### A GENERALIZED KINETIC MODEL OF SEDIMENTATION OF POLYDISPERSE SUSPENSIONS WITH A CONTINUOUS PARTICLE SIZE DISTRIBUTION

### Abstract

Polydisperse suspensions with particles of a finite number N of size classes have been widely studied in laboratory experiments. However, in most real-world applications the particle sizes are distributed continuously. In this paper, a well-studied one-dimensional kinematic model for batch sedimentation of polydisperse suspensions of small equal-density spheres is extended to suspensions with a continuous particle size distribution. For this purpose, the phase density function Î¦ = Î¦(t, x, Î¾), where Î¾ âˆˆ [0, 1] is the normalized squared size of the particles, is introduced, whose integral with respect to Î¾ on an interval [Î¾ 1, Î¾ 2] is equivalent to the volume fraction at (t, x) occupied by particles of that size range. Combining the MasliyahLockettBassoon (MLB) model for the solid-fluid relative velocity for each solids species with the concept of phase density function yields a scalar, first-order equation for Î¦, namely the equation of the generalized kinetic theory. Three numerical schemes for the solution of this equation are introduced, and a numerical example and an L 1 error study show that one of these schemes introduces less numerical diffusion and less spurious oscillations near discontinuities than the others. Several numerical examples illustrate the simulated behavior of this kind of suspensions. Numerical results also illustrate the solution of an eigenvalue problem associated with the equation of the generalized kinetic theory. Â© 2008 World Scientific Publishing Company.

### Más información

Título según WOS: | A GENERALIZED KINETIC MODEL OF SEDIMENTATION OF POLYDISPERSE SUSPENSIONS WITH A CONTINUOUS PARTICLE SIZE DISTRIBUTION |

Título según SCOPUS: | A generalized kinetic model of sedimentation of polydisperse suspensions with a continuous particle size distribution |

Título de la Revista: | MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES |

Volumen: | 18 |

Número: | 10 |

Editorial: | WORLD SCIENTIFIC PUBL CO PTE LTD |

Fecha de publicación: | 2008 |

Página de inicio: | 1741 |

Página final: | 1785 |

Idioma: | English |

URL: | http://www.worldscientific.com/doi/abs/10.1142/S0218202508003182 |

DOI: |
10.1142/S0218202508003182 |

Notas: | ISI, SCOPUS |