Volume envelopes

The bulk density of a powder is calculated by dividing its mass by the volume occupied by the powder (Abdullah Geldart, 1999). Tapped bulk density, or simply tapped density, is the maximum packing density of a powder achieved under the influence of well-defined, externally applied forces (Oliveira et al., 2010). Because the volume includes the spaces between particles as well as the envelope volumes of the particles themselves, the bulk and tapped density of a powder are highly dependent on how the particles are packed. This fact is related to the morphology of its particles and such parameters are able to predict the powder flow properties and its compressibility. 

The product granules are also assumed to be spherical and of uniform radius gr the envelope volume Vg and external surface area Sg of a single granule are given by equafions 5.19. and 5.20 respecfively. 

V particle volume Vb volume of binder per particle Vg granule envelope volume Wa mass flow rate of fluidizing gas XV mass flow rate of feed liquid Xs mass fraction of solute in feed liquid... 

The bulk density of a powder is obtained by dividing its mass by the bulk volume it occupies. The volume includes the spaces between particles as well as the envelope volumes of the particles themselves. The true density of a material (i.e., the density of the actual solid material) can be obtained with a gas pycnometer. The bulk density of a powder is not a definite number like true density or specific gravity but an indirect measurement of a number of factors, including particle size and size distribution, particle shape, true density, and especially the method of measurement. Although there is no direct linear relationship between the flowability of a powder and its bulk density, the latter is extremely important in determining the capacity of mixers and hoppers and providing an easily obtained valuable characterization of powders. 

EFFECTIVE (OR AERODYNAMIC) PARTICLE DENSITY is when the measured volume includes both the closed and the open pores. This volume is within an aerodynamic envelope as seen by the gas flowing past the particle the value of density measured is therefore a weighted average of the solid and immobilised gas (or liquid) densities present within the envelope volume. The effective density is clearly of primary importance in applications involving flow round particles like in fluidization, sedimentation or flow through packed beds. 

The bulk density of a powder is its mass divided by the bulk volume it occupies. The volume includes the spaces between particles as well as, of course, the envelope volumes of the particles themselves. The bulk density should not be confused with particle density which is dealt with in section 2.4. 

Practically, this method works well for spherical or near-spherical particles however, it produces erroneous results for nonspherical particles. Moreover, this method is not suitable for porous material because the effective particle density is not known and the volume measured is the envelope volume. Special care is required to avoid crowding of the orifice otherwise, special treatment is needed to analyze the instrument counts. 

The measurement of the bulk density of powders in no exception to the general situation outlined above, but it is so fundamental to their storage, processing, and distribution that it does merit particular consideration. The bulk density of a powder is its mass divided by the bulk volume it occupies. The volume includes the spaces between particles and the envelope volume of the particles themselves. The spaces between particles are denoted as porosity or voidage, and can be defined as the volume of the voids within the bulk volume divided by the total bulk volume. Bulk density and porosity are related by... 

For porous particles with small pores, the particle volume in Eq. (15) should be replaced with the envelope volume of the particle as if the particles were nonporous as shown in Fig. 2. This would be more hydrodynamically correct if the particle behavior in the flow field is of interest or if the bulk volume of the particles is to be estimated. For total weight estimation, then the skeleton density should be known. The skeleton density is defined as the mass of the particle divided by the skeletal volume of the particle. In practice, the pore volume rather than the skeletal volume is measured through gas adsorption, gas or water displacement, and mercury porosimetry. These techniques will be discussed in more detail later. There are also porous particles with open and closed pores. The closed pores are not accessible to the gas, water or mercury and thus their volume cannot be measured. In this case, the calculated skeleton density would include the volume of closed pores as shown in Fig. 2. For nonporous particles, the particle density is exactly equal to the skeleton density. For porous particles, the skeleton density will be larger than the particle density. 

Figure 1.2 shows the View menu. To view the Explorer Window, for example, press Alt +1 simultaneously. If you look at the View > Show Envelopes > Volume menu item, you ll notice the V next to it indicating that all you need to do is press V as the hotkey shortcut to do the same thing. While most menus can be navigated in ACID using keyboard shortcuts, only a limited subset of commands have hotkeys that can be executed without navigating menus. 

Insert a volume envelope into the track right-click anywhere in the track and, from the context menu, select Insert/Remove Envelope > Volume. 

S. Muresan, T. Sulea, D. Ciubotariu, L. Kurunczi, and Z. Simon, Quant. Struct.-Act. Relat., 15, 31 (1996). Min der Waals Intersection Envelope Volumes as a Possible Basis for Steric Interactions in CoMFA. See also Ref. 95. 

Because of these constraints many particle size methods are not applicable to floes. For example the uncertainty and variability of floe density within the outer envelope volume, the possible irregularity of shape and their fragile nature means, that all types of sedimentation method are inapplicable. 

The Coulter principle has been applied to floes but is severely constrained by the very severe shear stress that occurs within the vortex of fluid passing through a Coulter orifice. Indeed the Coulter Counter has been used as an on-line method for studying the disruption of floes. If a floe were entirely disrupted just before or in the orifice it is reasonable to assume that the additive volume of the fragments would be detected as one coincident group of particles. This would however assume that the fragments were of the same particle volume concentration as the parent, an unsafe assumption for floes. However breakup in an orifice is not normally complete and the observed size may also depend on the amount of distortion the floe experiences in the orifice. From the behaviour of other types of porous particle in die Coulter Counter it is often assumed that the instrument measures the external envelope volume if the floes are not disrupted. Attempts have been made to measure individual well characterised floes under realistic orifice conditions but the experiments are very difficult to do and the results remain ambiguous. ... 

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