### Abstract

The motion of a solid spherical particle entrained in a Poiseuille flow between parallel plane walls has various applications to separation methods, like field-flow fractionation and hydrodynamic chromatography. Various handy formulae are presented here to describe the particle motion, with these applications in mind. Based on the assumption of a low Reynolds number, the multipole expansion method coupled to a Cartesian representation is applied to provide accurate results for various friction factors in the motion of a solid spherical particle embedded in a viscous fluid between parallel planes. Accurate results for the velocity of a freely moving solid spherical particle are then obtained. These data are fitted so as to obtain handy formulae, providing e.g. the velocity of the freely moving sphere with a 1% error. For cases where the interaction with a single wall is sufficient, simpler fitting formulae are proposed, based on earlier results using the bispherical coordinates method. It appears that the formulae considering only the interaction with a nearest wall are applicable for a surprisingly wide range of particle positions and channel widths. As an example of application, it is shown how in hydrodynamic chromatography earlier models ignoring the particle-wall hydrodynamic interactions fail to predict the proper choice of channel width for a selective separation. The presented formulae may also be used for modeling the transport of macromolecular or colloidal objects in microfluidic systems.

Original language | English |
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Pages (from-to) | 4078-4089 |

Number of pages | 12 |

Journal | Chemical Engineering Science |

Volume | 66 |

Issue number | 18 |

DOIs | |

State | Published - Sep 15 2011 |

### Keywords

- Creeping flow
- Interaction with walls
- Particle
- Selectivity
- Separations
- Suspension

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## Cite this

*Chemical Engineering Science*,

*66*(18), 4078-4089. https://doi.org/10.1016/j.ces.2011.05.033