leverett equation. In one region (region I), the solutions are in the form of traveling waves, in rather good agreement with CT scanned foam experiments and numerical simulations reported in Simjoo and Zitha (2015). In region II, however, corresponds to solutions as a sequence of waves: one spreading wave and one traveling wave. These corresponding flow profiles are different from those found so far in the experiments.

Original languageEnglish
Pages (from-to)211-227
Number of pages17
JournalTransport in Porous Media
Issue number1
Publication statusPublished - 2021


  • Foam flow
  • Partial Differential Equations
  • Porous media
  • Traveling waves


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