Solids Mixing PDF

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GBH Enterprises, Ltd. Process Engineering Guide: GBHE-PEG-MIX-707 Solids Mixing Information contained in this publication or as otherwise supplied to Users is believed to be accurate and correct at time of going to press, and is given in good faith, but it is for the User to satisfy itself of the su...

Description

GBH Enterprises, Ltd.

Process Engineering Guide: GBHE-PEG-MIX-707

Solids Mixing

Information contained in this publication or as otherwise supplied to Users is believed to be accurate and correct at time of going to press, and is given in good faith, but it is for the User to satisfy itself of the suitability of the information for its own particular purpose. GBHE gives no warranty as to the fitness of this information for any particular purpose and any implied warranty or condition (statutory or otherwise) is excluded except to the extent that exclusion is prevented by law. GBHE accepts no liability resulting from reliance on this information. Freedom under Patent, Copyright and Designs cannot be assumed.

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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

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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

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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.

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(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

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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.

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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

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FIGURE 2

REPRESENTATION OF TYPICAL BINARY POWDER MIXTURE STATES

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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:

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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.

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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...