Grinding and cutting reduce the size of solid materials by mechanical action, dividing them into smaller particles. Perhaps the most extensive application of grinding in the food industry is in the milling of grains to make flour, but it is used in many other processes, such as in the grinding of corn for manufacture of corn starch, the grinding of sugar and the milling of dried foods, such as vegetables. Cutting
is used to break down large pieces of food into smaller pieces suitable
for further processing, such as in the preparation of meat for retail
sales and in the preparation of processed meats and processed vegetables.
In the grinding process, materials are reduced in size by fracturing them. The mechanism of fracture is not fully understood, but in the process, the material is stressed by the action of mechanical moving parts in the grinding machine and initially the stress is absorbed internally by the material as strain energy. When the local strain energy exceeds a critical level, which is a function of the material, fracture occurs along lines of weakness and the stored energy is released. Some of the energy is taken up in the creation of new surface, but the greater part of it is dissipated as heat. Time also plays a part in the fracturing process and it appears that material will fracture at lower stress concentrations if these can be maintained for longer periods. Grinding is, therefore, achieved by mechanical stress followed by rupture and the energy required depends upon the hardness of the material and also upon the tendency of the material to crack  its friability. The force applied may be compression, impact, or shear, and both the magnitude of the force and the time of application affect the extent of grinding achieved. For efficient grinding, the energy applied to the material should exceed, by as small a margin as possible, the minimum energy needed to rupture the material . Excess energy is lost as heat and this loss should be kept as low as practicable. The important factors to be studied in the grinding process are the amount of energy used and the amount of new surface formed by grinding. Grinding is a very inefficient process and it is important to use energy as efficiently as possible. Unfortunately, it is not easy to calculate the minimum energy required for a given reduction process, but some theories have been advanced which are useful. These theories 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:
where dE is the differential energy required, dL is the change in a typical dimension, L is the magnitude of a typical length dimension and K, n, are constants. 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 eqn. (11.1) is equal to 1. If
where K_{K} is called Kick's constant and f_{c} is called the crushing strength of the material, we have:
which, on integration gives: E = K_{K}f_{c} log_{e}(L_{1}/L_{2}) (11.2) Equation (11.2) is a statement of Kick's Law. It implies that the specific energy required to crush a material, for example from 10 cm down to 5 cm, is the same as the energy required to crush the same material from 5 mm to 2.5 mm. Rittinger, on the other hand, assumed that the energy required for size reduction is directly proportional, not to the change in length dimensions, but to the change in surface area. This leads to a value of 2 for n in eqn. (11.1) as area is proportional to length squared. If we put:
where K_{R} is called Rittinger's constant, and integrate the resulting form of eqn. (11.1), we obtain:
Equation (11.3) is known as Rittinger's Law. As the specific surface of a particle, the surface area per unit mass, is proportional to 1/L, eqn. (11.3) postulates 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, for example, 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. It has been found, experimentally, that for the grinding of coarse particles in which the increase in surface area per unit mass is relatively small, Kick's Law is a reasonable approximation. For the size reduction of fine powders, on the other hand, in which large areas of new surface are being created, Rittinger's Law fits the experimental data better. Bond has suggested an intermediate course, in which he postulates
that n is 3/2 and this leads to: Bond defines the quantity E_{i} by this equation: L is measured in microns in eqn. (11.4) and so E_{i} is the amount of energy required to reduce unit mass of the material from an infinitely large particle size down to a particle size of 100 mm. It is expressed in terms of q, the reduction ratio where q = L_{1}/L_{2}. Note that all of these equations [eqns. (11.2), (11.3), and (11.4)] are dimensional equations and so if quoted values are to be used for the various constants, the dimensions must be expressed in appropriate units. In Bond's equation, if L is expressed in microns, this defines E_{i} and Bond calls this the Work Index. The greatest use of these equations is in making comparisons between power requirements for various degrees of reduction. EXAMPLE 11.1. Grinding of sugar Sugar is ground from crystals of which it is acceptable that 80% pass a 500 mm sieve(US Standard Sieve No.35), down to a size in which it is acceptable that 80% passes a 88 mm (No.170) sieve, and a 5horsepower motor is found just sufficient for the required throughput. If the requirements are changed such that the grinding is only down to 80% through a 125 mm (No.120) sieve but the throughput is to be increased by 50% would the existing motor have sufficient power to operate the grinder? Assume Bond's equation. Using
the subscripts 1 for the first condition and 2 for the second, and letting
m kg h^{1} be the initial throughput, then if x
is the required power
So the motor would be expected to have insufficient power to pass the 50% increased throughput, though it should be able to handle an increase of 40%.
When a uniform particle is crushed, after the first crushing the size of the particles produced will vary a great deal from relatively coarse to fine and even to dust. As the grinding continues, the coarser particles will be further reduced but there will be less change in the size of the fine particles. Careful analysis has shown that there tends to be a certain size that increases in its relative proportions in the mixture and which soon becomes the predominant size fraction. For example, wheat after first crushing gives a wide range of particle sizes in the coarse flour, but after further grinding the predominant fraction soon becomes that passing a 250 mm sieve and being retained on a 125 mm sieve. This fraction tends to build up, however long the grinding continues, so long as the same type of machinery, rolls in this case, is employed. The surface area of a fine particulate material is large and can be important. Most reactions are related to the surface area available, so the surface area can have a considerable bearing on the properties of the material. For example, wheat in the form of grains is relatively stable so long as it is kept dry, but if ground to a fine flour has such a large surface per unit mass that it becomes liable to explosive oxidation, as is all too well known in the milling industry. The surface area per unit mass is called the specific surface. To calculate this in a known mass of material it is necessary to know the particlesize distribution and, also the shape factor of the particles. The particle size gives one dimension that can be called the typical dimension, D_{p}, of a particle. This has now to be related to the surface area. We can write, arbitrarily:
and
where V_{p} is the volume of the particle, A_{p} is the area of the particle surface, D_{p} is the typical dimension of the particle and p, q are factors which connect the particle geometries.(Note subscript p and factor p) For example, for a cube, the volume is D_{p}^{3} and the surface area is 6D_{p}^{2}; for a sphere the volume is (p/6)D_{p}^{3} and the surface area is pD_{p}^{2} In each case the ratio of surface area to volume is 6/D_{p}. A shape factor is now defined as q/p = l (lambda), so that for a cube or a sphere l = 1. It has been found, experimentally, that for many materials when ground, the shape factor of the resulting particles is approximately 1.75, which means that their surface area to volume ratio is nearly twice that for a cube or a sphere. The ratio of surface area to volume is:
If there is a mass m of particles of density r_{p, } the number of particles is m/r_{pVP }each of area A_{p.}
where A_{t} is the total area of the mass of particles. Equation (11.6) can be combined with the results of sieve analysis to estimate the total surface area of a powder.
Aperture
of Tyler sieves, 7 mesh = 2.83 mm, 9 mesh = 2.00 mm, 80 mesh = 0.177 mm,
115 mesh = 0.125 mm.
Jaw and gyratory crushers are heavy equipment and are not used extensively in the food industry. In a jaw crusher, the material is fed in between two heavy jaws, one fixed and the other reciprocating, so as to work the material down into a narrower and narrower space, crushing it as it goes. The gyrator crusher consists of a truncated conical casing, inside which a crushing head rotates eccentrically. The crushing head is shaped as an inverted cone and the material being crushed is trapped between the outer fixed, and the inner gyrating, cones, and it is again forced into a narrower and narrower space during which time it is crushed. Jaw and gyratory crusher actions are illustrated in Fig. 11.1(a) and (b).
In a hammer mill, swinging hammerheads are attached to a rotor that rotates at high speed inside a hardened casing. The principle is illustrated in Fig. 11.2(a).
Various forms of mills are used in which the material is sheared between a fixed casing and a rotating head, often with only fine clearances between them. One type is a pin mill in which both the static and the moving plates have pins attached on the surface and the powder is sheared between the pins. In plate mills the material is fed between two circular plates, one of them fixed and the other rotating. The feed comes in near the axis of rotation and is sheared and crushed as it makes its way to the edge of the plates, see Fig. 11.2(b). The plates can be mounted horizontally as in the traditional Buhr stone used for grinding corn, which has a fluted surface on the plates. The plates can be mounted vertically also. Developments of the plate mill have led to the colloid mill, which uses very fine clearances and very high speeds to produce particles of colloidal dimensions. Roller mills are similar to roller crushers, but they have smooth or finely fluted rolls, and rotate at differential speeds. They are used very widely to grind flour. Because of their simple geometry, the maximum size of the particle that can pass between the rolls can be regulated. If the friction coefficient between the rolls and the feed material is known, the largest particle that will be nipped between the rolls can be calculated, knowing the geometry of the particles.
The
range of milling equipment is very wide. It includes ball mills, in which
the material to be ground is enclosed in a horizontal cylinder or a cone
and tumbled with a large number of steel balls, natural pebbles or artificial
stones, which crush and break the material. Ball mills have limited applications
in the food industry, but they are used for grinding food colouring materials.
Cutting
machinery is generally simple, consisting of rotating knives in various
arrangements. A major problem often is to keep the knives sharp so that
they cut rather than tear. An example is the bowl chopper in which a flat
bowl containing the material revolves beneath a vertical rotating cutting
knife.
Size Reduction > EMULSIFICATION Back to the top 
