The document provides an overview of various mixing equipment used in industrial processes for solid particles, highlighting their mechanisms, such as convective and diffuse mixing. It also discusses size reduction, defining its meaning and explaining the energy requirements and empirical laws governing it, including Rittinger’s, Kick’s, and Bond’s laws. Additionally, it outlines the applications of these principles in crushing materials, exemplifying the calculation of power required for specific scenarios.

1. Mixing equipment
The efficiency and homogeneity of the mixing process significantly impact
the quality of the final product. Several types of equipment are employed
in industrial to achieve optimal mixing of solid particles. Here's an
overview of some commonly used industrial solid particles mixing
equipment:
❑For paste and heavy material
▪ Pony mixer
▪ Beater mixer
▪ Kneader mixer
❑ For granular solids
▪ Tumbling mixer
▪ Ribbon mixer
▪ Vertical screw mixer
▪ Paddle mixer

2. Mixers for paste and heavy material
Change can mixers:
Theses devices blend viscous liquids
or light pastes, as in food processing
or paint manufactures. A small
removable can 5-100 gal size holds
the material to be mixed.

3. Mixers for free-flowing solids (granular solids)
(a) (b)
Ribbon mixer: it has its unique twisted blades shaped like the inner
blade bar, are set up within static shell by rotating blades.
- Main mechanism is convective mixing
- Accompanied with diffuse and shear mixing
Tumbling mixer: Closed vessel rotating about its axis (cube, cone, or V shape).
- Main mechanism is diffuse mixing
- Problem segregation in free-flowing powders (to minimize use baffles)

4. Mixers for free-flowing solids (granular solids)
Vertical screw mixer
Paddle mixer
Paddle mixer: it I known as paddle blender, it has efficient and gentle
mixing action making it suitable for fragile or heat-sensitive material..
- Main mechanism is convective mixing with rotational motion.
Vertical screw mixer: it has its uniform mixing of materials through the
rotation and pushing screw. It has difficulty in handling sticky or
cohesive materials.
- Main mechanism is convective mixing
- Accompanied with diffuse and shear mixing

5. SIZE REDUCTION
What is the meaning of size reduction?
❑Size refers to physical dimension of an object.
❑ Reduction refers to decrement or the process of
decreasing the size.

6. Simple definition of size reduction

7. Objectives of SIZE REDUCTION

9. Mechanism of SIZE REDUCTION

10. Type of IMPACT
❖ Gravity impact
▪ In gravity impact ,the free falling material is momentarily stopped by
the stationary object.
▪ Example – coal dropped onto a hard steel surface.
❖ Dynamic impact
▪ Most often used when it is necessary to separate two materials which
have relatively different friability.
▪ Example – material dropping in front of a moving hammer.

11. Size reduction with COMPRESSION
Needed:

12. Energy for size reduction

13. Energy for size reduction
❖ It was shown that the energy (dE) required to effect a small change in
the size of unit mass of material (dL) is a simple power function of
size.
Where; P is a constant
C is a coefficient
❖ Three empirical laws have been proposed to solve the above

14. Energy for size reduction
1. Rittinger’s law (1867): In this law, P is put equal to (-2) Energy for size reduction
Put
Where 𝒌𝑹 is Rittinger’s constant ( )
𝒇𝑪 is the crushing strength of the material ( )
❖ The interpretation of this law is that the energy required for size reduction is
directly proportional to the increase in surface.
𝑵/𝒎𝟐
𝒎𝟒
/𝒌𝒈
𝑪 = 𝒌𝑹𝒇𝑪

15. Energy for size reduction
2. Kick’s law (1885): In this law, P is put equal to (-1)
Put
Where 𝒌𝑹 is Kick’s constant ( )
𝒇𝑪 is the crushing strength of the material ( )
❖ The energy required to crush a given amount is directly related to the reduction
ratio
𝑳𝟏
𝑳𝟐
.
𝑵/𝒎𝟐
𝒎𝟑/𝒌𝒈
𝑪 = 𝒌𝑹𝒇𝑪
𝑬 = 𝒌𝑹𝒇𝑪𝒍𝒏
𝑳𝟏
𝑳𝟐
C

16. Energy for size reduction
❑ Neither of these two laws give an accurate calculation of the energy
requirements.
❑ Rittinger’s law is applicable mainly to that part of the process where
the increase in surface per unit mass of material is large, i.e. used for
fine grinding.
❑ Kick’s law, however, is more accurate than Rittinger’s law for coarse
crushing where the amount of surface produced is considerably less.

17. Energy for size reduction
3. Bond’s law (1952): Bond has suggested a law intermediate between Rittinger’s and
Kick’s laws, by putting P = −3/2. After integration we get:
Where 𝑬𝒊 : the work index which represents the amount of energy required to reduce unit mass
of material from an particle size 𝑳𝟏 to a size 𝑳𝟐 of 100 μm.
❖ The size of material is taken as the size of the square hole through which 80 % of the
material will pass.

19. Applications

20. What is the power required to crush 100 ton/h of limestone if 80 percent of the feed
passes a 2-in screen and 80 percent of the product a 1/8-in screen?
Solution:
Form pervious Table, the work index for limestone is 12.74 (KW.h/ton)
The power required to crush is
Example:
𝑬 = 𝟏𝟎𝟎𝐱𝟏𝟐. 𝟕𝟒
𝟏𝟎𝟎
𝟑. 𝟏𝟕𝟓𝐱𝟏𝟎𝟑
𝟏 −
𝟏
𝟒
= 169.57 KW
𝑳𝟏 = 𝟐𝒙𝟐𝟓. 𝟒 = 𝟓𝟎. 𝟖 𝒎𝒎 𝑳𝟐 = 𝟎. 𝟏𝟐𝟓𝒙𝟐𝟓. 𝟒 = 𝟑. 𝟏𝟕𝟓 𝒎𝒎
ư
𝒎 = 𝟏𝟎𝟎 𝒕𝒐𝒏/𝒉
𝒒 =
𝑳𝟏
𝑳𝟐
= 𝟒

21. Problem 3