Educación

 

Packing of monosized spheres in a cylindrical container: models and approaches

 

L. Burtseva^a, B. Valdez Salas^a, F. Werner^b and V. Petranovskii^c

 

^a Universidad Autónoma de Baja California, Instituto de Ingeniería, Calle de la Normal, S/N, Insurgentes Este, 21280, Mexicali, B.C., México. e-mail: burtseva@uabc.edu.mx

^b Otto-von-Guericke-Universitat Magdeburg, Institut für Mathematische Optimierung, Universiätsplatz 2, 39106 Magdeburg, Germany.

^c Universidad Nacional Autónoma de México, Centro de Nanociencias y Nanotecnología, Km. 107 Carretera Tijuana-Ensenada, 22860, Ensenada, B.C., México: On the sabbatical leave at: Departamento de Investigación en Zeolitas, Instituto de Ciencias, BUAP, Puebla 72570, México.

 

Received 24 October 2014;
Accepted 16 February 2015

 

Abstract

Packing of monosized spheres in a cylindrical container of a fixed diameter is a frequently discussed subject in recent studies. It is motivated by the high applicability of these models, particularly by the advances in nanomaterial science and engineering, associated with the development of hierarchically ordered matters of specific structures and properties. Their features strongly depend on the arrangement and density of the filling atoms in the channels of a nanostructured porous matrix. A special interest is devoted to a dense random packing, which by its nature is not totally random when the spheres do not overlap. In this paper, related models of packing are classified basing on the space filling method, and the densities reached theoretically as well as experimentally for those classes are given. The effects produced by some parameters on the packing density and the main properties are analyzed. The experimental techniques and computer modeling approaches are summarized.

Keywords: Packing; monosized spheres; cylinder; density; porosity; modeling.

 

Resumen

El empaquetamiento de esferas del mismo tamaño en un contenedor cilíndrico de diámetro fijo es un tema que se discute frecuentemente en investigaciones recientes. Eso es motivado por la alta aplicabilidad de dichos modelos, debido a los avances en la ciencia e ingeniería de nanomateriales y el desarrollo de materiales jerárquicamente ordenados con estructuras y propiedades específicas. Sus características dependen estrictamente del arreglo y densidad de los átomos en canales de una matriz porosa nanoestructurada. Un interés especial está enfocado en un empaquetamiento aleatorio denso, el cual por su naturaleza no es totalmente aleatorio cuando las esferas no se traslapan. En este artículo, los modelos relacionados con el empaquetamiento son clasificados basándose en el método de llenado del espacio, y las densidades alcanzadas tanto teóricamente como experimentalmente para estas clases son dadas. Los efectos producidos por algunos parámetros en la densidad y las propiedades del empaquetamiento son analizados. Son resumidas las técnicas experimentales y los alcances del modelado por computadora.

Palabras clave: Empaquetamiento; esferas iguales; cilindro; densidad; porosidad; modelado.

 

PACS: 89.20.Ff

 

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Acknowledgments

This work was supported by the Department of Postgraduate and Research of the UABC, Project No. 111/739 and UNAM-PAPIIT (grant IN110713).

 

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