PARTICLE TECHNOLOGY Lecture ##  Bangladesh …teacher.buet.ac.bd/tanvir/Particle1.pdf · Angle of...
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PARTICLE TECHNOLOGYLecture ##
K. M. Tanvir Ahmmed
Lecturer, ChE, BUET

Angle of Repose, r
When bulk granular materials are poured onto a horizontal surface, a conical pile will form
The internal angle between the surface of the pile and the horizontal surface is known as the angle of repose

Angle of Repose
Lower the angle of repose, the more free flowing is the material
Very free flowing granules: 25 < < 30
Freeflowing granules: 30 < < 38
Fair to passable flow of powders: 38 < < 45
Cohesive solids: 45 < < 55
Very cohesive solids: 55 < < 70

Angle of Repose
Angle of repose is sensitive to the condition of the supporting surface  the smoother the surface the smaller the angle
Angle of repose is also sensitive to moisture it tends to increase the angle of repose

Angle of Repose
Used in the design of equipment for the processing of particulate solids
may be used to design an appropriate hopper or silo to store the material
It can also be used to size a conveyor belt for transporting the material
It can also be used in determining whether or not a slope will likely collapse

Angle of Repose

Angle of Repose

Angle of Internal Friction, m The angle of internal
friction is the ability of particles to withstand a shear stress
Defined as the equilibrium angle between flowing particles and stationary solids in a bin
The tangent of this angle is the coefficient of friction,

Angle of Repose & Internal Friction
If the mass are truly homogeneous both angles are equal
In practice, the angle of repose is smaller than the angle of internal friction
Moisture content
Degree of Packing

Pressures in Masses of Particles
The minimum pressure in a solid mass in the direction normal to that of the applied pressure
Ratio of the normal pressure to the applied pressure is a constant K
K depends on
Shape and interlocking tendencies of the particles
Stickiness of the grain surfaces
Degree of packing of the material

Storage of Solids
Open storage areas are used for the high range because of their lower cost
In low and mediumcapacity ranges partially or totally enclosed storage is used

Bulk Storage  Stockpiles
Stacked on a concrete or earthen pad
May be covered by a roof structure or left uncovered
Formed using various overhead conveyors

Silo!

Bin Storage
Cylindrical or rectangular vessels of concrete or metal
Silo is tall and relatively small in diameter
Bin is not so tall and usually fairly wide
Hopper is small bin with a slopping bottom

Pressures in Circular Bin

Janssen's Equations for Bins
One cannot solve Eq. ## directly since it contains two unknowns, the average vertical Pv and the average tangential stress PL. To obtain a solution, additional information is required as a correlation between the two stresses. Janssen proposed such a correlation in the form
PL / Pv = K 1

Janssen's Equations for Bins
where K is the socalled Janssen constant. Eq. (1) implies a constant relationship between the two average stresses, independent of the geometry of the slice and, while there is no physical reason that such a relationship should hold, it was found in practice that for routine industrial calculations the results are reasonably accurate.

Janssen's Equations for Bins
At very small distances, close to the upper surface of the bin, one can expand the exponential function
It yields the vertical stress Pb = ZT (g/gc)b. This is exactly the stress encountered in a static fluid of constant density as one moves down from its surface and is the socalled hydrostatic pressure.

Pressures in fluids and stresses in bulk solids (in principle)

Mass Flow & Tunnel Flow

Mass Flow

Core Flow/Tunnel Flow

ADIOS
N. B. Most of the pictures are taken from English Wikipedia. This document is prepared for educational purposes only.
For first section of this presentation the author is expressing his indebtedness to Ashfaq M. Ansery.