Friction of solids and flow of granular solids

Hardy Ankit
Assistant Professor
Food Engineering Department
National Institute of Technology

Friction of solids and flow of granular solids
Angle of repose
Coefficient of friction
Aero and hydrodynamic characteristics
Application of frictional properties in grain
Handling
Processing
Conveying

 Designing of storage bins, hoppers, chutes,
pneumatic conveyors, screw conveyors, threshers,
harvesters.
 Rolling friction: Rolling of round shape agricultural
materials, conveying of fruits and vegetables by
gravity flow.
 Conveying and mechanical systems: material moves
or slides in direct contact with your troughs, casings
and other components of the machine.
 So power requirement to drive the machine as
frictional losses is one of the factors to be overcome
by providing additional power to the machine.

Friction: Friction is the force that resists motion of
objects that are in contact with each other.

Frictional force (F) is proportional to the load (N)
F α N , F = µN,
Where,
F = Force
µ = Coefficient of friction (static or dynamic)
N = Load

i) Static coefficient of friction (µs): predicts the
force at the point in time when motion is initiated.
ii) Dynamic coefficient of friction (µd): predicts the
force required to maintain the motion once it is
initiated.
µd≤ µs (why???)
Reason: For a given applied normal force, the force
required to maintain motion is less than or equal to
the force required to initiate motion.

 In grain conveying systems : Two types of friction
1. External friction/wall friction: Friction between
grain mass of kernels and wall of bin or a surface
2. Internal friction: Friction of the kernels or grains
against each other.
 Higher angle of internal friction indicate the material
is cohesive.
Coefficient of friction (µ) between granular
materials is equal to tangent of the angle of internal
friction for that material.

Grains Angle of internal friction, degree
Minimum Maximum
Wheat 24 26
Maize 26 29
Barley 25 29
Rice 24 26

1. Static φ : It is an angle of friction taken up by granular
material to just slide upon itself .
2. Dynamic φ : When bulk of the grain is in motion like
discharge from bins and hoppers.
 It is an important property which helps to estimate
lateral pressures in storage silos.
 It is also used in designing : Storage bins (both
shallow and deep) and hopper for gravity discharge.
3. Effect of moisture content: φ increases with the
increase in moisture content.
Reason: Surface layer of moisture surrounding the
particle holds the aggregate of grain together by the
surface tension.

 It is the angle between the base and slope of the cone
formed on a free vertical fall of the angular material to
a horizontal plane.
 For understanding: The angle between the
horizontal and inclination of heap is called angle of
repose.
Angle of repose=Tan-1
(2H/B)

 Indicator of flow ability of product.
 Lower angle of repose: easy flow ability
 Cohesive material has larger angle of repose
 Factors affecting angle of repose:
Size, shape, moisture content and orientation of the
grains.
 Each product has its own angle of repose.
Examples
Barley (13% mc): 31ᵒ
(20% mc): 34ᵒ

Flow characteristics with respect to angle of repose
Flow characteristics angle of repose, degree
Very, free flowing 25-30
Free flowing 30-38
Cohesive 45-55
Very cohesive Beyond 55

1.Emptying angle of repose: Angle of repose in
situations where the material is being emptied from a
bin.
2. Piling angle of repose : Angle of repose formed
when material is allowed to flow from a spout or
elevator outlet so as to form a pile.
Use: For calculating the quantity of granular material
that can be placed in piles or on storage structures
with flat surfaces.

Through the orifice of given size and shape
1. Type of flow
2. Rate of flow two important factors
in designing and operation of processing facilities
Type of flow: Two types of flow
1. Mass flow
2. Funnel flow

1) Piping: When bulk solid above the outlet is flowing
out remaining bulk solids stays in place.
called dead regions
2) Arching: It is a stable obstruction that forms over the
point of narrowest cross section of the storage vessel
(usually the discharge outlet).

 Based on concept of plane of rupture
Plane of rupture: is that surface down which is
wedge of material bounded by one wall face, the
free face surface and the plane of rupture would
start sliding if bounding wall were to move.
a) Shallow bin: A bin in which plane of rupture
meets the grain surface before it strikes the
opposite side.
b) Deep bin: A bin in which plane of rupture
meets the opposite side before it emerges from
the grain

According to Rankin’s theory
Shallow bin: h<L tan(90+φ)/2
Deep bin: h>L tan(90+φ)/2
h= depth of storage bin
L=breadth of storage bin
φ= Angle of repose

For shallow bins
1. Rankin equation
P=KWh
P= Lateral pressure on the wall bin by grains
W= Wt density of grains
h=depth of grains from the top of the bin surface
K= Rankin coefficient= (1-sinφ)/(1+sinφ)
=tan2
(45- φ/2)
where φ = angle of internal friction of grains

2. Airy equation
Where,
W=grain bulk density, h= height/depth of grain
µ = Coefficient of internal friction= tanφ
µʹ= Coefficient of external friction= tanφʹ
For deep bins
Jannsen equation
K= Pressure ratio= (1-sinφ)/(1+sinφ)
R= hydraulic radius , µ =Coefficient of external friction

Rolling friction α W and µr(directly proportional)
α 1/r (inversely proportional)
Fr = µrN/r
Where
µr = Coefficient of rolling friction
N= Normal force
r= radius
Example : Separation of potatoes and stones.

Friction of solids and flow of granular solids

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Friction of solids and flow of granular solids