Transport in Porous Media

, Volume 118, Issue 2, pp 271–280 | Cite as

On the Flow Conditions at the Fluid: Permeable Surface Interface

  • R. V. Goldstein
  • U. N. Gordeev
  • E. B. SandakovEmail author


The present study covers the problem of rotation of a porous disk under a viscous incompressible fluid that fills the half-space above the disk, which is the generalization of the von Karman’s problem. It is found that, instead of solving the exact problem, which is rather complicated by coupling the motions of the free fluid and that contained inside the permeable disk, it is sufficient to solve a much simpler problem of the motion of the free fluid placed onto a permeable plane. Assuming the flow in the permeable disk is described by the Brinkman equations, we obtain a self-similar formulation of the problem. Employing this formulation, we also show that the boundary condition associated with continuity of the tangential strains and tangential velocity components is satisfied at the fluid–porous body interface. The coefficient for the vertical velocity component is furthermore obtained. Various extreme cases are identified.


Viscous flow Porous medium Brinkman equations Beavers–Joseph boundary condition 



This work was supported by the “Scientific and Academic Personnel of Innovative Russia” Federal Target Program for 2009–2013, State Contract P1109.


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Copyright information

© Springer Science+Business Media Dordrecht 2017

Authors and Affiliations

  • R. V. Goldstein
    • 1
  • U. N. Gordeev
    • 2
  • E. B. Sandakov
    • 2
    Email author
  1. 1.Ishlinsky Institute for Problems in Mechanics of the Russian Academy of Sciences (IPMech RAS)MoscowRussian Federation
  2. 2.National Research Nuclear University “MEPhI”MoscowRussian Federation

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