ANGLE OF REPOSE

PRACTICAL 4: ANGLE OF REPOSE

OBJECTIVE:

To determine the angle of repose of the sand particles with glidant and without glidant.

INTRODUCTION:

The angle of repose of a powder is important to determine a good flowability. Various methods can be used to measure the angle of repose of a powder. In this practical, students are given 4 different materials with different properties that were taken from dried 'bulk' and a glidant was added to it. Test was conducted to determine the angle of repose and factors that could influence angle of repose.

APPARATUS AND MATERIALS:

Ruler, funnel, 355mm, 500mm, 850mm, and various size of sand, magnesium stearate (glidant)

PROCEDURES:

1.      100g of sand particles were prepared.

2.      The sand was poured into the prepared funnel.

3.      The funnel was pulled up and the sand flows forming a heap or peak.

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

5.      The angle of repose of the sand was calculated.

6.      The steps were repeated with various materials of different properties.

7. Then, 0.5% w/w of Magnesium stearate, which is a glidant is added into the sand particles.  
8. The angle of repose of the sand with glidant was measured for various materials.
9. The steps were repeated with 1% w/w, 2% w/w, and 3% w/w of Magnesium stearate.

 

RESULT:

                                                                                                                            

                                                                                                                 

                                     h, cm                                     

                                                                              

                                                                w, cm

Diameter of heap = 4.8cm

\Width of heap (w) = 2.4cm

i)                    For 0.5% w/w of Magnesium stearate (glidant):

Sizes of sand particles (mm)	Height of heap, h (cm)		Angle of repose, q
	Without glidant	With glidant	Without glidant	With glidant
355	2.0	2.1	39.8˚	41.2˚
500	2.1	2.2	41.2˚	42.5˚
850	2.2	2.1	42.5˚	41.2˚
Various size	2.3	2.4	43.8˚	45.0˚

ii)                  For 1% w/w of Magnesium stearate (glidant):

Sizes of sand particles (mm)	Height of heap, h (cm)		Angle of repose, q
	Without glidant	With glidant	Without glidant	With glidant
355	1.4	1.7	30.3˚	35.3˚
500	1.3	1.7	28.4˚	35.3˚
850	1.3	1.2	28.4˚	26.6˚
Various size	1.5	1.8	32.0˚	36.9˚

iii)                For 2% w/w of Magnesium stearate (glidant):

Sizes of sand particles (mm)	Height of heap, h (cm)		Angle of repose, q
	Without glidant	With glidant	Without glidant	With glidant
355	1.7	2.0	35.3˚	39.8˚
500	2.0	2.2	39.8˚	42.5˚
850	1.8	1.9	36.9˚	38.4˚
Various size	2.2	2.6	42.5˚	47.3˚

iv)                For 3% w/w of Magnesium stearate (glidant):

Sizes of sand particles (mm)	Height of heap, h (cm)		Angle of repose, q
	Without glidant	With glidant	Without glidant	With glidant
355	2.0	2.6	39.8˚	47.3˚
500	2.1	2.5	41.2˚	46.2˚
850	1.7	2.0	35.3˚	39.8˚
Various size	2.4	2.9	45.0˚	50.4˚

CALCULATION:

Angle of repose, q can be calculated by using the formula:

                 

                                   

DISCUSSION:

1. What are the angles of repose for the various materials?

i) For 0.5% w/w of Magnesium stearate:

Sizes of sand particles (mm)	Angle of repose, q
	Without glidant	With glidant
355	39.8˚	41.2˚
500	41.2˚	42.5˚
850	42.5˚	41.2˚
Various size	43.8˚	45.0˚

ii) For 1% w/w of Magnesium stearate:

Sizes of sand particles (mm)	Angle of repose, q
	Without glidant	With glidant
355	30.3˚	35.3˚
500	28.4˚	35.3˚
850	28.4˚	26.6˚
Various size	32.0˚	36.9˚

iii) For 2% w/w of Magnesium stearate:

Sizes of sand particles (mm)	Angle of repose, q
	Without glidant	With glidant
355	35.3˚	39.8˚
500	39.8˚	42.5˚
850	36.9˚	38.4˚
Various size	42.5˚	47.3˚

iv) For 3% w/w of Magnesium stearate:

Sizes of sand particles (mm)	Angle of repose, q
	Without glidant	With glidant
355	39.8˚	47.3˚
500	41.2˚	46.2˚
850	35.3˚	39.8˚
Various size	45.0˚	50.4˚

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

·         The size of the particles. Fine grained material will form a shallower pile, with a smaller angle of repose than coarser grains. 

·         Particle shape

·         Moisture. Moist material has a much higher angle of repose than dry material.

·         The method by which the angle of repose is measured.

·         The different coefficients of friction between different substances.

·         Presence of other components such as glidants

·         Surface area where the pile is formed

3. What other methods that can be used to determine the angle of repose of a material?

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

ii) Fixed Funnel Method
This method is usually used to measure static angle of repose. 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. Stop pouring the material when the pile reaches a predetermined height or the base a predetermined width. Rather than attempt to measure the angle of the resulting cone directly, divide the height by half the width of the base of the cone. The inverse tangent of this ratio is the angle of repose.

iii) Revolving Cylinder Method
This method is recommended for obtaining the dynamic angle of repose. The material is placed within a cylinder with a clear, flat cover on one end and rotating it at specified speed. The dynamic angle of repose is the angle formed by the inclined surface of a powder with the horizontal when rotating in the cylinder. Increasing the rotation speed further deforms the flat surface to an S shaped profile. The internal angle of kinetic friction is defined by the plane separating those particles sliding down the top layer of the powder and those particles that are rotating with the drum (with roughened surface).

Glidant is a substance that is intended to promote flow of granulations or powder materials by reducing the friction between the particles. A glidant will only work at a certain range of concentrations. Above a certain concentration, the glidant will in fact function to inhibit flowability. The result is a decrease in the angle of repose which is an indication of an enhanced powder's flowability. Theoretically, the optimum concentration for the glidant to improve the flowability is 1% w/w. In the practical, for both 0.5% w/w and 1% w/w of magnesium stearate, the angle of repose had slightly increased for materials used except for size of 850mm. The angle supposed to be decreased as the glidant promote flow of sand particles. This is might due to some errors occurred throughout the weighing step of the sand and the glidant. There is also error when the method for measuring the angle is carried out. For concentration of 2% and 3%, the angle of repose had increased for all the materials used as the glidant had inhibited the flowability of the sand particles.      

CONCLUSION:

The angle of repose is defined as the angle formed between the horizontal plane and a sloped line extending along the face of a heap formed by pouring material onto the horizontal surface. The angle of repose provides a reliable, quick and simple method to measure the flowability of different powders. The greater the angle of repose, the greater is the cohesiveness of the powder (poor flowing), whereas the lower the angle of repose, the more free flowing the bulk material will be. A glidant is a substance that is added to a powder to improve its flowability. The result is a decrease in the angle of repose which is an indication of an enhanced powder's flowability. However, above a certain concentration, the glidant will in fact function to inhibit flowability.

PICTURE:

REFERENCES:

1)http://www.collectionscanada.gc.ca/obj/s4/f2/dsk3/SSU/TC-SSU-07032006115722.pdf

2)http://www.slideshare.net/visualbeeNetwork/angle-of-repose