A dynamical systems approach for the contact-line singularity in thin-film flows

Fethi Ben Belgacem, Manuel V. Gnann*, Christian Kuehn

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

13 Citations (Scopus)


We are interested in a complete characterization of the contact-line singularity of thin-film flows for zero and nonzero contact angles. By treating the model problem of source-type self-similar solutions, we demonstrate that this singularity can be understood by the study of invariant manifolds of a suitable dynamical system. In particular, we prove regularity results for singular expansions near the contact line for a wide class of mobility exponents and for zero and nonzero dynamic contact angles. Key points are the reduction to center manifolds and identifying resonance conditions at equilibrium points. The results are extended to radially-symmetric source-type solutions in higher dimensions. Furthermore, we give dynamical systems proofs for the existence and uniqueness of self-similar droplet solutions in the nonzero dynamic contact-angle case.

Original languageEnglish
Pages (from-to)204-235
Number of pages32
JournalNonlinear Analysis, Theory, Methods and Applications
Publication statusPublished - 1 Oct 2016
Externally publishedYes


  • Boundary-value problem
  • Center manifolds
  • Contact line
  • Resonances
  • Self-similar solution
  • Thin film equation


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