Size Reduction Laws

Introduction:

Size reduction or Comminution is an important unit operation in which solid materials are broken into smaller sizes by Mechanical stress .The important reasons for size reduction are easy handling, increase in surface area per unit volume, separation of entrained particles. And the mechanical methods which are commonly used for size reduction are (1) compression (2) impact (3) attrition (4) cutting. Depending upon the requirement of desired particles size, the end result is achieved in several steps. The operation is highly energy intensive; hence a variety of specialized equipment is available for specific applications. Reduction to very fine sizes is much more costly in terms of energy as compared to relatively coarse products.

Principles of size reduction:

Criteria for size reduction

An ideal crusher would (1) have a large capacity; (2)require a small power input per unit of product:(3) yield a product of the single size distribution desired.

Energy and power requirements in size reduction

The cost of power is a major expense in crushing and grinding, so the factors that control this cost are important.

Size Reduction laws:

  1. Rittinger’s law
  2. Kick's law
  3. Bond's law
Rittinger’s law: The energy required in crushing is proportional to the new surface created as a result of particle fragmentation.

Kick’s law: The Energy is proportional to the size reduction ratio.

Bond’s law: The total work input represented by a given weight of crushed product is inversely proportional to the square root of the diameter of the product particles.

Empirical relationships: Rittinger’s and Kick’s law

The work required in crushing is proportional to the new surface created. This is equivalent to the statement that the crushing efficiency is constant and, for a giving machine and material, is independent of the sizes of feed and product. If the sphericities F a (before size reduction) and F b (after size reduction) are equal and the machine efficiency is constant, the Rittinger’s law can be written as

Size Reduction Laws - Mineral Process Engineering
where P is the power required, Size Reduction Laws - Mineral Process Engineering is the feed rate to crusher, Size Reduction Laws - Mineral Process Engineeringis the average particle diameter before crushing, Size Reduction Laws - Mineral Process Engineering is the average particle diameter after crushing, and Kr is Rittinger’s coefficient. Kick’s law: The work required for crushing a given mass of material is constant for the same reduction ratio that is the ratio of the initial particle size to the finial particle size.
Size Reduction Laws - Mineral Process Engineering
Where Kk is Kick’s coefficient. Bond crushing law and work index: The work required to form particles of size Dp from very large feed is proportional to the square root of the surface-to-volume ratio of the product, sp/vp. Since F s = 6/Dp, it follows that
Size Reduction Laws - Mineral Process Engineering
Where Kb is a constant that depends on the type of machine and on the material being crushed. The work index, wi, is defined as the gross energy required in KWH/ short ton of feed to reduce a very large feed to such a size that 80% of the product passes a 100m m screen. If Dp is in millimeters in KW, and Size Reduction Laws - Mineral Process Engineering in tons per hour, then
Size Reduction Laws - Mineral Process Engineering
If 80% of the feed passes a mesh size of Dpa millimeters and 80% of the product a mesh of Dpb millimeters, it follows that
Size Reduction Laws - Mineral Process Engineering

Size Reduction Equipment:

Size Reduction Equipment is divided into crushers, grinders, ultrafine grinders, and cutting machines. Crushers do the heavy work of breaking large pieces of solid material into small lumps. Primary crushers operate on run-of -mine material accepting anything that comes from mine face and breaking it into 150 to 250 mm lumps. Secondary crushers reduce these lumps into particles perhaps 6mm in size. Grinders reduce crushed feed to powder. The product from an intermediate grinder might pass a 40-mesh screen; most of the product from a fine grinder would pass a 200-mesh screen with a 74mm opening. An ultrafine grinder accepts feed particles no larger than 6mm and the product size is typically 1 to 5mm. Cutters give particles of definite size and shape, 2 to 10mm in length. The principal types of size-reduction machines are as follows

A. Crushers (coarse and fine)
    1. Jaw crushers
    2. Gyratory crushers
    3. Crushing rolls
B. Grinders (intermediate and fine)
    1. Hammer mills; impactors
    2. Rolling-compression mills
    3. Attrition mills
    4. Tumbling mills
C. Ultrafine grinders
    1. Hammer mills with internal classification
    2. Fluid-energy mills
    3. Agitated mills
D. Cutting machines
    1. Knife cutters; dicers; slitters


Questions and Answers:

(1) What is size reduction?
Ans: Size reduction or Comminution is the process in which solid materials are reduced in size, by Crushing, grinding and other process .

(2) What are the mechanical methods used for size reduction?
Ans: (a) Compression (b) attrition (c) impact (d) cutting.

(3) What are the size reduction laws?
Ans: (a) Rittinger's law. (b) Kick's law. (c) Bond's law.

(4) Define Rittinger's law?
Ans: It is defined as the energy required in crushing is proportional to the new surface created as a result of particle fragmentation.

(5) Define Bond's work index (wi)?
Ans: It is defined as the gross energy required in KWH/ short ton of feed to reduce a very large size of feed to such a size that 80% of the product passes a 100mm screen.

References:

1 http://en.wikipedia.org/wiki/Crusher

2 Principles of Mineral Dressing by A.M.Gaudin

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