Traveling wave solutions in a generalized theory for macroscopic capillarity

O. Hönig, F. Doster*, R. Hilfer

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

4 Citations (Scopus)


One-dimensional traveling wave solutions for imbibition processes into a homogeneous porous medium are found within a recent generalized theory of macroscopic capillarity. The generalized theory is based on the hydrodynamic differences between percolating and nonpercolating fluid parts. The traveling wave solutions are obtained using a dynamical systems approach. An exhaustive study of all smooth traveling wave solutions for primary and secondary imbibition processes is reported here. It is made possible by introducing two novel methods of reduced graphical representation. In the first method the integration constant of the dynamical system is related graphically to the boundary data and the wave velocity. In the second representation the wave velocity is plotted as a function of the boundary data. Each of these two graphical representations provides an exhaustive overview over all one-dimensional and smooth solutions of traveling wave type, that can arise in primary and secondary imbibition. Analogous representations are possible for other systems, solution classes, and processes.

Original languageEnglish
Pages (from-to)467-491
Number of pages25
JournalTransport in Porous Media
Issue number3
Publication statusPublished - Sept 2013


  • Capillarity
  • Multiphase flow
  • Porous media
  • Traveling waves

ASJC Scopus subject areas

  • Chemical Engineering(all)
  • Catalysis


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