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**Bothe, D.** **Bockhorn, H. and Warnecke, H.-J. and Peukert, W. and Mewes, D. (eds.)** (2010):

*Evaluating the quality of a mixture: degree of homogeneity and scale of segregation.*

In: Micro and Macro Mixing – Analysis, Simulation and Numerical Calculation, In: Heat and Mass Transfer, Springer, pp. 17-35, [Book Section]

## Abstract

he evaluation of mixing requires measures for the quality of mixtures. Integral measures like the intensity of segregation are advantageous for practical purposes and such variance-based measures are shown to be especially meaningful in the context of reactive mixing. But the variance is insensitive to the scales on which segregation occurs, hence it is complemented by an integral scale of segregation. The latter is closely related to the concept of contact area and can be efficiently computed using a formula from geometric measure theory. This integral scale of segregation is also characterized by the rate at which the minimizing-total-variation-flow from image processing would alter the intensity of segregation. Applied to secondary flow mixing in a T-shaped micro-mixer, the dependence of the integral scale of segregation shows a new type of dependence on the Schmidt number, while the smallest length scales display the kind of dependence known from the Batchelor’s length scale.

Item Type: | Book Section |
---|---|

Erschienen: | 2010 |

Editors: | Bockhorn, H. and Warnecke, H.-J. and Peukert, W. and Mewes, D. |

Creators: | Bothe, D. |

Title: | Evaluating the quality of a mixture: degree of homogeneity and scale of segregation |

Language: | English |

Abstract: | he evaluation of mixing requires measures for the quality of mixtures. Integral measures like the intensity of segregation are advantageous for practical purposes and such variance-based measures are shown to be especially meaningful in the context of reactive mixing. But the variance is insensitive to the scales on which segregation occurs, hence it is complemented by an integral scale of segregation. The latter is closely related to the concept of contact area and can be efficiently computed using a formula from geometric measure theory. This integral scale of segregation is also characterized by the rate at which the minimizing-total-variation-flow from image processing would alter the intensity of segregation. Applied to secondary flow mixing in a T-shaped micro-mixer, the dependence of the integral scale of segregation shows a new type of dependence on the Schmidt number, while the smallest length scales display the kind of dependence known from the Batchelor’s length scale. |

Title of Book: | Heat and Mass Transfer |

Series Name: | Micro and Macro Mixing – Analysis, Simulation and Numerical Calculation |

Publisher: | Springer |

Uncontrolled Keywords: | pecific contact area - intensity of mixing - integral length scales - Schmidt number dependence - decay of variance |

Divisions: | Exzellenzinitiative > Clusters of Excellence > Center of Smart Interfaces (CSI) 04 Department of Mathematics > Mathematical Modelling and Analysis UNSPECIFIED Zentrale Einrichtungen 04 Department of Mathematics Exzellenzinitiative Exzellenzinitiative > Clusters of Excellence |

Date Deposited: | 05 Apr 2011 12:32 |

Identification Number: | doi:10.1007/978-3-642-04549-3_2 |

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