## Abstract

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(a^{2} 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 language | English |
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Pages (from-to) | 149-155 |

Number of pages | 7 |

Journal | Journal of Colloid and Interface Science |

Volume | 330 |

Issue number | 1 |

DOIs | |

State | Published - 1 Feb 2009 |

Externally published | Yes |

## Keywords

- Added mass force
- Drag force
- Oscillations
- Particle
- Permeability