SOLID
MIXING
SOLID MIXING
the process of blending or combining two or more
solid materials to create a homogeneous mixture.
commonly used in various industries such as
pharmaceuticals, food processing, and chemical
manufacturing.
Solid mixing can be achieved through various
methods such as tumbling, blending, and milling.
Each method has its own advantages and
disadvantages.
Whether cohesive or free-flowing, the mixing
of solids is similar to the mixing of lowviscosity liquids.
More power is normally required in mixing
pastes and dry solids than in blending liquids.
A well-mixed product is one that does what is
required and has the necessary property-visual
uniformity, high strength, uniform burning rate, or
other desired characteristic.
A good mixer is one that produces this well-mixed
product at the lowest overall cost.
MECHANISMS
OF SOLID MIXING
MECHANISMS OF SOLID MIXING
COHESIVE
MIXING
DIFFUSIVE
MIXING
SHEAR
MIXING
masses or groups of particles
collectively from one place to another.
move
known as dispersion mixing and micromixing.
It is caused by the randomly moving powder
particles where the particles are distributed
over a freshly developed interface.
With the formation of slipping planes within the
mass of the mixture, groups of particles are
mixed.
EQUIPMENT FOR
SOLID MIXING
Tumbling Mixers
A tumbling mixer comprises a
closed vessel rotating about its axis.
The vessel frequently has a cube,
double cone, or V form. Diffusive
mixing is the primary mechanism
ADVANTAGES
DISADVANTAGES
They handle large
capacities.
Easy to clean , load,
and unload.
This equipment requires
minimum maintenance.
TUMBLER
MIXER
Less effective for
cohesive/poorly flowing
powders
Segregation is likely to
occur if there are significant
differences in particle size
ADVANTAGES
DISADVANTAGES
They handle large
capacities.
Easy to clean , load,
and unload.
This equipment requires
minimum maintenance.
TUMBLER
MIXER
It is not suitable for fine
particulate systems or
ingredients of large
differences in the particle
size distribution
If powders are free
flowing, serial dilution is
required for the addition of
low dose active
ingredients.
Convective Mixers
use revolving paddles or blades to
create circulation patterns within a
static shell. As the name indicates,
convective mixing is the primary
mechanism.
ADVANTAGES
DISADVANTAGES
Baffles are useful for both
wet and dry mixing.
Wide range of shearing
force can be applied with
agitator bars permitting the
intimate mixing of very fine
as well as coarse powders.
CONVECTIVE
MIXER
Attrition is large, size
reduction of friable particles
results.
Scale-up can prove a
problem, because general
principles of scale-up do not
work
ADVANTAGES
Serial dilution is not needed
when incorporating lowdose active ingredients.
DISADVANTAGES
CONVECTIVE
MIXER
Cleaning may be difficult,
since agitator assembly
must be removed and the
packing should be replaced
for a product changeover
Potential packing (sealing)
problems occur.
Fluidized Bed Mixers
They rely on the fluidized bed's
particles' inherent movement.
With the circulation patterns
created by the bubble motion
inside the bed, the mixing is
primarily convective.
High Shear Mixers
Devices comparable to those
used in comminution, such as
high velocity spinning blades and
low velocity-high compression
rollers, produce local high shear
stresses. Shear mixing is the
primary process.
ADVANTAGES
Can be used for both wet
and dry mixing
For granulation purposes
DISADVANTAGES
HIGH SHEAR
MIXER
Materials being mixed can
fracture easily due to high
speed movement
Cannot be used for
blending lubricants
APPLICATIONS OF
SOLID MIXING
PHARMACEUTICAL
involves many millions of particles in the
smallest practical sample taken from a
mixture of two miscible liquids
When mixing solids, a small sample with
few particles will exhibit significant variation
in the overall composition of the mixture
FOOD PROCESSING
is a common and significant unit operation
in the food processing industry
many instances in the food industry where
powder blends are crucial and non-uniform
composition can be a major flaw
QUANTITATIVE
MEASURES FOR
SOLID MIXING
DEGREE OF MIXING
Although it is challenging to assess the degree of
mixing, any index should be connected to the
necessary mix's qualities, be simple to measure, and
be appropriate for a number of various mixers.
The statistical variance in composition across
samples taken at any time from a mix is frequently
employed as a measure of the degree of mixing when
working with solid particles
For a completely random mix of
uniform particles
where
s2r = variance for the mixture
p = overall proportion of particles of
one color
n = number of particles in each
sample.
The significance of the sample size in
respect to particle size is demonstrated
by this equation. In a system that is
totally unmixed, denoted by the suffix 0,
s2 will be bigger, and it can be
demonstrated that:
When a material is partially mixed,
the degree of mixing may be
described by some term b.
Sampling
can
help
get
an
approximation of y. Assuming N
compositional samples. The estimated
mixture composition y is given for each
of the components, yi to yN by:
The true variance is usually not known but an estimate s2 is defined
as:
if the true composition μ is known
if the true composition μ is unknown
SAMPLE
PROBLEM
A biscuit dough is prepared by mixing flour and other ingredients
along with tracer material (2%mass). After 10 minutes of mixing 6
random samples are collected and their composition (% of tracer
material) is given below. Calculate the mixing index after 10 minutes
of mixing
After 10 minutes:
2.021%
1.925% 1.826%
2.125%
2.210%
2.015%
Solution
Given:
p = 0.02
N=6
A biscuit dough is prepared by mixing flour and other ingredients
along with tracer material (2%mass). After 10 minutes of mixing 6
random samples are collected and their composition (% of tracer
material) is given below. Calculate the mixing index after 10 minutes
of mixing
After 10 minutes:
2.021%
1.925% 1.826%
2.125%
2.210%
2.015%
Solution
Given:
p = 0.02
N=6
A biscuit dough is prepared by mixing flour and other ingredients
along with tracer material (2%mass). After 10 minutes of mixing 6
random samples are collected and their composition (% of tracer
material) is given below. Calculate the mixing index after 10 minutes
of mixing
After 10 minutes:
2.021%
1.925% 1.826%
2.125%
2.210%
2.015%
Average composition of tracer Material (ȳ ) = (2.021+1.925 +1.826 + 2.125+ 2.210+ 2.015/6)
Solution
Given:
p = 0.02
N=6
A biscuit dough is prepared by mixing flour and other ingredients
along with tracer material (2%mass). After 10 minutes of mixing 6
random samples are collected and their composition (% of tracer
material) is given below. Calculate the mixing index after 10 minutes
of mixing
After 10 minutes:
2.021%
1.925% 1.826%
2.125%
2.210%
2.015%
Average composition of tracer Material (ȳ ) = (2.021+1.925 +1.826 + 2.125+ 2.210+ 2.015/6)
Average composition of tracer Material (ȳ ) = 2.020333333% or 0.02020333333
Solution
Given:
p = 0.02
N=6
A biscuit dough is prepared by mixing flour and other ingredients
along with tracer material (2%mass). After 10 minutes of mixing 6
random samples are collected and their composition (% of tracer
material) is given below. Calculate the mixing index after 10 minutes
of mixing
After 10 minutes:
2.021%
1.925% 1.826%
2.125%
2.210%
2.015%
Average composition of tracer Material (ȳ ) = (2.021+1.925 +1.826 + 2.125+ 2.210+ 2.015/6)
Average composition of tracer Material (ȳ ) = 2.020333333% or 0.02020333333
Variance ( s2 ) = (2.021%-0.02020333333)^2+(1.925%-0.02020333333)^2 .....+
((2.015%-0.02020333333)^2)/(6-1)
Solution
Given:
p = 0.02
N=6
A biscuit dough is prepared by mixing flour and other ingredients
along with tracer material (2%mass). After 10 minutes of mixing 6
random samples are collected and their composition (% of tracer
material) is given below. Calculate the mixing index after 10 minutes
of mixing
After 10 minutes:
2.021%
1.925% 1.826%
2.125%
2.210%
2.015%
Average composition of tracer Material (ȳ ) = (2.021+1.925 +1.826 + 2.125+ 2.210+ 2.015/6)
Average composition of tracer Material (ȳ ) = 2.020333333% or 0.02020333333
Variance ( s2 ) = (2.021%-0.02020333333)^2+(1.925%-0.02020333333)^2 .....+
(2.015%-0.02020333333)^2/(6-1)
Variance ( s2 ) =1.876226667 x 10^-6
Solution
Given:
p = 0.02
N=6
A biscuit dough is prepared by mixing flour and other ingredients
along with tracer material (2%mass). After 10 minutes of mixing 6
random samples are collected and their composition (% of tracer
material) is given below. Calculate the mixing index after 10 minutes
of mixing
After 10 minutes:
2.021%
1.925% 1.826%
s02 = p ( 1 - p)
s02 = 0.02 (1 - 0.02 )
s02 = 0.0196
2.125%
2.210%
2.015%
Solution
Given:
p = 0.02
N=6
A biscuit dough is prepared by mixing flour and other ingredients
along with tracer material (2%mass). After 10 minutes of mixing 6
random samples are collected and their composition (% of tracer
material) is given below. Calculate the mixing index after 10 minutes
of mixing
After 10 minutes:
2.021%
1.925% 1.826%
2.125%
s02 = p ( 1 - p)
s02 = 0.02 (1 - 0.02 )
s02 = 0.0196
sr2 = p ( 1 - p) / n where n is infinite since a large sample.
sr2 = 0.02 (1 - 0.02 ) / ∞
sr2 = 0
2.210%
2.015%
Solution
Given:
p = 0.02
N=6
A biscuit dough is prepared by mixing flour and other ingredients
along with tracer material (2%mass). After 10 minutes of mixing 6
random samples are collected and their composition (% of tracer
material) is given below. Calculate the mixing index after 10 minutes
of mixing
After 10 minutes:
2.021%
1.925% 1.826%
2.125%
s02 = p ( 1 - p)
s02 = 0.02 (1 - 0.02 )
s02 = 0.0196
sr2 = p ( 1 - p) / n where n is infinite since a large sample.
sr2 = 0.02 (1 - 0.02 ) / ∞
sr2 = 0
= ( 0.0196 -1.876226667 x 10-6) / (0.0196 - 0) = 0.9999042741
2.210%
2.015%
SOLID
MIXING