### Abstract

Given the surface areas of three different species A,B, and C, what is the most likely contact area between A and B? This problem finds many applications, but it is of specific importance in solid-phase reactions. Reactions in powder mixtures depend strongly on contact area between reactants, even when one species may melt. The surface of particles is meshed with small "tiles," and a combinatorial problem is formulated to map all tiles onto each other. The number of different contacts of n constituents is (formula presented); if pores are present, they are considered a constituent. The combinatorial problem for n > 3 is computationally overwhelming, but for two or three species, the desirable contacts can be calculated. The model was developed for contact between three different species (two species are included as a special case). This could constitute three different powders at 100% MTD, or a mixture of two powders that includes pores where the latter phase acts as a third species. The combinatorial approach is used to find the discrete probability-distribution function (PDF), viz., p(z, A, B, C), where z is the number of desirable contacts (for example, A\B), given the surface areas (A, B, C). The first moment of the PDF gives the expectancy value Ψ (A\B, A, B, C) for contact between species A and B. The theory was demonstrated by two examples. A simple contact problem is solved for two powders that also contain pores. The second example compares kinetic rates for different shapes and sizes of particles.

Original language | English (US) |
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Pages (from-to) | 1794-1803 |

Number of pages | 10 |

Journal | AIChE Journal |

Volume | 48 |

Issue number | 8 |

DOIs | |

State | Published - Aug 1 2002 |

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### ASJC Scopus subject areas

- Biotechnology
- Environmental Engineering
- Chemical Engineering(all)

### Cite this

*AIChE Journal*,

*48*(8), 1794-1803. https://doi.org/10.1002/aic.690480819