Review Mixing Particulates

8/9/2019 Review Mixing Particulates

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J. ugric. Engng Res. (1991) 49, 1-19

REVIEW PAPER

Mixing Processes for Agricultural and Food Materials:

3. Powders and Particulates

J. A. LINDLEY

Department of Agricultural Engineering, North Dakota State Univers ity, Fargo ND 5810.5, USA and formerly

Visiting Worker, Buildings and Livestock Divis ion, AFRC Institute of Engineering Research, Wrest Park,

Silsoe, Bedford MK45 4HS, UK.

Received 23 April 1989; accepted in revised form 16 September 1990)

Mixing of solid particulate materials s a common and ancient operation. The factors and

methods relating to mixing of solid materials have been reviewed. Considering the wide

application, the amount of information available appears quite limited. There is a general

understandingof what happens n the process,but the details of forces and mechanisms ave

not been completely elucidated and developed into design procedures. Inter-particle

percolation is an important mechanismn solidsmixing.

Mixing of solids s often accomplishedby manipulating material flows or by use of simple

tumblers. Ribbon impellers or large, open augers in vesselsare sometimesutilized. The

vesselsmay be open or closed, horizontal or vertical and may be cylindrical or someother

shapesuch asconical with the impeller inclined.

Total mixed rations for livestock are composedof materials with diverse characteristics.

Mixing, and prevention of segregationof such materialsare problems. Standard methods or

evaluating the performance of mixing equipment have been developed. Tracers are added to

a standard mixture and then the coefficient of variation determined for a seriesof samples.

There is a need to develop methods or determining when mixing is satisfactorily completed.

1. Introduction

Solid particulate materials have been subjected to mixing operations since ancient days.

One of the earliest devices used was a mortar and pestle. Today many mixing devices and

agitators are used in the food processing industry. Dry food materials that are mixed

include flour, sugar, salt, flavouring materials, flaked cereals, dried milk, and dried

vegetables and fruits. Solids mixing or blending of ingredients is an extensive processing

operation used for the preparation of animal feeds, fertilizers, seed stocks, insecticides,

fertilizer, and packaged foods. Solids may be mixed to facilitate reactions in the

preparation of cereal products. Other food products may be mixed to achieve agglomera-

tion or for coating.3

A random distribution is usually desired, and expected, when blending particulate

solids.4 An intimate mixture of solids may be required for the following reasons.

1. The materials being mixed may subsequently be required to react chemically with

one another, e.g. in dry explosives.

2. The mechanical properties of the final product may depend on the spatial

configuration of the various particles, e.g. as in concrete.

3. It may be desired to take from the mixture samples which can be relied upon to

contain a fixed proportion of each constituent e.g. production of pills and medicinal

powders.

1


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2

MIXING PROCESSES FOR AGRICULTURAL MATE RIALS: 3

Notation

a positive constant

Ab blade angle, rad

4

inter-facial area/unit volume of

the mixture, m2/m3

1

m

maximum interfacial area per

unit volume, m2/m3

ass minimum interfacial area

measurable, m/m

b positive constant

Dd agitator or impeller diameter, m

Or angle of friction between

material and blade, rad

d, particle diameter, m

fPP

diameter of percolating particles,

m

3 diameter of packing spheres, m

6 dispersion coefficient, m*/s

F force, N

g acceleration of gravity, m/s*

1

vertical height of blade, m

YL dimensionless horizontal force

on a blade, Ho/(Wsh~,L,)

Ho horizontal force, N

Hyi vertical immersion depth, m

j

order of reaction w.r. t. coated

component

J constant, dimensionless

k firs t order kinetic rate constant

K, passive earth pressure coefficient

Lb length of mixer blade, m

4

number of elements or

subvolumes

no maximum number of sub-

volumes

N, Zwieterings correlation

P, Peclet number (vD,,/E,)

s sample standard deviation

f time, s

V liquid volume, m3

V

P

vertical velocity of percolating

particle, m/s

u velocity, m/s

uk kinematic viscosity, m*/s

?s

volume of subelements m3

specific weight of material,

kg/m3

X percent of ingredient that is

unmixed

XC mass fraction of coated powder

in mixture

X, dye per unit mass, kg/kg

X, percent of solids in suspension

p liquid density, kg/m3

Ap density difference between solid

and liquid, kg/m3

0,

std. dev. of completely mixed

random mixture

(Y coefficient of restitution =

velocity of separation/velocity of

approach

There have been many reports relating to mixing processes, but there seems to be a

lack of fundamental relationships. In 1943, Lacey reported that many designs for mixing

machines had been patented, but little quantitative performance data provided. Many

systems have been tested since, but the resulting information applies to the specific

equipment and materials and cannot be generalized.

A satisfactory mixing process (1) produces a uniform mixture, (2) in a minimum time,

(3) with a minimum cost for overheads, power, and labour. Some variation between

samples should be expected in any mixture of discrete solid particles, but an ideal mixture

would be one in which the variation in composition between samples is minimal.

2. Material factors

Wide differences among properties such as particle-size distribution, density, shape,

and surface characteristics (such as electrostatic charge) may make blending very difficult.

Additional factors which may affect the mixing process are: flow characteristics, e.g. angle


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J. A. LINDLEY 3

of repose and flowability; friability which is the tendency of material to break into smaller

pieces; agglomeration-energy is required to cause breakdown; moisture content, and

temperature limitations of the ingredients or changes that might occur because of

temperature changes. 3 The relative absence of cohesive or adhesive forces in particulate

materials will be related to the size and moisture content of the material.

Segregation, which is the tendency of particles to separate out according to size and/or

density, is a problem that is generally found only in solids mixing.6 If mixtures of solid

particles have the same size and shape but different densities, or if they are of different

size or shape, difficulty in mixing may result. Heavier particles tend to remain near the

bottom of the container during a mixing operation. Henderson and Perry stated that

round or small particles tend toward the top. However, Perry reported that for

particles of the same density but different sizes,

the smaller particles would go to the

bottom. Also, the round smooth particles are found near the bottom, while the jagged or

polyhedral ones seek the top. The mixing process must overcome these natural

tendencies; this is accomplished by lifting the materials, more or less in mass, from the

bottom of the mixing vessel and turning them onto the top and allowing the voids to fill

by gravity.,

Avoiding segregation is a challenge in the food industry where materials with a wide

range of properties are often mixed. These materials may include spices, liquid flavours,

salt, hydrolyzed vegetable protein, monosodium glutamate and dehydrated vegetable

powders. Flow properties may be modified by the addition of anti-caking agents to

prevent undesired agglomeration and flow promoters when blending potato crisp and

snack food seasoning.*

3. Differences between solids and liquid mixing

Nienow, Edwards and Harnby6 presented the following differences between mixing

particulate systems and mixing liquid systems.

1. There is no particulate motion equivalent to the molecular diffusion of gases and

liquids. Thus a randomized state does not occur without the input of some external

energy.

2. Particulate and granular components do not usually have constant properties and

can differ widely in physical characteristics.

A mixer may cause a grading or

segregation of particles according to such characteristics as size, density, resiliency,

etc.

3. The ultimate element of a particulate mixture is much larger than for a liquid

mixture. Samples withdrawn from a randomized particulate mixture have a coarser

texture or poorer mixture quality.

Particles change their relative positions in response to movement and the subsequent

arrangement may be more random or there may be a tendency towards segregation. In

contrast to the mixing of miscible liquids, the mixing of particles is often a readily

reversible process. A mixture of miscible liquids leaving a mixing unit retains or even

improves its mixedness during the transport process, while a well-mixed batch of particles

can be separated almost completely at a subsequent process stage.

Dry materials with a particle size greater than 75 pm tend to be free-flowing. In a

free-flowing powder, particles have a high individual mobility and are prone to segregate.

Powders of smaller particles have a tendency to agglomerate because as the size of the

particles decreases the separation forces between particles become less dominant and

inter-particulate bonding forces such as Van der Waals, electrostatic or moisture bonding


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4


forces become more significant.6 Segregation is unlikely for particles of less than 10 pm.

Addition of quite small quantities of moisture can transform a strongly segregating

mixture into a cohesive and non-segregating mixture. A mixture containing quite coarse

particles can be surprisingly free of segregation if the major component has a rough or

fibrous shape. If one component in an otherwise coarse mixture is very fine, the fine

particles can coat the coarser particles, losing their freedom of movement, thus resulting

in a high-quality, non-segregating mixture.

4. Forces in mixing

For most mixing operations, the primary driving force for fluid motion is drag flow

caused by the relative motions of metal boundaries in the equipment. Pressure flow is

relatively unimportant for mixing.4 Forces acting on cohesionless materials during mixing

include gravity, vessel walls and the motion of mixing blades.

Bagster and Bridgwater,

studied the forces on a blade moving through granular

materials and the related effects on the material. They showed that while some of the

material undergoes convective transport, some undergoes local recirculation (Fig. I). A

dimensionless relationship of the horizontal force as a function of various parameters was

presented and the following expression for the total force per unit length of blade was

developed:

F 1 W&&)

-=-

Lb 2 sin A,, cos Df

or the horizontal force per unit length is:

Ho 1 (W&~,K, sin (A,, + Of))

L,=2 sin Ah cos D,

Circulating region

A

F

*

Material flow

(1)

Fig. 1. Flow of granular material passing a blade9


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J. A. LINDLEY

4

l

n

0

3-

I

n

n

l:

2-

I l

0.

m m

n +

l

m

m m

+A

l-

0

im+

l

+ A

.g n

n

0.

0

I

0.4

I

I I I

I I

0.6

1.2 1.6 2.0 2.4 2.8

Immersion depth dimensionless)

Fig. 2. Ef fec t of blade immersion depth on force. W, Glass beads with steel blade; +, Sand with

steel blade; 0, Polythene chips with steel blade; A, Glass beads with rough blade

where the passive earth pressure coefficient, K,, is a function of the specific weight of the

material, blade angle, angle of friction between material and blade, angle of internal

friction and angle of repose.

The forces were measured in the laboratory and it was concluded that:

1. The dimensionless immersion, Hvi/hb,

(distance from surface to bottom of

blade/vertical distance between top and bottom of the blade), is of key importance

(Fig. 2).

2. Blade roughness is not a very important variable.

3. Rake angle can have a considerable effect on the force on the blade and the relative

size of the recirculating volume to the total volume displaced.

4. Blade velocity is not very important.

5. Internal angle of friction of the material is moderately important, particularly for

IOW

values

Of H~i/hb,*

5. Mechanisms in cohesionless powders mixing

Mixing in a horizontal drum mixer has been described by Donald and Roseman.

Particles are carried round with the mixer until the angle of repose is exceeded, then the

particles near the top edge roll down the slope, as a thin layer, over the rest of the

particles.12 As the rotation speed is increased the particle velocity may become great

enough to project them into the air. On reaching the end of the slope, the particles are


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MIXING PROCESSES FOR AGRICULTURAL MATER IALS: 3

-Mixing zone

Fig. 3. Particle flow in a horizontal drum

b

tatic mass

again carried round with the mixer walls to complete the circuit (Fig. 3). The circuit made

by the particles is defined as the path of circulation.

Mixing is defined as occurring when any particle changes its path of circulation. Since

movement of particles relative to one another occurs only in the surface layers, this is the

only region where mixing can occur. If two identical particles exchange positions, this is

useless mixing; useful mixing occurs only when particles changing positions (or circulation

paths) are different.

It has been found that when cohesionless powders or granular materials are mixed, a

random state is generally not attained. If mixing proceeds beyond the optimum time an

ordering, rather than mixing, of the particles occurs.13 Force applied to powders develops

strain in the materials and causes particle dilation. Free-flowing granular materials and

powders are unstable in the mixed state. It is unlikely that the process of mixing

particulates will provide a normal distribution of concentration frequencies.14 An initially

satisfactory mixture may segregate readily when the particles dilate under applied

strain.14

Extensive studies of mixing of cohesionless powders have identified the primary

mechanisms acting on cohesionless powders as convection and inter-particle percolation.

Surface mixing is a third mechanism found in solids mixing.

The mixing mechanisms have been defined as:

1. Convection is the mass movement or the movement of a group of particles en mass

from one location to another, i.e. various parts of the particulate solid mass or

powder move with differing velocities.3


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J. A. LINDLEY 7

2. Surface mixing is sometimes misleadingly termed diffusive mixitrg. The mixing

process occurs by the rolling of particles down a free surface.

The random

movement of particles on the free surface results in their redistribution. The

movement of particles on a free surface can also give rise to segregation due to

percolation of fine particles if particles of different sizes are present.6 If particles

differ in diameter then significant band formation may occur perpendicular to the

axis of rotation.

3. Inter-particle percolation is a process more closely analogous to molecular diffusion.

The smaller particles under the influence of gravity tend to drain through an array of

deforming larger ones, this often occurring when the particle mass is dilated due to

applied strain.13

Sometimes the convective mechanism is divided into convection and shear.15 Mixing

due to shear forces occurs when slip planes are established within the powder. Mixing

takes place because of the interchange of particles between adjacent layers. Size or

density difference among the sheared particles can lead to a preferential particulate move-

ment or segregation.6

Drahun and Bridgwater noted that sometimes a smaller component congregates at

the top of a slope beneath a pouring point whereas at other times it is found at the bottom

of the slope as far from the pouring point as possible. An investigation using various

materials revealed that there wa s a variation in the fate of particles on an inclined plane.

It was concluded that three processes controlling free-surface segregation were:16

convection in avalanches, movement of material en mass rather than as individual

particles; inter-particle percolation removing particles from the active zone and particle

migration. Small particles may pass through gaps and thus not be carried by avalanches

down the slope; large particles are unable to pass through the gaps and thus are carried

down the slope. Particle migration causes particles to remain in avalanches and to rise to

the free surface.16

Mixing and segregating mechanisms cannot be separated within a powder-handling

system. The final mixture quality is determined by the relative importance of the

mechanisms. Segregation can occur only when particles possess an individual freedom of

movement. Only when the particles retain independence can variation in individual

particle characteristics influence particle movement and produce segregation. A free-

flowing mixture generally permits individual particulate freedom, while a cohesive

mixture generally has inter-particulate bonding mechanisms which permit particles to

move only with an associated cluster of particles.6

6. Inter-particle percolation

A force acting on particulate materials can cause both a localized failure and a

movement of a group of particles which are deposited or distributed over some other

region. The movement results in a thin layer, about lo-20 particle diameters across,

between the two groups where there is considerable motion. This region is termed a sh,p

plane, failure plane or failure zone. In the failure plane there is a high velocity gradient. 3

In this dilated state particles can readily drop or roll from one layer to another. In

deforming powders failure zones are regions of high strain and high strain rate.

Inter-particle percolation occurs: if with two powders of different sizes it is possible for

the smaller to drain through the larger simply due to gravity; if the powders are of similar

size, drainage may occur only if the local structure has a high void fraction or if it is

mobile due to strain.

result.

Smaller particles have a greater mobility and thus segregation can


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8


Bridgwater13 proposed that inter-particle percolation is increased in failure zones

during mixing, and this results in the creation of clumps of strong material that resist

failure. Failure thus tends to occur repeatedly in the weak areas resulting in non-uniform

conditions and preventing the formation of random mixtures.

The rate of inter-particle percolation is determined by the detailed motion in the failure

plane, particle sizes and shapes, proportion of powders, surface frictional properties,

elasticity and densities.* Bridgwater and Ingram found that if three packing spheres are

touching, the largest percolating sphere that may pass between them has a diameter ratio,

dPP/DPS, (ratio of diameters of percolating particle to packing spheres) of O-1546.

This mixing mechanism is also a mechanism of segregation and thus is significant in

determining the quality of the mixture that can be achieved on the fine scale.14 An

investigation of the percolation of spherical particles through a packed bed of larger

spheres showed that the radial dispersion of very small spherical particles falling through

a packing of spheres is in accord with a diffusional mechanism. The results may be

reduced to a single plot14 of Peclet number (P,) against coefficient of restitution ((u) (Fig.

4). For the conditions studied, the dispersion was independent of the diameter of the

percolating particles.14

Bridgwater and Ingram studied inter-particle percolation using table tennis balls and

glass beads as packing materials and steel, iron, glass, resin or lead spheres as percolating

particles. They concluded that the dimensionless mean vertical velocity, v,,/~(gD,,), is

determined by both the coefficient of restitution and the ratio of particle to packing

diameters (Fig. 5). The axial Peclet number was not equal to the radial Peclet number,

therefore, dispersion is not isotropic. When particles percolate downward through a

packed bed (larger particles) or a bar mixer or distributer, the dispersion is a function of

the Peclet number and the coefficient of restitution.4.20,2

41

0

I I I

I

0.2 0.4 0.6 0.8 a

Coefficient of restitution

Fig. 4. Peclet number versus coef ficient

of restitution


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J. A. LINDLEY. A. LINDLEY

9

0.5

n

211

Y

i 0.4 -.4 -

>

m

.zz

fiiii

+

>

z

5 0.3 -.3 -

5

A

z

X

A

A

E

.--

D

0

X

A

0.2.2

0

I

0.2.2

I I

0.4.4

0.6.6

Coefficient of restitutionoefficient of restitution

I I

088 1.0.0

Fig. 5. Relationship between dimensionless vertical veloci ty and coefficient of restitution. n ,

d,JD, = 0.035, + , d,JD,, = 0.043; 0, d,/D,, = 0.057; A, d,/D, = 0468; x , d,/D,, = O-068

7. Equipment performance

Mixing operations may be batch or continuous. A rotating drum, box, or barrel w ith

non-symmetrically located supports may be satisfactory for small agricultural operations.

A stationary container, often U-shaped, with rotating paddles or ribbons is used for larger

or more difficult operations. Continuous mixing procedures are most satisfactory fo r

large, extensive operations. The ingredients are usually added volumetrically by auger,

star wheel, or other device to a screw conveyor.* Automatic weighing machines can be

used to provide better control. In some cases no special mixing device is required as

satisfactory blending is achieved during the conveying operation.

Free flowing non-segregating powders may be readily mixed by use of tumbler mixers.

Tumbler mixers can be used to provide a gentle mixing required to avoid attrition of

friable materials. Careful design is required to minimize degree of segregation.*

A vertical screw blender (Fig. 6~) may be desired for larger batches, while the

horizontal ribbon mixer (Fig. 66) may give satisfactory results for smaller batches. For

difficult mixes, an orbiting screw mixer (Fig. 6c) may be used. A double ribbon in this

machine provides greater shear.= Ashton and Valentit? gave the following classification

of mixers for powders and granular materials:

1. Rotating shell, e.g. double cone (Fig. ti), rotocube, Y-blender (Fig. 6e).

2. Fixed shell, rotating horizontal impeller, e.g. ribbon blender

(Fig.

6b), universal

mixer, Z-blade mixer.

3. Fixed shell, rotating vetical impeller, e.g. Nauta mixer

(Fig.

6c), Turner-H&son

mixer, Fountain mixer, Henschel mixer, Kenwood mixer.

4. Fluidizing mixer, e.g. Air-mix, Young gravity blender, Steel-shaw air blender.


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MIXING PROCESSES FOR AGRICULTURAL MATER IALS: 3

a) Vertical screw

cl Orbiting screw

b) Horizontal ribbon

Cd) Double cone

Fig. 6. Solids mixers

e) Y-blender

The bulk of a ration fed to dairy cattle is composed of forage. A supplemental

concentrate which will typically include ground grains or grain parts, salts and various

minor ingredients is used to balance the animals nutritional requirements. This

concentrate was traditionally fed while cows were being milked. Recently it has been

found that high producing cows cannot consume sufficient concentrate during the milking

period; therefore, it must be fed at another time. Spreading the concentrate on the forage

as a top dressing allows cows to selectively eat what they prefer and does not ensure a

balanced nutritional intake.24 To overcome this problem dairymen have adopted the

practice of a total mixed ration.

The total mixed ration may be prepared on-farm using batch mixing utilizing horizontal

augers or rotating drums.25 These mixing systems may be stationary or mobile depending

on the feed storage and delivery systems. The minor ingredients are normally pre-mixed

and then spread over the forage.

In the USA, mobile farm batch mixers are evaluated by processing a standard test

mixture which includes a tracer. The tracer may be 0.5 salt and/or 5 whole kernel

shelled corn. The coefficient of variation is determined from 15 samples. Sample sizes are

at least 150 g for salt and at least 4000 g for shelled corn.26

The ASAE standard for testing stationary feed mixers also requires measuring power

requirements and makes provision for testing at other than the rated capacity.27 The

standard requires the use of three test periods for continuous mixers. Each test period

should be at least three times the average residence time of solids in the mixing

equipment.

The quality of the equilibrium mixture is one way of comparing mixer efficiencies.2*

However mixing too long may result in segregation and in the case of biological materials


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J. A. LINDLEY 11

may cause damage to the mixture.

endpoint .

Therefore there is a need to define the mixing

The area of interface between the particles at any instant can be used as a measure of

the degree of mixing. In a binary solid-solid system, if substance A is poured in the

bottom of a cylindrical vessel and substance, B is added to the top, the initial boundary

surface will be small. The process of mixing consists of causing some of A to pass into the

space occupied by B and similarly some of B to pass into the space occupied by A. This is

the diffusion of A across the initial boundary into B and of B in the reverse direction and

results in a considerable increase in the surface separating the two species. This process

can be continued until there is a maximum dispersion of one material in the other. Using

a,, the interfacial area per unit volume of the mix, in Ficks law of diffusion the following

equation is obtained?

da

-2 = k(a,, -a,)

dt

where

as,,,

is the maximum surface area per unit volume. The area,

as,

can be obtained by

integration giving:

a, = asm( 1 - eKk)

(4)

Although it is impossible to measure a, in most systems, small subvolumes can be

evaluated. If the sample contains both components then it will contain part of the

boundary surface.* The maximum number o f subvolumes is:

n0 = asmiass

(5)

where

ass

is the minimum area of the boundary surface measurable and this represents a

state of complete mixing. From Eqns (4) and (5) we get:

n, = a,/a,, =

n,(l - ePk)

(6)

An expression for the unmixed fraction at any time is:29

x/100 = n,u,/V - n,u,/V

or:

l-e+=l-X/100

(7)

(8)

and from this:

t = (l/k) In (100/X).

(9)

or the rate of mixing can be expressed by:

t = (llk)[a,,l(asm - 41.

(10)

Coulson and Maitra* evaluated the effects of several variables on k for a drum mixer

(152 mm diameter by 229 mm long). The experimental materials were: salt, coal, barium

nitrate, and lead nitrate. Bulk densities varied from 0.80 to 2.80; particle sizes were from

25 to 100 mesh; and the angles of repose varieda from 24 to 33.

Using salt and coal particles (70 mesh) at a drum speed of 55 rev/min the axis of

rotation of the drum was varied. A high degree of dispersion was never achieved when

the angle was greater than 30 or less than 8. The maximum k value occurred at 14. With

an angle of inclination of 23 the speed was varied and a maximum

k

value wa s found to

occur at 55 rev/min. Above that speed the whole mass tended to rotate with the drum; at


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12 MIXING PROCESSES FOR AGRICULTURAL MATE RIALS: 3

lower speed dispersion was never very good since the particles were not carried to the top

of the free surface. It appears that the drum should be operated at near the critical

speed.=

Carley-Macauley and Donald

found that for equal sized particles, 1.5-7 revolutions

were needed when starting from horizontal bands to achieve a ten-fold reduction in

sample variance.

The performance of several industrial mixers using non-segregating free-flowing powder

(test media w as sand, 60-100 mesh, 1*52g/cm3) was evaluated based on the ratio, s/o=,,

(sample standard deviation/standard deviation of the completely mixed random mixture)

as the mixing index.30

The mixer output (mass/time) was compared to the performance

ratio (index) for: different mixers; speed of rotation; and volume occupied. The results

showed: the air mixer was fastest; the ribbon mixer was next; and then the baffled mixer.

Other mixers evaluated were: rotating double cone; cube rotated about its diagonal with

internal rotating blades; simple drum rotated end over end; orbiting screw in a conical

vessel and Z-blade.

Bourne and Zabelka3 reported that agitation intensity, characterized by tip speed and

specific power input, required to attain homogeneous suspension of glass beads and

crystals in a contoured bottom tank was low (e.g. 1.9 ms- and O-3 kWmd3 for 1 mm

potash alum crystals having a settling rate of 0.073 ms-). Comparable or higher

intensities are required in conventional tanks to give complete suspension. The circulation

speed of the suspension in the tank was about four times greater than the settling rate of

the largest particle (e.g. 0.30 compared to O-073 ms-).

Cooker and Nedderman3 have developed equations for predicting the powder

circulation rate within a vertical helical ribbon agitator. Equations for torque on the

agitator and the vessel wall, derived by stress analysis, were equated to allow a solution.

A knowledge of the geometry and materials properties (friction, etc.) is required. A radio

pill tracer was used to verify the powder circulation rate.33

Additives (colloidal silicon dioxide products) are sometimes used to improve the mixing

characteristics of pharmaceutical powders such as acetylsalicyclic acid.34 Certain additives

provide increased mixture stability, improve flowabili ty characteristics and make mixing

quicker and more economical.

8. Blending in hoppers

It has been the practice in some industries where very large quantities of materials need

to be blended to use hopper blending. This concept may also be utilized as a premix prior

to a mechanical mixer. Hopper blending techniques may involve recycling through a

single hopper, flow through several hoppers or metering from multiple hoppers to a

combined discharge. These methods have been discussed by Schofield and TookeyJ5 and

Abbott .36 Fig. 7 shows the reduction in variation (ratio of measured standard

deviation/standard deviation of unmixed material) with repeated passes through non-

mass flow hoppers. The effect of recycling through a mass flow hopper is illustrated in Fig.

8. Use of twin hopper recycle mixing can greatly increase the rate of reduction (Fig. 9).

Taylor37 pointed out that it is necessary to understand the potential segregation

mechanisms when handling detergent powders in hoppers. Percolation, trajectory shear

and impact may be important to different degrees. In order to define segregation potential

the use of specialized equipment (e.g. particle size, density, shear cells) is required.37

Harrison 38 described the utilization of core-flow hopper blenders for use with polymers.

The blenders are filled in conical layers.


13/19

J. A. LINDLEY

0.9 .

i

+

0.8 A

0.7

t

s

Y

, 0.6

m

it

t

0.5

3

.x

0.4

I

t

n

0

0

01

I I I I I 1 I I

I

0.5 1.5 2.5 3.5 4.5 5.5 6.5 7.5 8.5

Number of passes

Fig. 7. Mixing by repeated discharge and loading of non-massfIow hoppemw W, Non-segregating,

centre loading; + , Segregating, centre loading; 0. Non-segregating, side loading; A, Segregating,

side loading

0.8 +

0.7

i

n

0.6

+

0.1 -

I

8

I n .

0

1 I I I I I I

1

L

I I

I

0.5 1.5 2.5 3.5 4.5 5.5 6.5 7.5 B5 9.5 10.5 11.5

Volumes recycled

Fig. 8. Mixing by recycle through a mass jlow hopper.35

n

, Non-segregating; + , Segregating


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14


UP

-

0.15 - +

0.14

-

0.13 -

0.12 -

>1 0.11

-

.e

ii 0.10 - 8

g 0.09

-

E

-0.08 0

.- 0.07 -

I

0.06 -

+

0.05 -

0.04 - 8 8 8

8

0.03 -

+

0.02

- +

+

0

0 0

001

I

I I I I

I

1 2

3 4 5 6

Number of cycles

Fig. 9. Twin hopper recycle mixing.35

W, Non-segregating, two layer; + , Segregating, two layers;

0, Non-segregating, ten layers

9. Powder coating

When a fine cohesive powder is mixed with a coarser granular material the structure of

the resulting mixture consists of a layer of fines adhered onto the surface of the larger

particles. 39 Hersheya first described powder systems produced by this cohesive interac-

tion as ordered mixes; the different constituent particles are held to one another in a rigid

structure, which does not become disordered by a procedure analogous to statistical

randomization. For an exact description of this mixing system, it is necessary to know: the

number of large particles that have been coated; the number of fine particles adhered to

each coated particle; the number of free fine particles and the changes of these quantities

with time.3s

Initially the fine powder or dye marker adheres to only a few coarse granules (carriers).

As the mixing progresses some of the dye is transferred to other particles which can then

mark additional particles. A typical coated powder concentration versus time curve has a

low initial but increasing slope which gradually tapers to a zero slope. i.e., at the

beginning the rate of coating is low because only a fe w carriers are present. As the

number of carriers increases the coating rate increases. However, this increasing rate

cannot be maintained for long because the amount of dye per unit mass of coated powder

(X,) decreases. The coating rate can be expressed as:3s

where

dX,/dt = kX,( 1 - XC)*-

k =b(~)- ~ and j = 1 - (l/b).

(11)


15/19

J. A. LINDLEY 15

The exponent, j, depends on rotation speed and is always less than one. Experiments

with a cylindrical mixer rotating about a horizontal axis that could be rocked through 20,

showed that the coating rate was positively influenced by rotation speed, but negatively

by rocking. The shearing and friction forces generated by the rotational movement of the

mixer exerted a strong, positive effect on the rate of coating. The rocking motion was

useful only for low rotational speeds.3s

Although ordered mixes by definition are formed with inter-particle attractions

resulting from surface forces produced by fine particles and random mixes are formed

without any particle interactions, there exists an area in which powder can become mixed

as a result of a combination of random and ordered mixing. As powder particle diameters

decrease, cohesive interactions increase; this effect is noticeable in powders with

diameters4 less than approximately 100 urn.

A perfect binary ordered mix contains coarse particles with an even coating of fine

adherent particles. Since each particle carries an identical number of fine particles the

standard deviation of the system is zero above a scale of scrutiny equivalent to one

ordered unit.40 In practice a real ordered mix has a finite variance due to errors in

sampling and analysis. The overall variance is the sum of the variances due to analytical

errors, sampling errors, purity errors and imperfect mixing.

10. Suspension of solid particles

Stirred vessels may be used for various purposes and the use determines the mixing

requirements. Sometimes a high degree of homogeneity is needed, e.g. when the stirred

vessel is used to continuously feed a chemical reactor,43 but in other cases it may be

satisfactory if all particles are suspended. Complete suspension exists when all particles

are in motion and no particle remains on the tank bottom for more than a short time.

Typical energy requirements (power input/unit mass) to achieve complete suspension

are from about 0.05 W/kg to 1.0 W/kg. Homogeneous suspension exists when particle

concentration is uniform throughout the vessel.44 This condition requires more energy

than merely complete suspension.

Mechanisms responsible for particle suspension are: drag forces arising from the fluid

moving in a complex boundary layer flow across the bottom, and turbulent burst which

originate in the turbulent mainstream flow and propagated intermittently through the

boundary layer (Fig. 10). Particle suspension in turbulent flow is sensitive to particle size.

Once lifted from the bottom of the vessel, the tendency to return due to gravity is

counteracted by the upward drag of vertical flows.&

Suspension requires an energy balance between the critical eddies and the height to

which a particle must be lifted to become entrained. Narayanan ef al,46 developed a

theoretical expression for mixing speed based on a balance of vertical forces. Baldi, Conti

and Alaria noted that at complete suspension conditions particles periodically may settle

and then be re-suspended, suggesting that suspension is a result of turbulent disturbances

rather than the average velocity field that exists near the bottom. They further assumed

that the suspension of particles was mainly due to eddies of a certain critical scale and that

the critical eddies have a scale of the order of (or proportional to) the particles size.

Nienow4* listed the factors that need to be considered in determining the impeller

speed to provide complete suspension. The factors include six particle-fluid properties,

solids concentration, six geometry considerations and scale-up factors. Twenty-three

references were given as having discussed these factors. The required suspension speed

based on Zwieterings correlation was given by Nienow47 as follows:

N =/U:.ldg2{g~p/p}.45 X)0.13

Z

@P

(12)


16/19

16


Flow direction

Turbulent

Turbulent burst

Laminar flow

Stagnation point

Fig. 10. Suspension of particles showing a turbulent burst*

NienowU recommended using Zwieterings correlation for small scale predictions except

where special geometries are involved (b) where the correlations of others have been

based on experimental conditions well away from those covered by Zwietering.

Although Zwieterings equation is most commonly recommended at least eight additional

correlations have been proposed for calculating the critical impeller speed for solids

suspension.-

11. Conclusions

Mixing of particulate solids has been carried out since ancient times and many

agricultural and food particulate materials are subjected to mixing processes. These

materials range from livestock feeds and fertilizers to cereals and dried vegetables. The

specific characteristics (particularly size, shape and density) of the materials influence how

readily they are mixed and their potential (or likelihood) to segregate.

Although there are similarities between liquid mixing and solids mixing, there are some

fundamental differences. A liquid mixture may become homogeneous from simply setting

because of molecular diffusion; however, solids mixing requires external energy input.

And the solids mixture never becomes totally homogeneous on the molecular scale. The

attainment of a uniform solids mixture does not ensure that it will remain; particulates of

differing characteristics have a potential for separation.

Concepts of soil mechanics have been used to develop expressions for forces on blades

moving through granular material but no correlation with actual power consumption was

given. Forces applied during mixing create shear zones or failure planes where the

particles are dilated which allows the smaller particles to percolate between the larger

ones. This inter-particle percolation provides a rearrangement and thus facilitates mixing.

Two other primary solids mixing mechanisms are convection and surface mixing.

Cohesionless powders are mixed by convective transport, surface mixing and/or

inter-particle percolation. Mixing and segregation will occur simultaneously in a free-

flowing mixture. Inter-particle bonding forces prevent independence of cohesive powders

and therefore, particles move in clusters.


17/19

J. A. LINDLEY

17

Applying a force, via a blade, to a particulate material will result in a localized failure

plane and movement of a group of particles. In the failure zone, the particles are dilated

and this allows inter-particle percolation.

Mixers used for solids are normally batch types and are relatively simple. Tumblers,

rotating shells or machines with open impellers such as ribbon or Z-blades are used.

Mixer performance tests have been performed for many years but few generalizations

have been developed that can be used in design of new and different types of systems.

Mixing speed required to achieve suspension of all particles can be estimated by

Zwieterings correlation. Additional energy input will be required to produce a uniform

mixture.

Acknowledgements

Thanks are due to North Dakota State University for granting a one year developmental leave

and provid ing financia l support, to AFRC Engineering for providing facilites, to the Underwood

Foundation for financia l support and to Drs John Randall and Roger Phillips for guidance.

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