Bond’s law

Bond postulated that 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. By relation Sp/Vp = 6/ɸsDp, from which it follows that

P/ ṁ = Kb/(Dp)^0.5

Where Kb is a constant that depends on the type of machine and on the material being crushed. To use this equation, a work index Wi is defined as the gross energy requirement in kilowatt-hours per ton of feed needed to reduce a very large feed to such a size that 80% of the product passes a 100-µm screen. This definition leads to a relation between Kb and Wi. If Dp is in millimeters, P in kilowatts, and ṁ in tons per hour,

Kb = 0.3162 Wi

If 80% of the feed passes a mesh size of Dpa millimeters and 80% of the product a mesh of Dpb millimeters, it follows

P/ ṁ = 0.3162 Wi [1/(Dpb)^0.5 - 1/(Dpa)^0.5]

Rittinger’s and Kick’s laws

Rittinger's law states that work required in crushing is proportional to the new surface created. In other words, crushing efficiency is constant and for a given machine and feed material is independent of the sizes of feed and product. Rittinger’s law is written as-

P/ ṁ = Kr(1/Dsb – 1/Dsa)

Kick proposed another law based on stress analysis of plastic deformation within the elastic limit, which states that the work required for crushing a given mass of material is constant for the same reduction ratio, that ia, the ration of the initial particle size to the final particle size. This leads to the relation

P/ ṁ = Kk ln(Dsa/Dsb)

Crushing efficiency

The ratio of surface energy created by crushing to the energy absorbed by the solid is the crushing efficiency ɳ_c. if e_s is the surface energy per unit area, in feet times pound force per square foot, and A_wb and A_wa are the areas per unit mass of product and feed, respectively, the energy absorbed by a unit mass of the material W_n is

W_n = e_s(A_wb- A_wa)/ ɳ_c

The surface energy created by fracture is small in comparison with the total mechanical energy stored in the material at the time of rupture, and most of the latter is converted into heat. Crushing efficiencies are therefore low.

The energy absorbed by the solid W_n is less than that fed to the machine. Part of the total energy input W is used to overcome friction in the bearings and other moving parts, and the rest is available for crushing. The ratio of the energy absorbed to the energy input is ɳ_m, the mechanical efficiency. Then, if W is the energy input,

W = W_n/ ɳ_m = e_s(A_wb- A_wa)/ ɳ_c ɳ_m

If ṁ is the feed rate, the power required by the machine is

P = W ṁ = ṁ e_s(A_wb- A_wa)/ ɳ_c ɳ_m

Energy and power requirements in comminution

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. 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.

Characteristics of comminuted products

The objective of crushing and grinding is to produce small particles from larger ones. Smaller particles are desired either because of their large surface or because of their shape, size and number. One measure of the efficiency of the operation is based on the energy required to create new surfaces. The surface area of a unit mass of particles increases greatly as the particle size is reduced.

Principles of comminution

Criteria for comminution- Comminution is a generic term for size reduction. Crushers and grinders are types of comminuting equipment. An ideal crusher or grinder would-
• Have a large capacity
• Requires a small power input per unit of product
• Yield a product of the single size or the size distribution desired

Size Reduction of particles

The term size reduction is applied to all ways in which particles of solids are cut or broken into smaller pieces. Commercial products must often meet stringent specifications regarding the size and sometimes the shape of the particles they contain. Reducing the particle size also increases the reactivity of solids; it permits separation of unwanted ingredients by mechanical methods; it reduces the bulk of fibrous materials for easier handling and for waste disposal.

The common ways in which solids are broken are as follows:-

· Compression: It is used for coarse reduction of hard solids, to give relatively few fines. Ex- nutcracker.

· Impact: It gives coarse, medium, or fine products. Ex- hammers.

· Attrition or rubbing: It yields very fine products from soft, nonabrasive materials. Ex- a file.

· Cutting: It gives a definite particle size and sometimes a definite shape, with few or no fines. Ex- a pair of shears.

Introduction

This is the perfect place for those people who wish to find information about unit operations of chemical engineering. So, you will find details about various processes taking place in industries relating to chemical engineering.