PARTICLE TECHNOLOGYLecture ##

K. M. Tanvir Ahmmed

Lecturer, ChE, BUET

Angle of Repose, αr

• 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° < β < 30°

– Free-flowing granules: 30° < β < 38°

– Fair to passable flow of powders: 38° < β < 45°

– Cohesive solids: 45° < β < 55°

– Very cohesive solids: 55° < β < 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, αm

• 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, μ’

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)ρb. 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.