## Abstract

Small particle motion in a linearized flow field is investigated analytically. The aim is to study the effects of relatively large Stokes numbers (St). It is assumed that the only dominant hydrodynamic force is the quasisteady Stokes drag where all other effects are neglected. An exact solution for a general, three-dimensional, unsteady flow field, including gravity, is obtained. Emphasis is placed on the role taken by the spatially varying flow field and the particle inertia. Although an immediate consequence of the linearization is that the long-term particle velocity is insensitive to initial conditions, no matter the value of St, the short-term behavior is quite intriguing. This behavior is found to be highly sensitive to the initial particle velocity when St exceeds critical values depending on the flow; this happens, for example, in shear flows. The exponential approach of the particle velocity to the fluid velocity, predicted by the asymptotic solution for St∼o(1), may under certain flow conditions transform into damped oscillations for critical values of the St number. An explanation is provided by showing the equivalence of the particle equation to that of a damped pendulum.

Original language | English |
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Article number | 112101 |

Pages (from-to) | 1-9 |

Number of pages | 9 |

Journal | Physics of Fluids |

Volume | 17 |

Issue number | 11 |

DOIs | |

State | Published - 1 Jan 2005 |

## ASJC Scopus subject areas

- Computational Mechanics
- Condensed Matter Physics
- Mechanics of Materials
- Mechanical Engineering
- Fluid Flow and Transfer Processes