Forces on a porous particle in an oscillating flow

P. Vainshtein*, M. Shapiro

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

13 Scopus citations


We investigate theoretically forces acting on a porous particle in an oscillating viscous incompressible flow. We use the unsteady equations describing the creeping flow, namely the Stokes equations exterior to the particle and the Darcy or Brinkman equations inside it. The effect of particle permeability and oscillation frequency on the flow and forces is expressed via the Brinkman parameter β = a / sqrt(k) and the frequency parameter Y = sqrt(a2 ω / 2 ν) = a / δ, respectively. Here a is particle radius, k is its permeability, ω is the angular frequency, δ is the thickness of Stokes layer (penetration depth) and ν is the fluid kinematic viscosity. It is shown that the oscillations interact with permeable structure of the particle and affect both the Stokes-like viscous drag and the added mass force components.

Original languageEnglish
Pages (from-to)149-155
Number of pages7
JournalJournal of Colloid and Interface Science
Issue number1
StatePublished - 1 Feb 2009
Externally publishedYes


  • Added mass force
  • Drag force
  • Oscillations
  • Particle
  • Permeability


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