Packing fraction of trimodal spheres with small size ratio: An analytical expression

In previous papers analytical expressions were derived and validated for the packing fraction of bimodal hard spheres with small size ratio, applicable to ordered (crystalline) [H. J. H. Brouwers, Phys. Rev. E 76, 041304 (2007);H. J. H. Brouwers, Phys. Rev. E 78, 011303 (2008)] and disordered (random) packings [H. J. H. Brouwers, Phys. Rev. E 87, 032202 (2013)]. In the present paper the underlying statistical approach, based on counting the occurrences of uneven pairs, i.e., the fraction of contacts between unequal spheres, is applied to trimodal discretely sized spheres. The packing of such ternary packings can be described by the same type of closed-form equation as the bimodal case. This equation contains the mean volume of the spheres and of the elementary cluster formed by these spheres; for crystalline arrangements this corresponds to the unit cell volume. The obtained compact analytical expression is compared with empirical packing data concerning random close packing of spheres, taken from the literature, comprising ternary binomial and geometric packings; good agreement is obtained. The presented approach is generalized to ordered and disordered packings of multimodal mixes

Random packing fraction of bimodal spheres: An analytical expression

In previous papers analytical equations were derived and validated for the packing fraction of crystalline structures consisting of bimodal randomly placed hard spheres [Phys. Rev. E 76, 041304 (2007); Phys. Rev. E 78, 011303 (2008)]. In this article it will be demonstrated that the bimodal random packing fraction of spheres with small size ratio can be described by the same type of closed-form equation. This equation contains the volume of the spheres and of the elementary cluster formed by these spheres. The obtained compact analytical expression appears to be in good agreement with a large collection of empirical and computer-generated packing data, taken from literature. By following a statistical approach of the number of uneven pairs in a binary packing, and the associated packing reduction (compared to the monosized limit), the number fraction of hypostatic spheres is estimated to be 0.548

Berechnungsverfahren zur Bestimmung des Temperaturniveaus in einem Trockenlager fuer waermeerzeugende Spaltprodukte bei indirekter Kuehlung durch freie Konvektion

SIGLETIB: RN 2689 (1978,15) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekDEGerman

Packing fraction of geometric random packings of discretely sized particles

The packing fraction of geometric random packings of discretely sized particles is addressed in the present paper. In an earlier paper [Brouwers, Phys. Rev. E 74, 031309 (2006);74, 069901(E) (2006)], analytical solutions were presented for the packing fraction of polydisperse geometric packings for discretely sized particles with infinitely large size ratio and the packing of continuously sized particles. Here the packing of discretely sized particles with finite size ratio u is analyzed and compared with empirical data concerning five ternary geometric random close packings of spheres with a size ratio of 2, yielding good agreement

Untersuchung der Effektivitaet von Kalkprodukten fuer die trockene Rauchgasreinigung. T. 2 Dynamisches Verfahren

Available from Forschungsgemeinschaft Kalk und Moertel e.V., Koeln (DE) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekSIGLEDEGerman

Theoretische Untersuchungen waerme- und stroemungstechnischer Vorgaenge in Schuettungen mittels der Finite-Elemente-Methode

TIB: RO 1973 (9) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekSIGLEDEGerman