Thin film flow over flexible membranes containing surface texturing: bio-inspired solutions

Y. C. Lee, H. M. Thompson, P. H. Gaskell

Research output: Contribution to journalArticlepeer-review

12 Citations (Scopus)


Gravity-driven continuous thin liquid film flow over a flexible membrane containing surface topography is modelled using lubrication theory. The associated coupled non-linear equation set, for the film thickness, pressure and membrane deflection, is solved using a state-of-the-art full approximation storage multi-grid algorithm with automatic mesh refinement and adaptive time-stepping, in order to maximize computational efficiency when fine-scale resolution is required while ensuring accurate mesh-independent solutions at the micro-scale. The robustness of the approach is demonstrated through the solution of a series of problems and comparisons drawn with the same flow on an equivalent completely rigid membrane. It is shown that the former differs considerably from the latter in that the film thickness affects the shape of the flexible membrane, the compliance of which in turn impinges on the profile of the resulting free-surface disturbance.

Original languageEnglish
Pages (from-to)337-345
Number of pages9
JournalProceedings of the Institution of Mechanical Engineers, Part J: Journal of Engineering Tribology
Issue numberJ3
Publication statusPublished - May 2009


  • thin film flow
  • flexible membrane
  • lubrication theory
  • adaptive mesh refinement
  • adaptive time-stepping
  • multi-grid


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