Extended lubrication theory: Improved estimates of flow in channels with variable geometry

Behrouz Tavakol, Guillaume Froehlicher, Douglas P. Holmes, Howard A. Stone

Research output: Contribution to journalArticlepeer-review

27 Scopus citations


Lubrication theory is broadly applicable to the flow characterization of thin fluid films and the motion of particles near surfaces. We offer an extension to lubrication theory by starting with Stokes equations and considering higher-order terms in a systematic perturbation expansion to describe the fluid flow in a channel with features of a modest aspect ratio. Experimental results qualitatively confirm the higher-order analytical solutions, while numerical results are in very good agreement with the higherorder analytical results. We show that the extended lubrication theory is a robust tool for an accurate estimate of pressure drop in channels with shape changes on the order of the channel height, accounting for both smooth and sharp changes in geometry.

Original languageEnglish (US)
JournalProceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
Issue number2206
StatePublished - Oct 1 2017

All Science Journal Classification (ASJC) codes

  • General Engineering
  • General Physics and Astronomy
  • General Mathematics


  • Lubrication theory
  • Perturbation expansion
  • Stokes flow


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