Practical 4

Practical 4 Angle of Repose

Objective

To determine the angle of repose of different types of materials and factors that affect the angle of repose of those materials.

Introduction

Angle of Repose

Angle of repose is one the important element in measurement of cohesion or adhesion of powders. There are different ways to determine the angle of repose of powders. In this practical, students were given 2 types of powders which had different characteristics such as taken from bulk, dried or mixed with glidant.

The angle of repose or the critical angle of repose, of a granular material is the steepest angle of descent or dip of the slope relative to the horizontal plane when material on the slope face is on the verge of sliding. This angle is in the range 0°–90°.

When bulk granular materials are poured onto a horizontal surface, a conical pile will form. The internal angle between the surface of the pile and the horizontal surface is known as the angle of repose and is related to the density, surface area and shapes of the particles, and the coefficient of friction of the material. Material with a low angle of repose forms flatter piles than material with a high angle of repose.

The term has a related usage in mechanics, where it refers to the maximum angle at which an object can rest on an inclined plane without sliding down. This angle is equal to the arctangent of the coefficient of static friction μ_s between the surfaces.

Materials/apparatus

i) weighing balance

ii) different types of sands (150 micrommeter, 355 micrometer, 500micrometer, 850 micrometer,varies size)

iii) ruler

iv) base

Procedure

1) 95g of sands of different sizes were prepared.

2) 5g of Magnesium Stearate was added to each of the different types of sands.

3) The mixture was inserted to funnel prepared.

4) The mixture was let to flow and formed a heap on a base.

5) The height, gradient and the diameter of the heap were measured.

6) Angle of repose of the mixture was measured.

7) The experiment was repeated with sands of another sizes.

Results and Calculations
Angle of repose with 5% of glidant

The width of stopper is 2.5 cm.

Materials/sand (µm)	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°

Angle of repose with 10% of glidant

The width of stopper is 2.5 cm.

Materials/sand (µm)	Height of the heap without glidant (cm)	Angle of repose without glidant	Height of the heap when added with 10% of magnesium stearate (cm)	Angle of repose with glidant
150	4.4	60.40°	4.0	57.99°
355	4.2	59.23°	2.3	42.61°
500	4.3	59.83°	2.2	41.35°
850	4.0	57.99°	2.1	40.03°
Various sizes	4.0	57.99°	2.4	43.83°

Angle of repose with 1% of glidant

The width of stopper is 2.5 cm.

Materials/sand (µm)	Height of the heap without glidant (cm)	Angle of repose without glidant	Height of the heap when added with 1% 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 15% of glidant

The width of stopper is 2.7 cm.

Materials/sand (µm)	Height of the heap without glidant (cm)	Angle of repose without glidant	Height of the heap when added with 15% of magnesium stearate (cm)	Angle of repose with glidant
150	3.2	49.84°	4.1	56.63°
355	2.8	46.04°	3.6	53.13°
500	2.5	42.80°	3.5	52.71°
850	2.3	40.43°	3.3	50.71°
Various sizes	2.7	45.00°	4.0	55.98°

Discussion

1. What are the angle of repose of those materials?

Materials/sand (µm)	Angle of repose without glidant	Angle of repose with 5% glidant
150	57.34°	58.63°
355	41.35°	54.46°
500	37.23°	43.83°
850	35.75°	48.23°
Various sizes	43.83°	50.19°

2. What are the factors that affect the angle of repose of the materials?

Properties of particles such as size and cohesion/adhesion of particles, angularity 

3. What are another method that can affect the angle of repose?

i) Tilting box method

This 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 0.3 degrees/second. Tilting is stopped when the material begins to slide in bulk, and the angle of the tilt is measured.

ii) 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.

Conclusion

As a conclusion, angle of repose of different materials with glidants are higher than materials without glidants.

References 
1. http://en.wikipedia.org/wiki/Angle_of_repose
2. http://www.oocities.org/wingian_chan/angle/factors.htm