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

High Precision Magnetic Float Densimeter

A simple, versatile, magnetic float densimeter that can be used to measure the density of liquids as a function of temperature is described. The system has been calibrated with water from 20 to 50°C demonstrating a sensitivity of 0.3 ppm and a precision of 2 ppm. The accuracy of the densimeter has been verified by measuring the densities of NaCl solutions at 25°C. Excellent agreement with previously published data was achieved