## Abstract

Diatomaceous Earth, also known as diatomite, diatomaceous silica, or kieselguhr is the material of natural origin which is

composed of the skeletons of diatoms, single-celled algae, which are accumulated in huge beds. Some diatomite’s are industrially

processed and used for different applications most frequently as filter aid. Particle size distribution of any filter granulation,

composed of these materials, has to be appropriately prepared. A mathematical model of particle size distribution of a kieselguhr

granulation is presented in this paper and experimentally verified. Particle sizes of a kieselguhr granulation are measured by the

microscopic morphometric method, ordinarily used in the experimental microbiology, and the empirical probability density function

(pdf) of particle sizes is formulated. Experimental pdf data are fitted according to the exponential function, which represents a

solution of a developed model of differential equation. The fitting procedure followed the iterative algorithm of LevenbergMarquardt to adjust the parameter values. This way, an experimentally determined pdf can be approximated with an analytic

function with a small number of constants in the adopted model of fit function. This approach facilitates further modeling and

analysis of filtering mediums. Based on the particle sizes, pdf’s of different kieselguhr, and perlite granulations, it is possible to

determine an optimal medium mixture (containing different filtration granulations), depending of the filtration requirements

composed of the skeletons of diatoms, single-celled algae, which are accumulated in huge beds. Some diatomite’s are industrially

processed and used for different applications most frequently as filter aid. Particle size distribution of any filter granulation,

composed of these materials, has to be appropriately prepared. A mathematical model of particle size distribution of a kieselguhr

granulation is presented in this paper and experimentally verified. Particle sizes of a kieselguhr granulation are measured by the

microscopic morphometric method, ordinarily used in the experimental microbiology, and the empirical probability density function

(pdf) of particle sizes is formulated. Experimental pdf data are fitted according to the exponential function, which represents a

solution of a developed model of differential equation. The fitting procedure followed the iterative algorithm of LevenbergMarquardt to adjust the parameter values. This way, an experimentally determined pdf can be approximated with an analytic

function with a small number of constants in the adopted model of fit function. This approach facilitates further modeling and

analysis of filtering mediums. Based on the particle sizes, pdf’s of different kieselguhr, and perlite granulations, it is possible to

determine an optimal medium mixture (containing different filtration granulations), depending of the filtration requirements

Original language | English |
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Pages (from-to) | 192-197 |

Journal | Metalurgia International |

Volume | 17 |

Issue number | 10 |

Publication status | Published - 2012 |

## Fields of Expertise

- Sonstiges

## Treatment code (Nähere Zuordnung)

- Application
- Experimental