Three-dimensional thin film flow problems solved accurately and efficiently

Rivulet formation, merger and evolution

Philip H. Gaskell, Yeaw Chu Lee, David Slade, Sergii Veremieiev

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

The evolution of a gravity-driven, thin, continuously-fed liquid film down an inclined planar substrate is modelled using the long-wave approximation with, as observed experimentally, a periodic pattern of finger-like rivulets forming at the unstable advancing front; note that, the film may be perfectly or partially wetting. The required long-time solution, with the merger of neighbouring rivulets a possibility, is obtained using a purpose designed efficient multigrid methodology incorporating complementary error-controlled automatic spatio-temporal adaptivity and mesh devolution strategies. Critical wavelengths are extracted from the various solutions showing the effect of inclination angle. The rivulet pattern formed is explored, revealing very good agreement with existing experimental results; partial wetting is demonstrated to have a strong influence on the evolution of the system.

Original languageEnglish
Title of host publicationECCOMAS 2012 e-book
PublisherVienna University of Technology
Pages2612-2624
Number of pages13
ISBN (Print)9783950353709
Publication statusPublished - 2012
Event6th European Congress on Computational Methods in Applied Sciences and Engineering 2012 - Vienna, Austria
Duration: 10 Sep 201214 Sep 2012

Conference

Conference6th European Congress on Computational Methods in Applied Sciences and Engineering 2012
Abbreviated titleECCOMAS 2012
CountryAustria
CityVienna
Period10/09/1214/09/12

Fingerprint

Thin Film Flow
Mergers
Three-dimensional Flow
Wetting
Thin films
Adaptivity
Liquid films
Inclination
Inclined
Gravity
Gravitation
Unstable
Substrate
Mesh
Liquid
Wavelength
Partial
Angle
Methodology
Experimental Results

Keywords

  • Automatic spatio-temporal adaption
  • Lubrication theory
  • Multigrid
  • Rivulets
  • Thin liquid films

ASJC Scopus subject areas

  • Computational Theory and Mathematics
  • Applied Mathematics

Cite this

Gaskell, P. H., Lee, Y. C., Slade, D., & Veremieiev, S. (2012). Three-dimensional thin film flow problems solved accurately and efficiently: Rivulet formation, merger and evolution. In ECCOMAS 2012 e-book (pp. 2612-2624). Vienna University of Technology.
Gaskell, Philip H. ; Lee, Yeaw Chu ; Slade, David ; Veremieiev, Sergii. / Three-dimensional thin film flow problems solved accurately and efficiently : Rivulet formation, merger and evolution. ECCOMAS 2012 e-book. Vienna University of Technology, 2012. pp. 2612-2624
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abstract = "The evolution of a gravity-driven, thin, continuously-fed liquid film down an inclined planar substrate is modelled using the long-wave approximation with, as observed experimentally, a periodic pattern of finger-like rivulets forming at the unstable advancing front; note that, the film may be perfectly or partially wetting. The required long-time solution, with the merger of neighbouring rivulets a possibility, is obtained using a purpose designed efficient multigrid methodology incorporating complementary error-controlled automatic spatio-temporal adaptivity and mesh devolution strategies. Critical wavelengths are extracted from the various solutions showing the effect of inclination angle. The rivulet pattern formed is explored, revealing very good agreement with existing experimental results; partial wetting is demonstrated to have a strong influence on the evolution of the system.",
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Gaskell, PH, Lee, YC, Slade, D & Veremieiev, S 2012, Three-dimensional thin film flow problems solved accurately and efficiently: Rivulet formation, merger and evolution. in ECCOMAS 2012 e-book. Vienna University of Technology, pp. 2612-2624, 6th European Congress on Computational Methods in Applied Sciences and Engineering 2012, Vienna, Austria, 10/09/12.

Three-dimensional thin film flow problems solved accurately and efficiently : Rivulet formation, merger and evolution. / Gaskell, Philip H.; Lee, Yeaw Chu; Slade, David; Veremieiev, Sergii.

ECCOMAS 2012 e-book. Vienna University of Technology, 2012. p. 2612-2624.

Research output: Chapter in Book/Report/Conference proceedingConference contribution

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N2 - The evolution of a gravity-driven, thin, continuously-fed liquid film down an inclined planar substrate is modelled using the long-wave approximation with, as observed experimentally, a periodic pattern of finger-like rivulets forming at the unstable advancing front; note that, the film may be perfectly or partially wetting. The required long-time solution, with the merger of neighbouring rivulets a possibility, is obtained using a purpose designed efficient multigrid methodology incorporating complementary error-controlled automatic spatio-temporal adaptivity and mesh devolution strategies. Critical wavelengths are extracted from the various solutions showing the effect of inclination angle. The rivulet pattern formed is explored, revealing very good agreement with existing experimental results; partial wetting is demonstrated to have a strong influence on the evolution of the system.

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Gaskell PH, Lee YC, Slade D, Veremieiev S. Three-dimensional thin film flow problems solved accurately and efficiently: Rivulet formation, merger and evolution. In ECCOMAS 2012 e-book. Vienna University of Technology. 2012. p. 2612-2624