On lubrication flows in geometries with zero local curvature

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The familiar examples of lubrication theory for the approximate analysis of the motion of cylindrical and spherical particles near boundaries takes advantage of the local parabolic shape near contact. We generalize these studies to particles and boundaries of more general shape, which have the feature that the curvature is zero at the point of minimum separation in the gap. Order-of-magnitude estimates and detailed solutions are given. The translation of such a close-fitting object in a circular tube, and the pressure-driven flows between two surfaces with zero curvature at minimum separation and in a saddle-shaped channel, are considered in a similar fashion.

Original languageEnglish (US)
Pages (from-to)4838-4845
Number of pages8
JournalChemical Engineering Science
Issue number17
StatePublished - Sep 2005
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • General Chemistry
  • General Chemical Engineering
  • Industrial and Manufacturing Engineering


  • Low Reynolds members
  • Lubrication
  • Particle motion


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