Chemical Engineering January 2011 - 47

250
200
150
100
50
60
50
40
30
10
20
100 200 300 400 500
Normal stress, lb/ft2
FIGURE 2. The wall yield locus, plotted
here for a sample of ine potash
powder, is a function of a material's
wall friction properties
COMMONLY USED BINDERS
Inorganic
binders
Alkali silicates
Gypsum
Alum
Lime
Bentonite and
other clays
Lime hydrate
Caustic soda
Magnesia/magnesium
oxide
Colloidal alumina
and silica
Magnesium
chloride
Cement
Plaster of Paris
Dolomite
Sodium borate
Fuller's Earth
Organic
binders
Asphalt
Maltose
Asphalt
emulsions
Molasses
Cellulose
Paraffin
Corn starch
Peat
Coal tar
PVA (polyvinyl
alcohol)
Dextrine
Rosin
Gelatine
Starches
Lignosulfonates
(lignin)
Sucrose
between the powder and the hopper
wall material. Wall friction is measured
by a method described in ASTM
D-6128 [1]. Various normal loads are
applied to a sample of powder, which
is forced to slide along a coupon of wall
material. The resulting shear force is
measured as a function of the applied
normal force, and a wall yield locus
is constructed by plotting shear force
against normal force. The angle of wall
friction at a particular pressure (φ') is
the angle that is formed when a line is
drawn from the origin to a point on the
wall yield locus. A wall yield locus for
a sample of fine potash powder on 304,
No.-2B finish stainless steel is given
in Figure 2.
Design charts originally developed
by Jenike [2] provide allowable hopper
angles for mass flow, given values of the
wall friction angle. An example chart
for conical hoppers is shown in Figure
3. Values of the allowable hopper angle
500
400
300
200
100
200 400 600 800 1,000
Consolidation pressure, lb/ft2
FIGURE 4. The relationship between
cohesive strength and pressure is called
the low function, and is shown here for
ine potash powder
(θC; measured from vertical) are on
the horizontal axis, and values of the
wall friction angle (φ') are on the vertical
axis. Any combinations of φ' and θC
that lie within the mass flow region of
the chart will provide mass flow.
Designing right to the limit of the
mass flow region is not recommended
for conical bins. If the combination of
wall friction angle and hopper angle
lies too close to the funnel-flow line, a
switch to funnel flow can occur. Hence,
a 4-5 deg margin of safety is employed
with respect to the mass flow boundary.
For the potash powder whose wall
friction properties are described by
Figure 2, a conical hopper with walls
sloped 12 deg from vertical is recommended
to ensure mass flow.
Flow stoppages will be prevented if
the stresses imparted on an obstruction
to flow (such as a cohesive arch or stable
rathole) are greater than the cohesive
strength that the material gains due to
10
20
30
40
50
Hopper angle from vertical
FIGURE 3. In design charts, such as
this one for conical hoppers, any combination
of wall friction angle (ϕ') and allowable
hopper angle (θC) that lie within
the mass low region of the chart will
provide mass low
60
Funnel flow
Uncertain region
Mass flow
its consolidation in a hopper, bin or silo.
The cohesive strength of a bulk solid
can be determined using the method
described in ASTM D-6128 [1] where
a direct shear tester is used to measure
the shear strength of a material
under varying consolidation pressures.
The relationship between strength and
pressure is called the flow function. The
flow function for a sample of fine potash
powder is shown in Figure 4.
The stresses imparted on an arch
of powder that forms at the vessel
outlet are proportional to the material's
bulk density. Once a material's
flow function has been determined
and its bulk density has been measured,
the minimum outlet diameter
that will prevent a cohesive arch
from developing can be calculated
using an analysis developed by Jenike
[2]. For the powder whose flow
function is given in Figure 4, the
analysis shows that a conical massflow
hopper requires a 6-in. dia. outlet
to prevent arching. Note that this
outlet diameter will prevent arching
but does not ensure that the desired
discharge rates can be achieved. Fine
powder flowrates are limited because
of high permeability, as discussed in
Johanson [3].
Wet agglomeration processes
Wet agglomeration processes combine
powder, liquid (usually water) and, if
necessary, a binder, imparting shear
to form agglomerates. Also known as
tumble-growth agglomeration, wet agglomeration
processes (Figures 5 and
6) include rotating drums, disc or pan
agglomerators, pin and ribbon mixers,
and fluidized beds.
In general, particle size enlargement
by wet agglomeration occurs
in three stages. The first is a mixing
stage where powder, liquid and binder
are combined. Next, moist particles
are joined together to form so-called
green agglomerates. Drying or curing
takes place in a final stage. The
wet agglomerates are formed by first
forming nuclei that then grow into
larger aggregates by layering or coalescence.
In some cases, nucleation
and aggregate growth take place in
two separate pieces of equipment that
are operated in series.
Nucleation gives rise to seed parCHEMICAL
ENGINEERING WWW.CHE.COM JANUARY 2011 47
Shear stress, lb/ft2
Cohesive strength, lb/ft2
Wet friction angle
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Chemical Engineering January 2011

Table of Contents for the Digital Edition of Chemical Engineering January 2011
