Practical 1D: Angle of Repose

Section D : Angle of Repost

Objective

 To investigate the angle of repost of 355mic, 500mic, 850mic and various sizes of sands and factor affecting it.

Introduction

The angle of repose is produced when a granular material is poured on to a horizontal surface. Angle of repost is the angle formed between side of heap and the horizontal surface. It is related to the density, surface area and coefficient of friction of the material concerned. The tangent of the angle of repose (in degrees) can be determined by reading off the height of the powder cone in mm and dividing it by 50. The measurement of angle of repost is an indirect method to measure the cohesive force of particles. A bigger angle of repost shows that particles with greater cohesive force. Cohesive particles will has lower flowability. 

Apparatus and Materials

 355mic, 500mic, 850mic and various sizes of sands

 Funnel and its rubber stopper

 Ruler

Procedure    

1.   100g for each size of sand was weighted by using electronic balance.

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

3.   The cylinder was removed and the sand allowed to flow out and heap formed.

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

5.   The experiment was repeated by using other sand or with the addition of glidant or water.

      

Question

1. What are the angles of repose for  355mic, 500mic, 850mic and various sizes of sands?

Sand (mic)	Height without glidant (cm)	Angle of repost ( θ )
355	1.9	38.37
500	1.8	36.87
850	1.6	33.69

Sand	Height without glidant (cm)	Angle of repost ( θ )	Height with water (cm)	Angle of repost ( θ )	Height with 1% magnesium stearate	Angle of repost ( θ )
Various Sizes	1.6	33.69	4.8	63.43	2.2	32.41

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

Cohesive force of particles influences the angle of repost of powders, the greater cohesive force resulted in a greater angle of repost.

The next factor influencing angle of repost is water content which affects cohesiveness of particles. If water is added to particles such as sand, water coat the particle surface and tend to bind them together by its surface tension, cause greater internal cohesion and shear strength.

Next, particles’ angularity also affects angle of repost of powder. Greater angularity of particles will increase inter-granular friction and interlocking of particles, thus there will be greater shear strength and a bigger angle of repose.

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

This first method is tilting box method which used form fine-grained, non-cohesive materials, with individual particle size less than 10 mm. The material is placed in a transparent box in order to material. Initially, it placed parallel to the base of the box. The box is slowly tilted at a constant rate of approximately 3 degrees/second. The box will be stop tilted when the material begins to slide in bulk and the angle of the tilt is measured.

Secondly, we can use fixed funnel method. The material is poured through a funnel to form a cone. 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. Material is slowly poured when the pile reaches a predetermined height or the base a predetermined width. The height will be divided by half of the width of the cone base. The inverse tangent of this ratio obtained will be the angle of repost.

Next, revolving cylinder method is used. Material is placed in a cylinder with transparent face. The cylinder is rotated at constant speed and the movement of material within the rotating cylinder is observed. The granular material will assume a certain angle as it flows within the rotating cylinder. This method generally used to determine the dynamic angle of repose, because it might be different from the static angle of repose measured by other methods.

In the absence of tilting box apparatus, we can use shipboard test method to determine approximate angle of repose. Material to be tested is poured very carefully out of a flask onto a sheet of rough textured paper, a symmetrical cone is formed. Thus, angle of repose can be measured from the cone formed.

Discussion

   

      This experiment was conducted to study the angle of repost of 355mic, 500mic, 850mic and various sizes of sands with and without the presence of glidant. Besides, the effect of water on the angle of repost of particles was determined too. The angle of repost is the indirect measure of the particles’ cohesive forces. The greater the cohesive force of the particles, the bigger the angle of repost.The particle with greater cohesive force will has lower flowability.

The angle of repose (θ) was calculated based on the following equation:

tan ( θ) = height /( 0.5 x base)

Height = height of the cone of sand

      Generally, particle shape and particle size influence powder flow. Spherical particles(regular shape particle) flow better than needle-shaped particles(irregular shape particles). It is because spherical shape particle has a regular shape which has minimum inter-particle contact area and thus decrease the cohesive force. A smaller cohesive force increases the flowability of particles. In term of particle size, fine particles do not flow as well as large particles. There is a general correlation between particle size and its flowability. Based on the experiment, sands with size of 850 mic has smallest angle of repost ( 33.69º) can flow freely. Sands with size of 500 mic has greater angle of repost (36.87 º) and thus a lower flowability. When the particle size is 355 mic, it has greatest angle of repost (38.37 º), particle flow become problematic. Hence, the experiment shows that the flowability increases with the increasing particle size. It is because there is greater cohesive force for smaller particle size and thus interferes with its flowability.

      The amount of moisture of the particles often has important effects on the physical and chemical properties of pharmaceutical solids. Flowability is influenced by moisture. The presence of water within sample gives a larger angle of repost (63.43º) than angle for the particle without water (33.69º). It is because moisture will increase cohesive force of particles, thus angle of repost increases, flowability will decrease.

       Magnesium sterate is used as a glidant in the experiment. Glidant is used to improve flowability of particles. It can decrease the cohesive force of the particle and thus a smaller angle of repost will be obtained. It was proven in this experiment, presence of glidant( magnesium sterate) give smaller angle of repost (32.41º) than the angle for particles without glidant. The smaller angle of repost shows that there is smaller cohesive force and greater flowability. However, optimum amount of glidant is used, because excess amount will retard the particles flow.

Conclusion

The greater the angle of repost, it shows that the particles have high cohesive force and low flowability. The presence of water and glidant can influence the flowability of particles too. Water content decrease flowability, result in large angle of repost. Glidant decreases the cohesive force of particles and thus reduce the angle of repost. 

References

1.  http://www.copleyscientific.com/home/pharmaceutical-testing/powder-testing/powder-flowability-testers/angle-of-repose

2. https://www.inkling.com/read/aultons-pharmaceutics-4th/chapter-12/characterization-of-powder-flow