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

Free-flowing 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 medium-capacity 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 so-called 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 so-called 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.