# Random close packing fractions of lognormal distributions of hard spheres

*Powder Technology* 245, 28 (2013)

#fractals#spherepacking#materials

Lognormal distributions (and mixtures of same) are a useful model for the size distribution in emulsions and sediments.

We apply a recent one-dimensional algorithm for predicting random close packing fractions of poly-disperse hard spheres [Farr and Groot, J. Chem. Phys. 133, 244104 (2009)] to the case of lognormal distributions of sphere sizes and mixtures of such populations. We show that the results compare well to two much slower algorithms for directly simulating spheres in three dimensions, and show that the algorithm is fast enough to tackle inverse problems in particle packing: designing size distributions to meet required criteria. The one-dimensional method used in this paper is implemented as a computer code in the C programming language, available at http://sourceforge.net/projects/spherepack1d/ under the terms of the GNU general public licence (version 2).

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