# Theory of Size Reduction

Size reduction is the process of breaking down solid particle to smaller one. When energy is applied in the form of a stress on a material, it breaks into two or more pieces resulting in generation of new surface area. Energy is used to break or overcome the intramolecular forces of the solid particles so that they are broken into pieces and new area is created. Size reduction is also known as comminution in engineering literature. Size reduction is commonly used in food industries with many purposes. some of the purposes are given below.Advantage of size reduction:
1. Materials of desired size are desired for certain processing as in canning of fruits and vegetables or making of fruit bars.
2. Increased surface area will help in enhanced heat and mass transfer and hence race process are enhanced.
3. The reduced particle size would enable accessibility to the interior of food materials as in leaching of spice oleoresins or oil from oilseeds.
4. In preparation of certain baby foods, soup mixes, gruel. Reduced particle size is necessity and not an option.

Various types of methods used in size reduction.
1. Compression: Example; Nut cracker, Crushing Rolls
2. Impact: Example; Hammer, Hammer mill
3. Shear: Example; Grinding and Milling
4. Cutting: Example; Cutting with knife / saw

Laws of comminution: It is almost impossible to find out the accurate amount of energy requirement in order to affect size reduction of a given material, mainly because
1. There is wide variation in the size and shape of particles both in feed and product
2. Some energy is wasted as heat and sound which cannot be determined exactly.
Laws of comminution proposed by different authors help us to determine the energy consumed in comminution that is the creation of new surface. Many of them do not take care of mechanical losses in the crusher. Most popular comminution laws are those proposed by Kick, Rittinger and Bond.

Kick’s Law (1885):
Kick’s law that can be applied to crushing states that “the work required for crushing a given quantity of material is constant for a given reduction ratio irrespective of its original size”. Mathematically this law can be expressed as

Thus, comminution energy depends only on the reduction ratio and is independent of original size of feed.
Limitation of Kick’s law: The energy required for reducing a 200 mm particle to 50 mm size will be the same as that for a 2 mm particle to 0.5 mm. In fact, higher amount of energy is required for reducing fine particles to still finer size than for breaking down of large pieces of rock. This is because, when we consider smaller particle, more collisions are required and collisions that do not participate in size reduction is wasted. Thus kicks law can be applied to coarse crushing where feed size is quite large and reduction ratio is quite low.

Rittinger’s Law (1867 AD):
A more accurate law of comminution has been proposed by Rittinger. According to this law, work required for size reduction is directly proportional to new surface area created. Mathematically,

Different material have different Rittinger’s number and can be obtained by drop weight test.

 Material Rittinger’s number (m2/J) Galena 0.0957 Pyrite 0.02303 Quartz 0.0179 Calcite 0.07745

Limitations of Rittinger’s law: The chemical losses due to friction and inertia in the grinding equipment are not accounted in Rittinger’s law. These mechanical losses of the crusher can be predicted by running the crusher empty without any charge. Thus overall energy efficiency of crusher can be defined as

Rittinger’s law is applicable mainly to that part of process where new surface is being created and hold most accurately for fine grinding where the increase in surface per unit mass of material is predominant. Thus, it gives better results for fine grinding where there is much larger change in surface area. This law is applicable for feed size less than 0.05 mm.
Both Kick’s and Rittinger’s law have been shown to apply over limited ranges of particle size, provided KK and KR are determined experimentally by tests in a machine of the type to be used and with the material to be crushed. They thus have limited utility.

Bonds law:
An intermediate and more realistic method of predicting power consumption for crushing and grinding was proposed by Bond in 1952.  It states that “the work required to from particles of size is proportional to the square root of the volume ratio (SP/SV) of the product.

Table below shows work indices for some compounds. These data do not vary greatly among different machines and apply to wet crushing. For dry crushing the materials, these values are multiplied by 4/3.

 Material Work index (Kwh/ton) Limestone 12.74 Gypsum rock 6.73 Quartz 13.57 Coal 13.00 Bauxite 8.78
Since work index has been defined with respect to gross energy, it includes the mechanical losses as well. Bonds law therefore predicts gross power consumption in comminution. It applicably has been found for feed size 0.05 – 50 mm.

Summary:

 Laws of comminution Feed size 1. Rittinger’s Law < 0.05 mm 2. Bond’s Law 0.05 – 50 mm 3. Kick’s Law > 50 mm

Reference:

Yahyaei M., Hilden M., Shi F., Liu L.X., Ballantyne G., Palaniandy S. (2016) Comminution. In: Merkus H., Meesters G. (eds) Production, Handling and Characterization of Particulate Materials. Particle Technology Series, vol 25. Springer, Cham