Apparatus and Materials:
Funnel,
hopper, stopper, ruler, Magnesium Stearate as glidant, 100g of
355, 500, 850 micron and various size of sand, newspaper, weighing boats,
spatula and weighing balance
Procedures:
1. 100g
of 355 micron sand, without the addition of glidant was measured by using
weighing balance.
2. The
sand was then inserted into a funnel.
3. The
funnel was then lifted up and the sand was left to form a heap.
4. The
height, slope and the diameter of the heap of the sand was then measured by
using the ruler.
5. The
angle repose of the heap of the sand was measured.
6. Steps
1 to 5 were repeated by using 100g of 500 micron, 850 micron and various size
of sand respectively, without the addition of glidant.
7. Steps
1 to 5 were repeated by using 90g of 355 micron, 500 micron, 850 micron and
various size of sand respectively. For each material, 10g of magnesium stearate
was added as a glidant.
Results:
a)
Angle of repose with and without 1% glidant
Diameter of stopper is
4.70 cm
Radian of stopper is
2.35 cm
Materials/sand
(microns)
|
Height
of the heap without glidant (cm)
|
Slope
of the heap without glidant (cm)
|
Angle
of repose without glidant
|
Height
of the heap with 1% magnesium stearate (cm)
|
Slope
of the heap with 1% magnesium stearate (cm)
|
Angle
of repose with glidant
|
150
|
2.2
|
3.2
|
43.11°
|
3.8
|
4.5
|
58.27°
|
355
|
2.0
|
3.1
|
40.40°
|
2.3
|
3.3
|
44.38°
|
500
|
1.9
|
3.0
|
38.96°
|
2.1
|
3.2
|
41.78°
|
850
|
1.8
|
2.9
|
37.45°
|
2.1
|
3.2
|
41.78°
|
Various
sizes
|
2.3
|
3.3
|
44.38°
|
2.2
|
3.2
|
43.11°
|
Calculations:
1.
Angle of repose without glidant:
a)
Sand 150 microns : tan θ = 2.2cm/2.35cm
θ
= 43.11°
b)
Sand 355 microns: tan θ = 2.0cm/2.35cm
θ = 40.40°
c)
Sand 500 microns:
tan θ = 1.9cm/2.35cm
θ
= 38.96°
d)
Sand 850 microns: tan θ = 1.8cm/2.35cm
θ = 37.45°
e)
Various size: tan θ = 2.3cm/2.35cm
θ = 44.38°
2.
Angle of repose with 1% glidant:
a)
Sand 150 microns: tan θ = 3.8cm/2.35cm
θ = 58.27°
b)
Sand 355 microns: tan θ = 2.3cm/2.35cm
θ = 44.38°
θ = 44.38°
c)
Sand 500 microns: tan θ = 2.1cm/2.35cm
θ = 41.78°
d)
Sand 850 microns: tan θ = 2.1cm/2.35cm
θ = 41.78°
e)
Various size: tan θ = 2.2cm/2.35cm
θ = 43.11°
b) Angle
of repose with and without 5% glidant
Diameter of stopper is
5.00 cm
Radian of stopper is 2.50 cm.
Materials/ sand (mm)
|
Height of the heap
without glidant (cm)
|
Slope of the heap without
glidant (cm)
|
Angle of repose
without glidant
|
Height of the heap
with 5% magnesium stearate
(cm)
|
Slope of the heap
with 5% magnesium stearate (cm)
|
Angle of repose with
glidant
|
150
|
3.90
|
4.6
|
57.34°
|
4.10
|
4.8
|
58.63°
|
355
|
2.20
|
3.3
|
41.35°
|
3.50
|
4.3
|
54.46°
|
500
|
1.90
|
3.1
|
37.23°
|
2.40
|
3.5
|
43.83°
|
850
|
1.80
|
3.1
|
35.75°
|
2.80
|
3.8
|
48.23°
|
Various sizes
|
2.40
|
3.5
|
43.83°
|
3.00
|
3.9
|
50.19°
|
Calculations:
1) Angle
of repose without glidant:
a) 150 microns : tan
θ = 3.9cm/2.5cm
θ
= 57.34 °
b) 355 microns : tan
θ = 2.2cm/2.5cm
θ = 41.35 °
c) 500 microns : tan θ = 1.9cm/2.5cm
θ =
37.75 °
d) 850 microns : tan
θ = 1.8cm/2.5cm
θ = 35.75 °
e) Various sizes : tan θ = 2.4cm/2.5cm
θ = 43.83 °
2) Angle
of repose with 5% glidant:
a) 150 microns : tan
θ = 4.1cm/2.5cm
θ = 58.63 °
b) 355 microns : tan
θ = 3.5cm/2.5cm
θ = 54.46 °
c) 500 microns : tan θ = 2.4cm/2.5cm
θ =
43.83 °
d) 850 microns:
tan θ = 2.8cm/2.5cm
θ = 48.23 °
e) Various sizes : tan θ = 3.0cm/2.5cm
θ = 50.19 °
c)
Angle of repose with and without 10% glidant
Diameter of stopper is
4.80 cm
Radian of stopper is
2.40 cm
Materials/sand
(mm)
|
Height
of the heap without glidant (cm)
|
Slope
of the heap without glidant (cm)
|
Angle
of repose without glidant
|
Height
of the heap with 10% magnesium stearate (cm)
|
Slope
of the heap with 10% magnesium stearate (cm)
|
Angle
of repose with glidant
|
150
|
3.65
|
4.3
|
56.67 °
|
4.60
|
5.2
|
62.45 °
|
355
|
1.90
|
3.1
|
38.37 °
|
4.30
|
4.9
|
60.83 °
|
500
|
1.75
|
2.9
|
36.10 °
|
3.50
|
4.2
|
55.56 °
|
850
|
1.75
|
2.9
|
36.10 °
|
3.40
|
4.1
|
54.78 °
|
Various
sizes
|
2.00
|
3.1
|
39.81 °
|
4.15
|
4.7
|
59.96 °
|
Calculations:
1. Angle of repose without glidant:
a) 150
microns : tan θ = 3.65cm/2.4cm
θ
= 56.67 °
b) 355
microns : tan θ = 1.9cm/2.4cm
θ
= 38.37 °
c) 500
microns : tan θ = 1.75cm/2.4cm
θ
= 36.10 °
d) 850
microns : tan θ = 1.75cm/2.4cm
θ
= 36.10 °
e) Various
sizes : tan θ = 2.0cm/2.4cm
θ
= 39.81 °
2. Angle of repose with 10% glidant:
a) 150
microns : tan θ = 4.6cm/2.4cm
θ =
62.45 °
b) 355
microns : tan θ = 4.3cm/2.4cm
θ
= 60.83 °
c) 500
microns : tan θ = 3.5cm/2.4cm
θ
= 55.56 °
d) 850
microns : tan θ = 3.4cm/2.4cm
θ
= 54.78 °
e) Various
sizes : tan θ = 4.15cm/2.4cm
θ
= 59.96 °
d) Angle of repose with and without 15%
glidant
Diameter of stopper is
4.6 cm
Radian of stopper is 2.3 cm.
Materials/sand (mm)
|
Height of the heap without glidant (cm)
|
Slope
of the heap without glidant (cm)
|
Angle of repose without glidant
|
Height of the heap when added with 15% of
magnesium stearate (cm)
|
Slope
of the heap with 15% magnesium stearate (cm)
|
Angle of repose with glidant
|
150
|
2.2
|
3.2
|
43.73 °
|
3.8
|
4.4
|
58.82 °
|
355
|
2.0
|
3.0
|
41.00 °
|
3.7
|
4.4
|
58.13 °
|
500
|
1.9
|
2.9
|
39.56 °
|
3.5
|
4.2
|
56.69 °
|
850
|
1.8
|
2.9
|
38.05 °
|
3.0
|
3.8
|
52.52 °
|
Various sizes
|
2.3
|
3.3
|
45.00 °
|
3.3
|
4.0
|
55.12 °
|
Calculations:
1. Angle
of repose without glidant
a) 150 mm : tan
θ = 2.2cm/2.3cm
θ = 43.73 °
b) 355 mm :
tan θ = 2.0cm/2.3cm
θ = 41.00 °
c) 500 mm : tan θ = 1.9cm/2.3cm
θ = 39.56 °
d) 850 mm : tan
θ = 1.8cm/2.3cm
θ = 38.05 °
e) Various sizes : tan θ = 2.3cm/2.3cm
θ
= 45.00 °
2. Angle
of repose with 15% glidant
a) 150 microns : tan
θ = 3.8cm/2.3cm
θ
= 58.82 °
b) 355 microns : tan
θ = 3.7cm/2.3cm
θ = 58.13 °
c) 500 microns : tan θ = 3.5cm/2.3cm
θ
= 56.69 °
d) 850 microns : tan
θ = 3.0cm/2.3cm
θ = 52.52 °
e) Various sizes : tan θ = 3.3cm/2.3cm
θ = 55.12 °
Discussions:
Based
on the results obtained from the several tables above, it is clearly shown that
the results of the angle of repose varies even though the same material is
used. The factors that contribute to the differences in results is discussed in
the question section. According to the general guide found in the Aulton’s
Pharmaceutics, materials that have the angle of repose greater than 45
are materials that have poor flow properties
while the materials that have the angle of repose greater than 25
are materials that have excellent flow
properties.
Questions:
1. What is the angle of repose of
the materials?
Size of
particles of sand (microns)
|
Angle of
repose
(Without
Glidant)
|
Angle of
repose
(With
Glidant)
|
|||
1% Glidant
|
5% Glidant
|
10% Glidant
|
15% Glidant
|
||
150
|
43.11°
|
58.27°
|
58.63°
|
62.45 °
|
58.82 °
|
355
|
40.40°
|
44.38°
|
54.46°
|
60.83 °
|
58.13 °
|
500
|
38.96°
|
41.78°
|
43.83°
|
55.56 °
|
56.69 °
|
850
|
37.45°
|
41.78°
|
48.23°
|
54.78 °
|
52.52 °
|
Various
Size
|
44.38°
|
43.11°
|
50.19°
|
59.96 °
|
55.12 °
|
2. What are the factors that influence the angle of repose of the materials?
There
are several factors that influence the angle of repose of the material. The
factors can be categorized into internal and external factors. The internal
factors affecting the angle of repose are the particle size, particle shape and
the cohesiveness. For the external factors, they are the method of measurement
and the presence of other components including moisture. For the method of
measurement, the ledge and the crater methods will give a higher angle of
repose than the angle of repose obtained from the heap formation. For presence
of glidants and moisture will increase the angle of repose of the sand as
compared to the dry sand.
3. What are the other methods that
can be used to calculate angle of repose of the materials?
a) Tilting box method
This
method is used for materials which have an individual particle size less than
10 mm, non-cohesive and fine-grained. The process begins by placing the
material within a box with a transparent side to observe and obtain the result
for the granular test material. The result must be level and parallel to the
base of the box. After that, the box is slowly tilted at the rate of 3
per second until the material begins to slide
in bulk. The angle of tilt is then measured.
A
shape of a cone is formed by using the material poured through a tunnel. The
tip of the funnel should be held close to the growing cone and raised when the
pile grows. This is to minimize the impact of falling particles. The pouring
process stops when the pile reach the targeted height or width. The height and
the width of the base are measured and the inverse tangent of these ratio is
calculated. the inverse tangent of this ratio is the angle of repose.
c) Revolving /Rotating
cylinder method
The
material is placed in a cylinder that has a transparent face. The cylinder is
rotated at a fixed speed the observations of the movement of the material
within the rotating cylinder is made. The speed of rotating cylinder is slow
and the granular material will be used to assume a certain angle when it flows
within the rotating cylinder.
Conclusion:
In
conclusion, the angle of repose varies for every material due to the internal
and the external factors contributing to the angle repose. Thus, the
determination of the angle of repose should be carried out with the presence
and absence of glidant at the same time. The surface charge and the
interparticular friction must also be reduced in order to improve the powder
flow properties and improve the readings of the angle of repose.
References:
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