D. Angle of Repose

Title

Angle of repose

Objective

To determine the flow characteristics of a powder

Introduction

The angle of repose for a particular powder can be used to determine the flow characteristics of a powder. Various methods are available to measure this value. In this practical, students are given sand of various sizes and with/without the addition of glidant. The sample is poured onto a horizontal surface and the angle of the resulting pyramid is measured. The powder may also be tumbled in a rotating drum to give the dynamic angle of repose. Free-flowing powders will tend to lower angles of repose. This test is conducted to determine the angle of repose and the factors that may influence it.

Material

·         150mg sand mixture

·         355mg sand mixture

·         500mg sand mixture

·         850mg sand mixture

·         Various size sand mixtures

·         Various size + water sand mixture

Apparatus

·         Cylinder

·         Rubber stopper

·         Newspaper

·         Weigh balance

·         Spatula

·         Weighing boat

Procedure

1. 100g of sand is prepared.

2. The sand is placed in the cylinder with the rubber base at the bottom.

3. The cylinder is removed and the sand is allowed to flow out and form a heap.

4. The height, slope and diameter of the heap is measured.

5. The angle of repose is calculated.

6. The experiment is repeated using other sand or with the addition of glidant/water.

Results and calculations

Diameter of the heap is = 4.7cm

Angle of repose, θ = tan^-1 [height of slope(cm) / radius of heap(cm)]

Materials/sands	Height of slope (cm)	Angle of repose (ᵒ)
150mg	3.8 cm	58.27
355mg	1.9 cm	38.96
500mg	2.0 cm	40.40
850mg	1.8 cm	37.45
Various sizes	2.1 cm	41.78
Various sizes + water	4.3 cm	61.34

150mg sand mixture

Angle of repose, θ = tan^-1 [height of slope(cm) / radius of heap(cm)]

                               = tan^-1(3.8/2.35)      

                               = 58.27 ᵒ

355mg sand mixture

Angle of repose, θ = tan^-1 [height of slope(cm) / radius of heap(cm)]

                               = tan^-1(1.9/2.35)      

                               = 38.96 ᵒ

500mg sand mixture

Angle of repose, θ = tan^-1 [height of slope(cm) / radius of heap(cm)]

                               = tan^-1(2.0/2.35)      

                               = 40.40 ᵒ

  

850mg sand mixture

Angle of repose, θ = tan^-1 [height of slope(cm) / radius of heap(cm)]

                               = tan^-1(1.8/2.35)      

                               = 37.45 ᵒ

Various sizes sand mixture

Angle of repose, θ = tan^-1 [height of slope(cm) / radius of heap(cm)]

                               = tan^-1(2.1/2.35)      

                               = 41.78 ᵒ

Various sizes + water

Angle of repose, θ = tan^-1 [height of slope(cm) / radius of heap(cm)]

                               = tan^-1(4.3/2.35)      

                               = 61.34 ᵒ

Questions

1. What are the angles of repose for the sands that you use?

Materials/sands	Angle of repose (ᵒ)
150mg	58.27
355mg	38.96
500mg	40.40
850mg	37.45
Various sizes	41.78
Various sizes + water	61.34

2. What are the factors that can influence the angle of repose of a powder?

• Size of powders : powder size increase, the angle of repose decrease.
• Shape of powder : more circular the powder, more easier the powder to flow, and angle of repose will decrease
•  Cohesiveness : increase the cohesiveness of a powder, angle of repose will increase
• Water content : if there are present of water in the powder, the angle of repose will increase

3. What other methods can you use to measure the angle of repose?

• Tilting box method : this method for fine grained , non-cohesive materials with individual particle size less than 10mm.
  
  
• Fixed funnel method : the powder is poured through a funnel to form a cone. The tip of funnel should be held close to the growing cone and slowly raised as the pile grow.
• Revolving cylinder method : the powder 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.

Discussion

This experiment is to determine flow characteristics of the powder by using angle of repose. The greater the angle of repose, the greater the cohesion of powder. From the result, we can see that 355mg and 850mg of sand mixture has angle of repose 38.96ᵒ and 37.45ᵒ which can be categorized as fair flow property. Both of these sands do not need any aid to flow. Therefore it can flow easily. For 500mg and various sizes of sand mixture their angle of repose is 40.40ᵒ and 41.78ᵒ. This shows that both mixtures have passable flow property. Lastly for 150mg and various size + water their angle of repose is 58.27ᵒ and 61.34ᵒ which shows that very poor flow property. This is because 150mg is small sizes sand, which has a strong bond between the molecules. Therefore the flow property is poor compared with the bigger size. For various sizes add with water, is also a very poor flow property, this is because the sand contains water which prevent the sand to flow easily.

Conclusion

1. The higher the angle of repose, the greater the cohesion of powder. Therefore the sand has difficulty to flow easily.
2. The smaller the sizes of particle, the more difficult the sand to flow. This is because there have a stronger interaction between the sand molecules.

References

1. http://www.pharmacopeia.cn/v29240/usp29nf24s0_c1174.html
2. http://www.gardco.com/pages/density/powderangle.cfm