Transport in Porous Media

, Volume 116, Issue 2, pp 533–566 | Cite as

Slip–Brinkman Flow Through Corrugated Microannulus with Stationary Random Roughness

  • M. S. Faltas
  • E. I. SaadEmail author
  • Shreen El-Sapa


This paper presents a boundary perturbation method of the Brinkman-extended Darcy model to investigate the flow in corrugated microannuli cylindrical tubes with slip surfaces. The stationary random model is used to mimic the surface roughness of the cylindrical walls. The tube is filled with a porous medium. We shall consider the two cases where corrugations are either perpendicular or parallel to the flow, and particular attention is given to the effect of the phase shift. The effects of the corrugations on the flow rate and pressure gradient are investigated as functions of wavelength, the permeability of the medium, the radius ratio and the slip parameter. Particular surface roughnesses are examined as special cases of stationary random surface. It is found that the effect of the partial slip is significant on the corrugation functions. The limiting cases of Stokes and Darcy’s flows and no-slip case are discussed.


Corrugated microannulus Slip–Brinkman flow Flow rate and pressure gradient 


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© Springer Science+Business Media Dordrecht 2016

Authors and Affiliations

  1. 1.Department of Mathematics, Faculty of ScienceAlexandria UniversityAlexandriaEgypt
  2. 2.Department of Mathematics, Faculty of ScienceDamanhour UniversityDamanhourEgypt

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