### 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) |
---|---|

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

**Role of particle geometry and surface contacts in solid-phase reactions.** / Kostogorova, J.; Viljoen, Hendrik J; Shteinberg, A.

Research output: Contribution to journal › Article

*AIChE Journal*, vol. 48, no. 8, pp. 1794-1803. https://doi.org/10.1002/aic.690480819

}

TY - JOUR

T1 - Role of particle geometry and surface contacts in solid-phase reactions

AU - Kostogorova, J.

AU - Viljoen, Hendrik J

AU - Shteinberg, A.

PY - 2002/8/1

Y1 - 2002/8/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=0036706722&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0036706722&partnerID=8YFLogxK

U2 - 10.1002/aic.690480819

DO - 10.1002/aic.690480819

M3 - Article

AN - SCOPUS:0036706722

VL - 48

SP - 1794

EP - 1803

JO - AICHE Journal

JF - AICHE Journal

SN - 0001-1541

IS - 8

ER -