Page 177 - Book Hosokawa Nanoparticle Technology Handbook

3.5 INTERACTIONS BETWEEN PARTICLES FUNDAMENTALS
For adhesive fine powder with low flowability, the b) Angle of repose
porosity shows a high value and, so adhesion and The angle of repose is the angle between the horizontal
flowability of a powder can be judged from the plane and the free surface of the powder bed. The angle
absolute value of the measured porosity. In addition, of repose is widely used practically because adhesion
from the tap apparent density and loose apparent and flowability of the powder bed can be appraised
t
density of sieve packing, the compressibility C c simply based on it. As shown in Fig. 3.5.26, the meas-
b
can be calculated by the following equation. uring method of the angle of repose is classified into
three kinds as the feeding method where the powder
feeds from the funnel, the discharge method where the
C t b powder discharge from a hole on bottom of the bed, and
c (3.5.59)
t the gradient method where the powder bed in tabling
bin collapse by rotation. There is a report [3] of the cor-
relation between the angle of repose and the internal
The compressibility C shows the degree of flowabil- friction angle by powder shear tests. Carr’s flowability
ity of a powder. The relationship between particle index [4] can be calculated from the angle of repose,
diameter D p and void fraction is shown in compressibility, the angle of spatula, homogeneity, and
Fig. 3.5.25 which has been obtained in a compression the degree of agglomeration. Using the Carr’s flowabil-
packing test. The figure shows that the void fraction ity index, powder can be classified into seven types
is increasing with the decreasing of particle size. The such as excellent flow: 90–100, good flow: 80–90, fair
effect of the particle size on the void fraction can be flow: 70–79, average: 60–69, poor flow: 40 59, very
expressed by Roller’s equation (3.5.60) [2]. The high poor: 20 39, and sticky: 0–19.
exponent value n in the equation means the strong
effect of particle size on packing and this result can be c) Tensile test
usually found in the adhesive fine powder The concept of powder bed tensile test is shown in
Fig. 3.5.27. The procedure of the test is as follows. A
powder bed is packed in the divided cell, and a half of
1
the cell is fixed and another cell is moving with ten-
⎛ 1 ⎞ ⎛ Dp ⎞ n (3.5.60) sile force. The tensile strength of powder bed can
T
1 ⎜ ⎝ 1 ⎟ ⎜ c ⎠ ⎟ be calculated from the tensile force at the breaking
⎠ ⎝ Dp
c
point divided by the breaking area. The tensile tester
is roughly classified into two types such as horizontal-
where Dp is the critical particle size beyond which type tensile and vertical-type tensile by the tensile
c
the effect of particle size on the porosity disappears, force direction [5]. In each of the tester, the powder is
and is the constant value of void fraction above crit- packed in the cell, and pre-consolidated in vertical
c
ical particle size Dp . direction before the tensile test. The measurement
c
result of the vertical type tensile tester which pulls the
cell in the same direction with pre-consolidation is
larger than the horizontal type tester which pulls the
cell in a direction perpendicular to pre-consolidation.
For the vertical-type tensile tester, the packed powder
slide on the container wall surface and is easy to fall
down. The dense packing of nanoparticle is very dif-
ficult, in general, and therefore the tensile strength of
nanoparticles becomes small. Therefore, it is neces-
sary to make the friction of the device small. In order
to achieve small friction, the horizontal tensile tester
uses the suspended type rather than the ball bearing
system as in the figure. Tensile strength decreases
T
linearly with void fraction on the semi-logarithmic
paper with on the vertical axis of the logarithmic
T
scale. Thus, the following equation can be derived
experimentally

= k exp( − k ) (3.5.61)
/
1
2
T
where k and k are the constants which show the
2
1
Figure 3.5.25 adhesion of powder and the void fraction dependency
Effect of particle size on void fraction. of tensile strength, respectively. The following
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