Solids Mixing

GBH Enterprises, Ltd.

Process Engineering Guide:
GBHE-PEG-MIX-707

Solids Mixing

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Process Engineering Guide:
CONTENTS

Solids Mixing
SECTION

0

INTRODUCTION/PURPOSE

3

1

SCOPE

3

2

FIELD OF APPLICATION

3

3

DEFINITIONS

3

4

BACKGROUND

3

5

MIXING QUALITY

4

5.1
5.2
5.3

Qualitive Mixture Quality
Quantitative Mixture Quality
Sampling of Mixtures

4
5
8

6

THE MIXING PROCESS

9

6.1
6.2
6.3

Powder Mobility
Mixing Free-Flowing Powders
Mixing Cohesive Powders

9
9
10

7

MIXER SELECTION

12

7.1
7.2

Available Equipment
A Selection Procedure

12
16

8
9

LATERAL THINKING
BIBLIOGRAPHY

18
18


FIGURES
1

DIVISION BETWEEN FREE FLOWING SOLIDS AND
COHESIVE POWDERS

4

REPRESENTATION OF TYPICAL BINARY POWDER
MIXTURE STATES

6

POSSIBLE STRUCTURES FOR BINARY COHESIVE
POWDERS

11

4

TUMBLER MIXERS

12

5

CONVECTIVE MIXERS

13

6

HIGH SHEAR MIXERS

14

7

HIGH IMPACTION MIXERS

15

8

MIXER SELECTION DECISION CHART

17

2

3

DOCUMENTS REFERRED TO IN THIS PROCESS
ENGINEERING GUIDE

19


0

INTRODUCTION/PURPOSE

This Guide is one of a series of Mixing Guides prepared for GBH Enterprises.

1

SCOPE

This Guide covers only the mixing of dry particulate solids.

2

FIELD OF APPLICATION

This Guide applies to Process Engineers in GBH Enterprises worldwide.

3

DEFINITIONS

For the purposes of this Guide, the following definitions apply:
Scale of
Scrutiny

The quantity of mixture on which the quality of the mixture is
judged.

With the exception of terms used as proper nouns or titles, those terms with initial
capital letters which appear in this document and are not defined above are
defined in the Glossary of Engineering Terms.

4

BACKGROUND

The mixing of dry particulate solids differs from that of liquid and gaseous
systems in three important respects:
(a)

There is no particulate motion equivalent to the molecular diffusion of
gases and liquids. The mobility of the mixture is dependent on an energy
input and without this there will be no relative movement of the particles.


(b)

Whilst the molecules of a single phase liquid system or of a gaseous
system may differ and may diffuse at different rates, they will ultimately
achieve a random distribution within the confines of the system.
Particulate and granulate components do not have the constant properties
of molecular species and these differences can cause non-random
movements, or segregation with a resultant loss of mixture quality.

(c)

The ultimate element of the particulate mixture is several degrees of
magnitude larger than the ultimate molecular elements of the liquid or
gaseous mixture. In practical terms this means that samples withdrawn
from a randomized particulate mixture shall have a coarser texture,
greater content variation or poorer mixture quality than the equivalent
samples taken from a gaseous or liquid mixture.

These differences accentuate the problems of mixing particulate solids. An ideal
mixing system would have high mobility and fine texture of its ultimate elements.
Particulate solids have poor mobility and coarse texture.
Within the spectrum of industrial solids there are great variations in flow and
texture. An initial division can be made between free-flowing solids and cohesive
powders (see Figure 1)
FIGURE 1 DIVISION BETWEEN FREE FLOWING SOLIDS AND COHESIVE
POWDERS


As can be seen texture is obtained at the expense of mobility and vice versa. A
ladies face powder has good texture but poor mobility whilst a synthetic
detergent has high mobility and poor texture. In many cases the nature of the
particulate solid can be adjusted to be more or less cohesive /free-flowing by
controlling the properties, and notably the size, of the particles.
For large tonnage industrial products a free-flowing solid has obvious process
advantages. Flow rates can be controlled, packages can be filled consistently,
dust is minimized and the customer receives an attractive product. The cohesive
powder has little to commend it except that the texture or quality of mixture can
be higher. This can be a dominant requirement.
It is recommended that the temptation to control particulate solids properties
such that the bulk flow is just free-flowing should be avoided. While potentially
giving the best texture commensurate with satisfactory flow, it is a dangerous
balancing point as small changes in the process could transform the flow
characteristics and make the process inoperable.

5

MIXING QUALITY

5.1

Qualitive Mixture Quality

When is a mixture well-mixed? This fundamental question has to be asked of all
mixtures but it is especially important when coarsely textured powders are
involved.
Danckwerts [Ref. 1], gives some helpful qualitative ideas on mixture quality. A
Scale of Segregation of a mixture measures the size of regions of unmixed
material. The Intensity of Segregation measures the amount of dilution of regions
of unmixed material.
Evidently, the quality of a mixture is improved by reducing both the scale and
intensity of segregation. As they are reduced the mixture will pass through a
critical quality where it can be deemed satisfactory or well mixed. Further mixing
is unnecessary. This concept of a critical mixture quality was described by
Danckwerts in terms of a Scale of Scrutiny for the mixture. This is the quantity of
mixture on which the customer will base a judgment of quality. Thus, in the case
of dispersing a pigment in a face powder the judgment would be based on the
ability of an eye to detect any patchiness when the powder is spread on the skin
and the scale of scrutiny would be measured in fractions of a gram of powder.


With a detergent the scale of scrutiny is probably the contents of a cup added to
a washing machine and would be up to 50 grams of powder.
The smaller the scale of scrutiny the greater the mixing problem.
In the limits, if the scale of scrutiny was the contents of the batch mixer then the
mixture would always be perfect and if the scale of scrutiny was one particle then
the mixture would be completely unmixed.
It is essential to identify this scale of scrutiny for every process because:
(a)

it identifies the objective of the mixing process;

(b)

it enables the mixing problem to be defined statistically;

(c)

it is the scale at which the mixture shall ultimately be sampled for quality
control purposes.

5.2

Quantitative Mixture Quality

Having determined the scale of scrutiny for a product it is possible to define three
limiting variance values for a powder mixture:
(a)

the variance of a completely separated system (So2);

(b)

the variance of a randomized mixture (SR2);

(c)

the variance of an ideal or ordered mixture (SI2).

See Figure 2 for pictorial representation of a binary powder system


FIGURE 2

REPRESENTATION OF TYPICAL BINARY POWDER MIXTURE
STATES


This can also be done for multi-component multi-sized particulate systems and
provides a basis of comparison for experimental results as well as a desk-bound
method of checking the feasibility of a variety of competing mixture formulations.
The simplest case is that for a two-component mixture of equi-sized particles
[Ref. 2 and!3]

where p and q are the proportions of the two components and A the number of
particles in the sample. Lessons from this simple case can be applied to the
more complex multi-component, multi-sized systems. Note that;
(1)

Randomization is normally the goal of an industrial mixer so that SR2
should be as small as possible. This can be done either by having a large
scale of scrutiny, (i.e. large A), or for a constant weight of sample to
reduce the particle size. This is the numerical expression for the improved
texture of a cohesive powder.

(2)

For scale-up purposes So2 is independent of scale of scrutiny whilst SR2 is
inversely proportional to scale of scrutiny. Between these limiting mixture
values there is an unknown dependence on scale of scrutiny which makes
it essential that intermediate mixtures are sampled at the required process
scale of scrutiny.

(3)

With free-flowing powders SR2 is the limiting variance of the mixed
product. In some circumstances with cohesive powders a positive
structuring of particles can be achieved so that the zero variance of the
ideal mixture SI2, can be approached (see 6.3).
For binary systems with multi-sized particles the value of SR2 is given by:


Within the mixture and f a is the size fraction of one component of average weight
Wa in a particle size range [Ref. 4].
The denominator in equation (4) is the estimate of the mean number of particles
in a sample and is directly comparable with the denominator value A of equation
(2). In order to estimate the limiting variance by equation (4), the size analysis of
the components is required along with a knowledge of particle shape and specific
gravity. This limiting equation for random mixtures has been extended to cover
multi-component mixtures by Stange so that:

In this expression one component is regarded as the 'key' component. If the
variance of more than one component is regarded as critical in a process it could
be necessary to monitor the state of mixedness of these components
independently [Ref. 5].
Equations (2), (4) and (5) are extremely important in that they provide a method
of estimating the best theoretically obtainable mixture quality for any particulate
mixture. Desk calculations shall show the effect of varying mixture formulations
or the scale of scrutiny on attainable mixture quality. In practice this mixture
quality may prove to be unobtainable due to segregation or poor mixer design but
at least the boundaries of possibility in a randomizing process are established.
The likeliest circumstances in which a random mixture shall not be satisfactory
for its duty are:
(a)

When the scale of scrutiny is very small.

(b)

When one or more components are in a minor proportion.

(c)

When an ingredient is composed of large particles.


As a 'rule of thumb' if at a given scale of scrutiny a mixture contains less than 500
particles of an ingredient then the formulation is asking for a statistically difficult
or impossible performance from the mixer.
For more quantitative mixing statistics the reader is referred to [Ref. 6 Chapter 2].
5.3

Sampling of Mixtures

A comparison of process performance with the limiting statistical variance or
quality values requires samples to be taken in order to determine the
experimental variance Sex2.
Samples should be taken of a size equal to the scale of scrutiny. It is very difficult
to avoid bias in the selection and retrieval of samples from free-flowing solids
mixtures [Ref.7]. Rules for the sampling of free-flowing powders would be:
(a)

Avoid sampling from bulk and look for points in the process where the
mixture is flowing: e.g. as a batch mixer is discharging.

(b)

Sample the entire section of flow.

(c)

Sample frequently and avoid a sampling frequency which coincides with a
process frequency.

The sampling of cohesive powders is less of a problem because of the reduction
in segregation.
A sample withdrawn from a mixture is a 'point' sample at a carefully chosen scale
of scrutiny. When this sample is analyzed for quality it is unlikely that the quality
required for analysis is the same as the scale of scrutiny for the process and it is
vital that sub-sampling of the point sample is done in an efficient spinning riffler.
That is, for analytical purposes a 'bulk' sample has to be taken from the point
sample. Alternative methods of obtaining a bulk analysis of the point sample
would be to dissolve the entire point sample in a liquid or to grind the sample
down to a fine cohesive state.


6

THE MIXING PROCESS

6.1

Powder Mobility

The mixture quality of a powder shall be improved if the scale and intensity of
segregation are reduced. In order to generate inter-particulate motion and give
individual particles the opportunity of relocating themselves within the mixture,
the particles may be kneaded, tumbled, fluidized, sheared or scooped.
The ability of particles to move freely is an important mixing characteristic and
leads to a general division of particulate solid mixtures into:
(a)

free-flowing mixtures, and

(b)

cohesive or structured mixtures.

The division between the two regimes is not easily defined. The bulk effect can
be seen by rolling the mixture in a bottle. The free-flowing powder solids move
smoothly with well defined planes of movement whilst the cohesive powder
exhibits 'stick-slip' motion with irregular surface characteristics.
Particle size is probably the dominant influence on the type of flow regime. The
gravitational force associated with a large particle is much larger than any
restraining interparticulate forces with the result that individual particles retain
their freedom of movement. As the particle size decreases various
interparticulate forces can potentially dominate and the particles attempt to
retain a structured arrangement.
For particulate solids on the boundary between free-flow and cohesivity the
determination of aeratable and tapped bulk density has been found to be a
sensitive guide to the structural strength or cohesivity of the powder [Ref. 8].
The identification of the flow regime of the solids is important as it determines the
best type of mixer to be used.
6.2

Mixing Free-Flowing Powders

The disadvantage of such mixtures is that they can be subject to segregation or
'un-mixing' on a severe scale. The very mobility which allows a particle to move
smoothly and independently of its neighbors gives it the freedom to preferentially
move in a particular direction. Thus a small particle shall preferentially percolate
through a bed of moving particles.

A large particle shall be projected further than a fine particle given an equal initial
velocity. Such preferences can result in a very large scale of segregation.
The reader is recommended to view the video 'Filling a box' [Ref.9] to get a feel
for the potential gravity of the problem of segregation on mixture quality. If batch
mixing is a requirement for such free-flowing systems then mixers should be
chosen which inhibit the freedom of movement of individual particles and
promote the movement of changing groups of particles. Examples of such mixers
are ribbon blenders and a variety of scooping blade machines (see Clause 7).
The rolling of particles on an inclined plane is one of the chief causes of gross
segregation in industrial applications and is also one of the main causes of the
segregation in 'tumbler' mixers which find wide industrial application in batch
processes. The rotation of the vessel provides an excellent free tumbling or
percolation plane for the solids and extreme segregation can occur even with
relatively small particle size differences.
The potential of a mixture to segregate may be quantified by means of a
segregation test in an inclined cylinder [Ref. 10].
For a suitable process continuous mixing is an excellent way of avoiding gross
segregation. Within the continuous mixer the quantities of mixture at the point of
mixing are minimized and the potential scale of segregation is considerably
reduced.
Even if a large mass of free-flowing solids is 'satisfactorily' mixed great care has
to be taken in subsequently using the mixture. Many storage and handling
processes can destroy the mixture quality that has been so carefully created.
Only when the mixture has been 'frozen' at its final point of usage can the mixture
be regarded as safe. This is the point at which the particles lose their mobility or
at which segregation is no longer important and could be the formation of a
tablet, the filling of a package or a point at which the powder is put into solution.
The advice for the process engineer must be to locate the mixing point as closely
as possible to the point of usage and if possible to avoid all bulk storage and
transport between these points.


6.3

Mixing Cohesive Powders

If for the free-flowing mixture the art of the process engineer is to restrict the
freedom of movement of individual particles, then for the cohesive mixture the
problem is reversed. The cohesive system has a natural structure which has to
be repeatedly broken down in order to give individual particles within the
structure an opportunity of relocating themselves. It is for this reason that the
most suitable 'mixers' for cohesive powders are often to be found in the
comminutor catalogues. The breaking of powder structure resembles the
breakage of particles. The major reason for processing a cohesive powder rather
than a free-flowing solid is to achieve high mixture quality. Sub-clause 6.2
highlighted the statistical advantage of using small cohesive particles. Another
major bonus of mixing cohesive powders is that the structural nature of the
powder prevents the mobility of individual particles and the gross segregation
encountered with free-flowing powders is seldom met.
The nature and the strength of the interparticulate forces acting within a cohesive
powder structure is receiving a great deal of attention. The reason for this is that
if the structure of the powder can be manipulated by the careful choice of particle
shapes and sizes then an approach can be made to the ideal or ordered mixture
with zero variance, SI2. Figure 2 illustrates the basic mixture conditions for
unstructured, free-flowing particles for a binary system. If the particles are
structured then some interesting possibilities arise.
If there is an equal structural strength between black and white particles and
black and black particles then a randomly structured powder will result.
If one of the ingredients is 'self loving' e.g. black particles bond by preference to
black particles then the structure of Figure!3 (a) is obtained. If one of the
ingredients prefers to bond to a dissimilar particle then the preferred structure 3
(b) is an approach to ordered mixing.
The self loving preference of Figure 3 (a) is a common problem in the fine
chemicals industry. A minor ingredient such as a pigment is well dispersed
throughout the bulk of the mixture but at a small scale of segregation has a high
intensity of segregation. Usually such mixtures have to be subjected to a high
shear in order to break down the preferential structure. Edge runner
mills or powder rollers are good examples of mixers able to achieve this (see
Clause 7). The ordered structure of Figure 3 (b) offers mixtures of the highest
standards. The creation of coated powders is one practical means whereby this
structure can be approached.


A carrier particle provides attractive sites for very fine particles to preferentially
structure and a form of positive segregation takes place in particle location. Such
systems have a double advantage in that the bulk carrier particle ensures bulk
free-flow characteristics and the structuring ensures a very high quality of
mixture. Powder lubrication is one form of the coating process. The coated
mixture is best created in an impaction mixer where the carrier particles are
subjected to impaction by a high speed impeller (see Clause 7).
FIGURE 3 POSSIBLE STRUCTURES FOR BINARY COHESIVE POWDERS


7

MIXER SELECTION

7.1

Available Equipment

Figures 4, 5, 6 and 7 show some of the major mixer types following the mixer
mechanism categorizations of 6.2 and 6.3.
FIGURE 4

TUMBLER MIXERS

A variety of shapes.

Good process advantages.

Poor mixture quality for
free-flowing powders.

Gentle shearing action useful for
some cohesive and lubrication
processes.

A high speed impactor or
intensifier can be added to
give greater process
flexibility.

Good for product integrity.

See video [Ref. 12] for more detail of mechanisms.


FIGURE 5

CONVECTIVE MIXERS

Better mixture quality for
free-flowing powders.

Higher shear rates than tumblers
can cause degradation of product.

Contamination possible.

Cleaning difficult.

Paddles introduce air and add
to powder mobility.

This speeds up mixing but can
blow off fines.

Cohesive can be difficult to
empty from this category.


FIGURE 6

HIGH SHEAR MIXERS

Mechanized equivalents of the
mortar and pestle.

Often require pre-mixing of the
bulk powder before exerting local
high nip or shear.

Cause particle degradation.

Useful for breaking very small
aggregates to give very high
mixer quality.

Shear rate should be adjustable.


FIGURE 7

HIGH IMPACTION MIXERS

Like the high shear mixers very
useful for breaking structures
in cohesive powders.

Good for coating process.

Hold up in unswept regions
can be a problem.

With all these mixer types it is
worth examining the flexibility
of the system.

How is performance affected by How would the mixer perform if
degree of fill?
the flow characteristics of the
powder changed?
Look for mixers with a variety
of mixing mechanisms.

For example an edge runner mill
with a fitted ribbon blender,
a tumbler mixer with a high speed
impactor or a high speed impactor
which also permits gentle
circulation of the powder.


7.2

A Selection Procedure

A mixer has to satisfy the following requirements:
(a)

it has to satisfy process requirements;

(b)

it has to produce mixtures of a satisfactory quality;

(c)

it has to meet these requirements at the lowest unit price.

Process requirements are usually easy to identify as products and processes
impose their own conditions [see Ref. 6, Chapter 3]. Producing a mixture of the
correct quality is more problematical but a decision sequence would be:
(1)

Is the process statistically possible (see 5.1 and 5.2)?

(2)

What is the flow nature of the powder to be mixed (see!6.1)?

(3)

What mechanism of mixing should be used (see 5.3 and 6.4)? and if
possible view video [Ref. 11] 'Mechanisms of Mixing Powders'.

(4)

Choose a mixer. It is often desirable to choose a mixer with more then one
mixing mechanism as the process and role of the mixer might well change
(see 7.1).

(5)

If possible test the mixer before installation at the correct scale of scrutiny
(see!5.1) using non-biased sampling techniques (see 5.3) at a mixer
capacity as close as possible to the required duty. Check performance
quality and mixing time (see 5.2).

Figure 8 gives a parallel selection procedure based on a decision chart.


8

LATERAL THINKING

Powder mixing can be a difficult process and for free-flowing powders it can be
an equally difficult task to retain mixture quality up to the point of usage. Is there
a way round the problem rather than through it? Some examples of alternative
solutions would be;
(a)

Process orientated
(1)

To avoid gross segregation of ingredients would it be possible to
granulate the mixture of chemically different ingredients to provide
a product which had physical but no chemical segregation?
(for example granular fertilizers).


(2)

Can the product be put into liquid or paste form?
(for example synthetic detergents).

(b)

Market orientated

(1)

Can the customer be encouraged to mix the raw ingredients
(for example salt package in crisp packet).

(2)

Would the customer accept a 'shot-filled' package at a scale of scrutiny
corresponding to its usage (for example a tea bag).

Other opportunities for originality become evident on close examination of how
the customer actually uses the process mixture.


9

BIBLIOGRAPHY

Ref

Source

[1]

Danckwerts, P.V., Research, London, 1963 6, 355.

[2]

Lacey, P.M.C., Trans. Inst. Chem. Eng., 1943 21, 53.

[3]

Hersey, J.A., Pow. Tech. 1975 11, 41.

[4]

Poole, K.R., Taylor, R.F. and Wall, G.P., Trans. Inst. Chem. Eng., 1964,
42, 166.

[5]

Stange, K., Chem. Ing. Tech., 1963, 35, 580.

[6]

Harnby, N., Edwards, M.F. and Nienow, A.W., Mixing in the Process
Industries, 1985, Pub. Butterworth.

[7]

Allen, T. and Khan, A.A., The Chem. Eng., 1970, 109.

[8]

Harnby, N., Hawkins, A.E., and Vandame, D., Chem. Eng. Sci., 1987, 42
879.

[9]

Harnby, N., Video 'Filling a Box with Powder'.

[10]

Williams, J.C., and Knan, H.I., The Chem. Eng., 1973,!1,!19.

[11]

Harnby, N., Video 'Mechanisms of Powder Mixing'.


Solids Mixing

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