The mechanism of size reduction depends upon the nature of the material and each material requires separate treatment. Generally, fracture occurs along the lines of weakness. During size reduction, fresh surfaces are created or existing cracks and fissures are opened up, wherein the former requires more energy. There may be a tendency that after processing agglomerates of particles are formed. Size reduction is an energy-inefficient process because a small amount of energy is required in subdividing the particles. A lot of the energy is spent in overcoming the friction and inertia of machine parts and the friction between particles and deforming the particles without breaking them. This energy is released as heat.
Laws Governing Size Reduction Process
One of the mechanisms of
size reduction called grinding is very inefficient and thus it is important to
use energy as efficiently as possible. It is not easy to calculate the minimum
energy required for a given size reduction process. Fortunately, certain
theories are useful in approximately calculating energy requirements. Although several
theories have been put forth to predict the energy requirements, none give
accurate results.
The theories of size
reduction and estimation of energy requirement depend upon the basic assumption
that the energy required to produce a change dL in a particle of a typical size
dimension L, is a simple power function of L:
`\frac{dE}{dL}=KL^n ...(1)`
Where dE is differential
energy required, dL is changed in a typical dimension; L is the magnitude of a
typical length dimension, and K, n, are constants.
Kicks Law:
Kick assumed that the
energy required to reduce a material in size was directly proportional to the
size reduction ratio dL/L. This implies that n in equation (1) is equal to −1.
If,
`K=K_kf_c ...(2)`
Where K_{K} is called Kick's constant and f_{c} is called the crushing strength of the material. Thus, we have:
`\frac{dE}{dL}=K_kf_cL^{-1} ...(3)`
On integrating equation (3)
gives:
`E=K_kf_c\log_e\frac{L_1}{L_2} ...(4)`
Equation (4) is a statement of Kick's Law. It states that the specific energy required to crush a material, for example, is from 10 cm to 5 cm. The same energy is required to crush the same material from 5 mm to 2.5 mm. Thus, in simple terms Kicks law can be stated as the energy required to reduce the size of a given quantity of material is constant for the same reduction ratio regardless of the original size.
Rittinger’s Law:
Rittinger assumed that
the energy required for size reduction is directly proportional to the change
in surface area. This leads to a value of −2 for n in equation (1) as the area
is proportional to the length squared. If we put:
`K=K_Rf_c ...(5)`
Then,
`\frac{dE}{dL}=K_Rf_cL^{-2} ...(6)`
where KR is called
Rittinger's constant. On integrating equation (6), we obtain:
`E=K_Rf_c\left(\frac1{L_2}-\frac1{L_1}\right) ...(7)`
Equation (7) is known as
Rittinger's Law.
The specific surface of a
particle (the surface area per unit mass) is proportional to 1/L. Rittinger's
Law states that the energy required to reduce L for a mass of particles from 10
cm to 5 cm would be the same as that required to reduce the same mass of 5 mm
particles down to 4.7 mm. This is a very much smaller reduction, in terms of
energy per unit mass for the smaller particles than that predicted by Kick's
Law. Thus in simple terms, Rittinger's law can be stated as the energy used for
particulate size reduction is directly proportional to the new surface
produced.
Griffith theory:
The Griffith theory states that the amount of force to be applied depends on
the crack length and focus of stress at the atomic bond of the crack apex.
Bond’s law:
Bond's law states that energy used to reduce particle size is proportional to the
square root of the diameter of the particle produced.
For the grinding of
coarse particles wherein the increase in surface area per unit, mass is
relatively small, Kick's Law is a reasonable approximation. For size reduction
of fine powders where large areas of new surfaces are being created better fits
Rittinger's Law.
Size reduction of
pharmaceutical products involves a reduction mechanism consisting of deforming
the material pieces until it breaks or tear. This deformation may be achieved
by applying diverse forces. The types of forces commonly used in the size
reduction process are compression, impact, attrition or shear, and cutting Fig.1.
In this operation, more than one type of force is usually acted. Table.1
summarizes these types of forces and examples of some of the mills commonly
used in the pharmaceutical industry.
Table.1: Types of Forces
Used In Size Reduction
Force |
Principle |
Example
of equipment |
Approximate
particle size (Âµm) |
Compression |
Nutcracker |
Roller
mill Pestle-Mortar Crushing rolls |
50
- 10,000 |
Impact |
Hammer |
Hammer
mill disintegrator |
50
- 8000 |
Attrition |
File |
Colloidal
mill roller mill |
1
- 50 |
Cutting |
Scissors |
Scissors
shears cutter mill rotary knife cutter |
100
- 80,000 |
Combined
impact and attrition |
Ball |
Ball
mill |
1
- 2000 |
Compression
In this mechanism, the
material is crushed by the application of pressure. Compressive forces are used
for the coarse crushing of hard materials. Coarse crushing implies reduction to
a size of about 3 mm.
Impact
Impact occurs when the
material is more or less stationary and is hit by an object moving at high
speed or when the moving particle strikes a stationary surface. In both cases,
the material is crushed into smaller pieces. Usually, both will take place,
since the substance is hit by a moving hammer and the particles formed are then
thrown against the casing of the machine. Impact forces can be regarded as
general-purpose forces and may be associated with the coarse, medium, and fine
grinding of a variety of materials.
Attrition
In attrition, the
material is subjected to pressure as in compression, but the surfaces are
moving relative to each other, resulting in shear forces that break the
particles. Shear or attrition forces are applied in fine pulverization when the
size of products can reach the micrometer range. Sometimes a term referred to as
ultra-fine grinding is associated with processes in which the sub-micron range
of particles is attained.
Cutting
Cutting reduces the size
of solid materials by mechanical action (sharp blade/s) by dividing them into
smaller particles. Cutting is used to break down large pieces of material into
smaller pieces and definite shapes suitable for further processing, such as in
the preparation of powders and granules.
Fig.1: Mechanisms of Size Reduction |
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