Spheres irregular packing

Figure 7.2. Sections of the pore space between solid spheres in irregular packing. First (a) and second (b) stage of condensation.

Fig. 3.38 Packing of spheres of the same size and void fraction a cubic packing b irregular packing...

Air at = 40 °C and relative humidity p = 0.2 flows over an irregular packing of spheres whose surface temperature is kept constant at the wet bulb temperature 21.5 °C by evaporating water. The air becomes loaded with water vapour. 

Huang, A.T.L., Huang, M.Y.E, Capart, H., Chen, R.H., 2008. Optical measurements of pore geometry and fluid velocity in a bed of irregularly packed spheres. Exp. Fluids 45, 309-321. 

Particle diameter is a primary variable important to many chemical engineering calculations, including settling, slurry flow, fluidized beds, packed reactors, and packed distillation towers. Unfortunately, this dimension is usually difficult or impossible to measure, because the particles are small or irregular. Consequently, chemical engineers have become familiar with the notion of equivalent diameter of a partiele, which is the diameter of a sphere that has a volume equal to that of the particle. 

Adsorbents are available as irregular granules, extruded pellets and formed spheres. The size reflects the need to pack as much surface area as possible into a given volume of bed and at the same time minimise pressure drop for flow through the bed. Sizes of up to about 6 mm are common. 

This later expression is very convenient for generating a close approximation to the P-surface. Townsend et al. (1992) have used it and other such expressions as manifolds on which to construct irregular sphere packings which can represent (after removing the spheres at the centres of rings of 5, 6 or 7 spheres) the graphite network. 

Based on the above general principles, quite a number of models have been developed to estimate pore size distributions.29,30,31-32,33 They are based on different pore models (cylindrical, ink bottle, packed sphere,. ..). Even the so-called modelless calculation methods do need a pore model in the end to convert the results into an actual pore size distribution. Very often, the exact pore shape is not known, or the pores are very irregular, which makes the choice of the model rather arbitrary. The model of Barett, Joyner and Halenda34 (BJH model) is based on calculation methods for cylindrical pores. The method uses the desorption branch of the isotherm. The desorbed amount of gas is due either to the evaporation of the liquid core, or to the desorption of a multilayer. Both phenomena are related to the relative pressure, by means of the Kelvin and the Halsey equation. The exact computer algorithms35 are not discussed here. The calculations are rather tedious, but straightforward. 

Figure 37. Cross Section of Packings Containing Spheres and Irregular Materials. (A) Iron Ore, 6/8-mesh (B) Iron Ore, 3/4-mesh (C) 3-0 Shot ...

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