Page 38 - Book Hosokawa Nanoparticle Technology Handbook

1.4 PARTICLE DENSITY FUNDAMENTALS
voids within particles themselves. Consequently, the When the density of individual particles is relatively
density of a powder can be defined in several ways. homogeneous, the density reference liquid method [3]
Important definitions that are practical and useful are may be applicable: particles are put into density refer-
as follows. ence liquids that have been prepared to have several
known densities, and the particle density is determined
(a) Material density by judging whether the particles float to the liquid sur-
Material density of a powder is defined as the mass of face, settle at the bottom, or remain suspended in the
the powder divided by the volume occupied by solid liquid, after a certain holding time.
matter of the powder. It can be regarded as the density
of a homogeneous material composed of the same 1.4.2 Density measurement of individual particles
material as the constituent particles. It is also referred
to as true density. Material density might be measured (1) Effective density of individual particles
after removing internal voids by breaking the particles.
When particles are not in a powder state, but are dis-
(b) Particle density persed in a gas or a liquid, the density of individual
Particle density is defined as the mass of the powder particles is often of concern. For particles dispersed in
divided by the volume occupied by particles including a gas, there are three major methods of measuring the
internal closed voids. This volume is equivalent to the density of individual particles: (A) the combined
sum of volumes enclosed by the external surfaces of measurement of mobility and mass, (B) the combined
particles. When there are no closed voids within par- measurement of mass and volume, and (C) the com-
ticles, the particle density is the same as the material bined measurement of mobility and aerodynamic
density. In actual measurements, open voids that have diameter.
only small openings at the surfaces of particles might Let m and d denote the mass and the mobility
b
behave as closed voids. Therefore, the particle density equivalent diameter (diameter of a sphere with the
value obtained can depend on the details of the meas- same mechanical mobility as the particle of concern)
urement procedure. of a particle, respectively. The density obtained by
methods (A) and (C) is the effective density defined by
(c) Bulk density
Bulk density is defined as the mass of the powder m .
divided by the volume of the space below the upper e d 3 6 (1.4.1)
surface of the powder when it is placed in a container. b
The bulk density refers to the volume including both
the gaps between constituent particles and the voids For a spherical particle, d coincides with its geomet-
b
within particles. Two types of bulk density are often rical diameter, and hence is equivalent to the par-
e
1
used: initial bulk density is the bulk density when ticle density defined in 1.4.1. For a nonspherical
2
well-dispersed particles are put gently into a container, particle, d depends on the particle shape. Although
b
while tap density is that obtained after a tapping pro- the effective density in such cases is not an intrinsic
cedure in which the powder container is repeatedly material property, it is still useful for particle charac-
lifted and dropped onto a solid surface. The ratio of the terization. The density obtained by method (B), on
tap density to the initial bulk density is called the the other hand, is the particle density, and leads to the
Hausner ratio, and is used as a measure of powder material density, if there are no closed voids within
flowability or compressibility. the particles.
These methods are also applicable to particles
(2) Measurement methods of powder density suspended in a liquid, if the liquid suspension can be
In conventional methods of measuring the density of converted into an aerosol by atomizing the suspension
a powder, the mass of the powder is measured with a and drying the droplets thus generated.
balance, and its volume measured either by the liquid
immersion method or the gas replacement method. (2) Mass classification of aerosol particles
These methods are, of course, applicable also to pow- The method of classifying aerosol particles according
ders composed of nanoparticles. For details of the to their mass, which is employed in methods (A) and
methods see references [1, 2]. (B), is briefly described here. Fig. 1.4.1 shows the
It has been reported that bulk density of a powder
tends to remain unchanged by the tapping procedure 1
Note, however, that the particle density in 1.4.1 is an average
when the powder is composed of nanoparticles, which property of particles contained in a powder, whereas the density
suggests that the Hausner ratio might not be a good here is a property of an individual particle.
measure of the flowability or compressibility of 2 If we denote the volume equivalent diameter of a particle by d ,
nanoparticles [2]. Further study will be required to the shape dependence of d can be expressed by d C(d ) v
b
b
b
establish a method for characterizing nanoparticles in d C(d ), where is the dynamic shape factor and C(d) the
v
v
terms of bulk density. Cunningham slip correction.
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