TITLE
Angle of repose
OBJECTIVE
To evaluate angle of
repose of different compositions of sand and factors affecting the angle of
repose of materials.
INTRODUCTION
Angle of repose of powder is
important in determining good powder flow. Several methods can be used to
measure angle of repose of powder. In this experiment, students are given two
different materials with different characteristics, which are taken from dried
bulk and mixed with glidant.
MATERIALS AND APPARATUS
1.
100g of sand with particle
size of various size, 150µm, 355µm, 500 µm, 850 µm,
2.
10 % Magnesium Stearate.
EXPERIMENTAL PROCEDURES
1.
100g of sand is
prepared.
2.
The sand material is
poured through a funnel to form a cone.
3.
The tip of the funnel
should be held close to the growing cone and slowly raised as the pile grows,
to minimize the impact of falling particles.
4.
Stop pouring the
material when the pile reached a predetermined height or the base a
predetermined width.
5.
Rather than attempt to
measure the angle of the resulting cone directly, the height is divided by half
the width of the base of the cone.
6.
The inverse tangent of
this ratio is the angle of repose.
7.
The experiment is
repeated with sand material of different characteristics.
RESULTS
Angle of repose with 1% of glidant
Materials/sand
(mm)
|
Height of the
heap without glidant (cm)
|
Angle of repose
without glidant
|
Height of the
heap when added with 5% of magnesium stearate (cm)
|
Angle of repose
with glidant
|
150
|
2.2
|
43.11°
|
1.7
|
39.00°
|
355
|
2.0
|
40.40°
|
2.0
|
43.60°
|
500
|
1.9
|
38.96°
|
2.3
|
47.60°
|
850
|
1.8
|
37.45°
|
1.9
|
42.14°
|
Various sizes
|
2.3
|
44.38°
|
2.9
|
54.09°
|
Angle of repose with 5% of glidant
The width of stopper is 2.5 cm.
Materials/sand
(mm)
|
Height of the
heap without glidant (cm)
|
Angle of repose
without glidant
|
Height of the
heap when added with 5% of magnesium stearate (cm)
|
Angle of repose
with glidant
|
150
|
3.9
|
57.34°
|
4.1
|
58.63°
|
355
|
2.2
|
41.35°
|
3.5
|
54.46°
|
500
|
1.9
|
37.23°
|
2.4
|
43.83°
|
850
|
1.8
|
35.75°
|
2.8
|
48.23°
|
Various sizes
|
2.4
|
43.83°
|
3.0
|
50.19°
|
1.
100g
of sand
Particle size of sand
|
150 µm
|
355 µm
|
500 µm
|
850 µm
|
Various
|
Height
|
4.4
cm
|
4.2
cm
|
4.3
cm
|
4.0
cm
|
4.0
cm
|
Half
of base width
|
2.5
cm
|
2.5
cm
|
2.5
cm
|
2.5
cm
|
2.5
cm
|
Angle
of repose, θ (˚)
θ
= tan ̄ ¹ (y/x)
|
60.40
|
59.23
|
59.83
|
57.99
|
57.99
|
90g of sand with 10g of
magnesium stearate (10%)
Particle size of sand
|
150 µm
|
355 µm
|
500 µm
|
850 µm
|
Various
|
Height
|
4.0
cm
|
2.3
cm
|
2.2
cm
|
2.1
cm
|
2.4
cm
|
Half
of base width
|
2.5
cm
|
2.5
cm
|
2.5
cm
|
2.5
cm
|
2.5
cm
|
Angle
of repose, θ (˚)
θ = tan ̄ ¹ (y/x)
|
57.99
|
42.61
|
41.35
|
40.03
|
43.83
|
100g
of sands without magnesium stearate:
Materials
|
Diameter, x(cm)
|
Height, y(cm)
|
Angle of repose, θ(˚) θ = tan ̄ ¹ (y/x)
|
150µm
|
2.7
|
3.2
|
49.84
|
355 µm
|
2.7
|
2.8
|
46.04
|
500 µm
|
2.7
|
2.5
|
42.80
|
850 µm
|
2.7
|
2.3
|
40.43
|
Variety of sands
|
2.7
|
2.7
|
45.00
|
100g
of sands with 15% magnesium stearate:
Materials
|
Diameter,
x(cm)
|
Height, y(cm)
|
Angle of
repose, θ (˚)
θ = tan ̄ ¹ (y/x)
|
150 µm
|
2.7
|
4.1
|
56.63
|
355 µm
|
2.7
|
3.6
|
53.13
|
500 µm
|
2.7
|
3.5
|
52.35
|
850 µm
|
2.7
|
3.3
|
50.71
|
Variety of
sands
|
2.7
|
4.0
|
55.98
|
DISCUSSION
There are many factors affecting the angle of repose
of a material, which include particle size, individual material, moisture and
measurement method of angle of repose.
The individual material will affect the angle of
repose, a reflection of the different coefficients of friction between
different substances. The size of the particles is a factor. Greater angularity
of particles will result in more inter-granular friction and interlocking of
particles, contributing to greater shear strength and angle of repose. Other
factors being equal, fine grained material will form a shallower pile, with a
smaller angle of repose than coarser grains.
Moisture affects the angle of repose, as anyone who
has ever built a sand castle can confirm. Water content affects the cohesiveness of particles.
If water is added to particles such as sand, water coating the grains would
tend to bind them together by its surface tension, giving rise to greater
internal cohesion, and therefore shear strength. However, if water is added to
completely saturate the pore spaces, the pore water would act as a lubricant
between grains and the pore pressure would force the grains apart. Moist sand
has a much higher angle of repose than dry sand. Furthermore the method by
which the angle of repose is measured can also affect the measurement.
The method used in this experiment to measure angle of
repose is called fixed funnel method. However, there are also other methods
that can be used to measure the angle of repose of materials
The other methods include tilting box and revolving
cylinder method. Tilting Box method is appropriate for fine-grained,
non-cohesive materials, with individual particle size less than 10 mm. The
material is placed within a box with a transparent side to observe the granular
test material. It should initially be level and parallel to the base of the
box. The box is slowly tilted at a rate of approximately .3 degrees/second.
Tilting is stopped when the material begins to slide in bulk, and the angle of
the tilt is measured.
The next method is Revolving Cylinder Method. The
material is placed within a cylinder with at least one transparent face. The cylinder
is rotated at a fixed speed and the observer watches the material moving within
the rotating cylinder. The effect is similar to watching clothes tumble over
one another in a slowly rotating clothes dryer. The granular material will
assume a certain angle as it flows within the rotating cylinder. This method is
recommended for obtaining the dynamic angle of repose, and may vary from the
static angle of repose measured by other methods. When describing the angle of
repose for a substance, we should always specify the method used.
The glidant added in the experiment is magnesium
stearate is used to enhance the flowability of sand mixture. Different
concentration of glidant gives different effect on the angle of repose
obtained. Generally, powders with angle of repose greater than 50° have
unsatisfactory flow whereas powders with angle of repose less than 25° have
excellent flow properties.
From the results obtained, there is deviation between
the actual angle of repose obtained experimentally with the theoretical value.
It showed that some errors had occurred during the experiment. It is suggested
that the same person should carry out the experiment from beginning to the end
to minimize human error. Furthermore, tapping should be avoided when removing
the cylinder to allow the flow of sand. The same measuring method should be
utilized throughout the experiment.
CONCLUSION
The angle of repose depends on the
shape, particle size and the cohesive property between particles. The value of
the angle of repose will be high if the powder is cohesive and low if the
powder is non-cohesive. Glidant added improves flowability of powders thereby
decreasing the angle of repose.
REFERENCES
2.
Pharmaceutics,
The science of dosage form design (2nd Edition) Michael E.Alton Edinburgh
London New York Philadophia St Louis Sydney Toronto 2002.
3.
Physicochemical
Principals of Pharmacy (2nd Edition)
4.
http://en.wikipedia.org/wiki/Angle_of_repose
