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**Dr. Akmal Hadi Ma’ Radzi School of Bioprocess Engineering**

SIZE REDUCTION Dr. Akmal Hadi Ma’ Radzi School of Bioprocess Engineering

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SIZE REDUCTION Particles of solids are cut or broken into smaller pieces In process industries, solids are reduced by different methods for different purposes Examples: -Chunks of crude ore are crushed to workable size -Synthetic chemicals are ground into powder - Sheets of plastic are cut into tiny cubes or diamonds

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Commercial products must often meet stringent specifications regarding the size and sometimes the shape of the particles they contain The importance of reducing the particle size ; (a) Increases the reactivity of solids (b) Permits separation of unwanted ingredients by mechanical methods (c) Reduces the bulk of fibrous materials for easier handling and for waste disposal

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Size of solids may be reduced in many different ways, but only 4 are commonly used in size-reduction machines: (1) Compression -is used for coarse reduction of hard solids, to give relatively few fines (2) Impact (crash) - gives coarse, medium or fine products (3) Attrition (wear) /rubbing yields very fine products from soft, nonabrasive materials (4) Cutting -gives a definite particle size and sometimes a definite shape, with few or no fines

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**Characteristics of Comminuted Products**

Objective of crushing & grinding-to produce small particles from larger ones Smaller particles are desired because of: -their large surface -their shape, size and number One measure of the efficiency of the operation is based on the energy required to create new surface, since the surface area of a unit mass of particles increases greatly as the particle size is reduced

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Unlike an ideal crusher or grinder-an actual unit does not yield a uniform product, whether the feed is uniformly sized or not The product always consists of a mixture of particles (from maximum size-very small particles) Some machines especially in the grinder class, are designed to control the magnitude of the largest particles in their products, but the fine sizes are not under control

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**In some types of grinders, fines are minimized, but they are not eliminated**

If the feed is homogenous, both in the shapes of the particles and in chemical and physical structure, then the shapes of the individual units in the product may be quite uniform; otherwise, the grains in the various sizes of a single product may differ considerably in shape

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crusher Grinder

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The ratio of the diameters of the largest and smallest particles in a comminuted product is on the order of 10ˆ4 Because of this extreme variation in the sizes of the individual particles, relationships adequate for uniform sizes must be modified when applied to such mixture Unless they are smoothed by abrasion after crushing, comminuted particles resemble polyhedrons with nearly plane faces and sharp edges corners The particles may be compact with length, breadth and thickness nearly equal; or they may be plate like or needlelike

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**Energy And Power Requirement**

The cost of power is a major expense in crushing and grinding During size reduction, the particles of feed material are first distorted and strained The work necessary to strain them is stored temporarily in the solid as mechanical energy of stress, just as mechanical energy can be stored in a coiled spring As additional force is applied to the stressed particles, they are distorted beyond their ultimate strength and suddenly rupture into fragments New surface is generated

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Since a unit area of solid has a definite amount of surface energy, the creation of new surface requires work, which is supplied by the release of energy of stress when the particle breaks By conservation of energy, all energy of stress in excess of the new surface energy created must appear as heat

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**Crushing Laws And Work Index**

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. The relationship between the diameter of the particles and the energy required for grinding is expressed from the equation below: For n = 2 and if the sphericities Фa (before size reduction) and Фb (after size reduction) are equal and the machine efficiency is constant, the Rittinger’s law can be written as d𝐸=− 𝐾𝑑 𝐷 𝑝 ( 𝐷 𝑝 ) 𝑛 where K and n are constant. where P is the power required, m is the feed rate to crusher, D1 is the average particle diameter before crushing, D2 is the average particle diameter after crushing, and Kr is Rittinger’s coefficient 2 1

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**where Kk is Kick’s coefficient.**

Kick’s law: for n =1, 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 where Kk is Kick’s coefficient. 1 2

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Bond’s Law: for n= 1.5 Kb – a constant that depends on the type of machine and on the material being crushed Work Index, Wi - defined as the gross energy requirement in kilowatthours per ton (kWh/ton)of feed needed to reduce a very large feed to such a size that 80% of the product passes a 100µm screen

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**If Dp in mm, P in kW, in ton/hr**

If 80% of feed passes a mesh size of Dpa mm and 80% of the product a mesh of Dpb mm, The work index includes the friction in the crusher and the power given by the above equation is gross power or (English unit)

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**Equipment for Size Reduction**

Size reduction equipment is divided into: Crusher Grinder Ultrafine grinder Cutting machine

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Crusher Do the heavy work of breaking large pieces of solid material into small pieces A slow speed machines for coarse reduction of large quantities of solids Primary crusher- breaking solids into mm size Secondary crusher- reduced the particle from primary crusher to 6mm in size Reduce the solid size by compression Type of crusher- jaw crusher, gyratory crusher, smooth-roll crusher and toothed-roll crusher

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**Grinder Reduce crushed feed to powder**

Product from a crusher is often fed to a grinder for further reduction. The product from an intermediate grinder might pass a 40-mesh screen. Most product from a fine grinder would pass a 200- mesh screen with 74 μm opening. Reduce the solid size by impact and attrition, sometimes combine with compression Types of commercial grinder – hammer mills and impactors, rolling compression machine, attrition mills and tumbling mills.

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**Ultrafine Grinder Reduce solids to fine particles**

Accepts feed particles not larger than 6 mm. The product size is typically 1 to 50 μm. Reduce the solid size by attrition Types: Classifying hammer mills, fluid energy mills, agitated mills and colloid mills.

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Cutting machine Give particles of definite size and shape 2-10mm in length Reduce the size by cutting, dicing and slitting Type: -Granulators- yield more or less irregular pieces -Cutters – produce cube, thin squares or diamonds.

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Exercise 1 What is the power required to crush 100 ton/h of limestone if 80% of the feed passes a 2-in. screen and 80% of the product a 1/8-in. screen?

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Solution 1 From Table 28.2,the work index for limestone is Other quantities for substitution into are: The power required is:

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Exercise 2 It is desired to crush 10 ton/h of iron ore hematite. The size of the feed is such that 80% passes a 3-in (76.2 mm) screen and 80% of the product is pass to 1/8-in (3.175-mm) screen. Calculate the gross power required in English unit. Use a work index Wi for iron hematite is 12.68

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Solution 2

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Exercise 3 Calculate the power ratio to crush the coffee extract from 38 mm to 17 mm and from 10 mm to 6 mm. Use Rittinger’s law.

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**Solution 3 From Rittinger’s Law: 𝑃1=𝐾r . 𝑚( 1 17 - 1 38 )**

𝑃1 𝑃2 = or 𝑃2 𝑃1 = 2 1

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