Solids Handling Bench

Table of Contents

I. Introduction 5

II. Equipment Schedule

7

III. Installation and Commissioning 8

IV. Sieving 9

V. Bulk Density and Angle of Repose

20

VI. Flow from a Hopper 21

VII. Solids Mixing 23

VIII. Non-Standard Electrical Supplies 27

IX. Graphical Representation

30

Solids Handling Bench

RG 3700 Solid Handling Study Bench – the latest equipment for Solid Handling Study Bench, a size reduction with a ball mill can also be studied.

Solid Handling Bench – handling of bulk solids forms an important part of many process operations, particularly in the fertilizer, coal, etc.

The major parts of the solid handling study bench

Solid Mixing Tank – for Solid Mixing with its efficient high-torque impeller generates high mixing forces for the preparation of high viscosity materials and the dissolution and dispersion of concentrated powders in liquid.

Switch Control – a remotely controlled relay that is placed which consume large amounts of electricity and controller unit of the equipment.

Metal Frame for Mixing Cabinet – method often requires extensive cutting of individual framing members or solids and a practical, code approved solution to many for mixing materials form the bends that make the shapes.

Electric Motor – converts electrical energy into mechanical energy and operate through the interaction of magnetic fields and current-carrying conductors to generate force.

Cylindrical Vessel – is a closed container designed to hold gases, solids or liquids at a pressure substantially different from the ambient pressure.

I. Introduction

The handling of bulk solids forms an important part of many process

operations, particularly in the fertilizer, coal, pharmaceutical, food and

mineral processing plant. The arm-field bench introduces students to many

aspects of solids behaviour, including measurement of bulk density, angle of

response, sieving and particle size analysis, flow of solids from hoppers and

solids mixing. In later versions (1977 onwards), size reduction with a ball mill

can also be studied. The apparatus is essentially self-contained, and allows

more than one experiment to be conducted at any one time, this increase

the economic range of the solids handling bench.

RG 3700 Solid Handling Study Bench

(Armfield Technical Education Co. Ltd)

The characterization new Solids Handling Study Bench of the solids in

bulk form an important part in the process industries, particularly in the

handling of fertilizers, cement, crystals, pharmaceutical, and foodstuffs. The

Armfield Solids Handling Study Bench contains a number of simple items of

equipment designed to introduce students to the basic understanding of

solids and its behaviour. Each experiment may be undertaken separately

from the others, so increasing the economic benefit of the Bench as

experimental capabilities, description of equipment, and exclusions

Experimental Capabilities

1. Study of sieving techniques, including size distribution plots, effect of

sieve load on screen blinding, etc.

2. Angle of repose measurements.

3. Efflux rates from storage hoppers, as affected by hopper load, exit

geometry, size distribution, angle of repose, etc.

4. Studies of mixing solids and appropriate sampling size and position

and effect of vessel shape.

5. The apparatus is also a useful vehicle for demonstrating the

application of statistical techniques.

Description of Equipment

Specification: The basic bench consists of a framework containing storage

drawers and a table top for experimentation.

Services Required: Electrical and single phase about 220-240 Volts, 50 Hz

Shipping Specification: Volume of 4 metre and gross weight of 400 kilogram

Overall Dimensions: Width at 2 metre, Height at 1.5 metre, Depth at 1 metre

The following equipment is provided:

1. Set of standard sieves and sieve shaker.

2. Storage hopper, together with interchangeable exit orifice and solids

collecting vessel.

3. 0 – 5 kilogram balance with weights.

4. Cylindrical vessel for solids mixing, driven by a variable speed electric

drive and sampling equipment.

5. An alternative shaped mixing vessel to replace the cylinder.

6. Conductivity cell and meter/.metre for concentration measurement of

particular mixture of solids e.g. salt and sand mixtures.

Exclusions

Supply of distilled or deionisid water, approximately 5 L per

experiment

Sand and salt for mixing studies, although any ither materials

may be used.

Stop Clock

An extra charge will be made for non-standard electrical supply

systems (different voltage, frequency, number of phases). The

electrical supply available in the laboratory must be quoted at

the time of ordering.

II. Equipment Schedule

1. Partial Inspection- The arm-field advice notes sent with the equipment

provide a detailed list of the component parts of the equipment as

packed for shipping. This list must be checked against the individually

packed and labelled items immediately on arrival. Any breakage or

omissions must be reported to the company within 3 days of arrival.

2. The main functional items of equipment, with their specification are as

follows, (refer to drawing);

a. Main support frame and bench, on which are mounted the following

items

Variable speed belt-driven motor and pulley.

Two alternative (drum and V-arm) mixers, the drum type

having a protractor arrangement for angle of repose

measurement.

Plexiglas hopper, with 4 alternative orifice and shut-off valve,

plus 2 litres plastic collecting beakers for collecting solids.

b. Separately packed

Automobile sieve shaker with timer

6 British standard sieves of sizes 8, 16, 22,30,44,60.

Lid-and base units for sieve stacking

c. Conductivity cell and meter, for analyzing concentration of

dissolved solids when sampling solids mixing experiment.

d. Solids sampler means hollow tubes to be connected to a vacuum

water ejector, for solids mixing experiment.

e. Single beam balanced, with S weights, for weighing solids

discharged from the hopper.

f. In the 1977 a ball mill, cylindrical steel type with porcelain balls.

This fits into the same urunnious as Plexiglas mixers.

III. Installation and Commissioning

A part from identifying the separate items of equipment and their

experimental use, the only installation work needed is to wire the single

phase supply for the motor the bench, and separately, the automobile sieve

shaker. Care should be taken to observe the equipment wire colour coding:

Brown-Live Blue-Neutral Green-Earth Yellow-

Earth

The sieve shaker is extended not to the used on the bench, but on the

floor of the laboratory as there is considerable variation during operations.

Commissioning involved running the variable speed meter and laminar with

the various for the meter derives urunnion meaning. Calibration of the

conductivity cell with accurately made up solutions of sodium chloride in

distilled or deionised water is also necessary, in order that solids mixing

experimentally with salt and sand can be analyzed for the mixing

experiment. Practice at taking solid samples of a fixed and known bulk

volume with the samples should also be undertaken.

IV. Sieving

Introduction:

A test sieve is an instrument which is used for the measurement of

particle size in its most common form; it consists of a woven wire screen,

with square apertures, rigidly mounted in a shallow cylinder metal frame. For

coarse sieving range down to 4 mm, and round whole sieves down to about 1

mm apertures. The sizes of solid particles from 125mm (5in) down to 38

microns can be measured rapidly and efficiently by means of a test sieve.

Special screens with apertures, smaller than as microns are available, but it

should be appreciated that the liner screen. It is the more easily with certain

types of particulate solids tend to block or blind the openings.

Particle size as measured by test sieving, may be specified simply by

quoting the size of two screens, one through which the particles have

passed, and the other on which they are retained., However, the most

frequent use of test sieving is for measuring the size spread, and the particle

size distribution.

Choice of sieve sizes:

For most size analyses it is usually impracticable, and indeed quite

unnecessary, to use all the available screens in any standard sieve series.

However, for best number of sieves to use a given test can present a

problem. Broadly speaking, it sieves in the mind range of a given series are

employed, not more than about 5 percent on the sample should pass the

finest sieve or be retained on the coarsest. For detailed work, these limits

may be lowered. Once the terminal sieves have been decided upon, the

intermediate screens can be chosen.

For most purposes, alternate sieves (2series) in the range are quite

adequate. Over certain size ranges of particular interest, or for accurate

work, consecutive sieves (2series) may be used. The intermediate sieves

should never be chosen at random. The following four examples indicate

some of the choices that could be made from BS sieves in the range 16-60

mesh:

A 16 18 22 25 30 36 44 52 60

B 16 22 30 44 60

C 16 22 25 30 36 44 60

D 16 18 36 44 60

a. Consecutive sieves which obey the 2 raise to ¼ relationships.

Necessary only for detailed size analysis over the whole range.

b. Alternate sieves which obey the 2 raise to ½ relationships.

Adequate for most purposes. This is the series chosen for this

equipment bench.

c. Bad choice, random selection, difficult to interpret for this

equipment in tabular form or graphically.

The weight of the simple must not be allowed to change during the

test. Damp materials should be dried in an oven if necessary, but care must

be taken not to alter the physical characteristics of the material. If the

material has been heated in an oven it should be cooled in the atmosphere

before the test. Samples of desecrater, and then sieved with the minimum

amount of exposure content during the test, the weights of the charge and

the sieve fractions should be corrected to their dry weights. The

recommended weights are shown in the given table.

Table 1: Quantity of material for test sieving on 200 mm round sieves

Normal width of aperture Volume of material

Primary sizes

(mm)

Supplementar

y sized (mm)

Recommended

volume of test

sample (cm3)

Maximum

volume of

residue

permitted on

the sieve at

the completion

of sieving

(cm3)

22.4 25

20

1800

1600

1400

900

800

700

16

12.2

12.5 1000

800

800

500

400

400

8 10

6.3

600

500

400

300

250

200

5.6

4

2.8

400

350

240

200

150

120

2

1.4

1

200

160

140

100

80

70

Microns

700

500

355

120

100

80

60

50

40

250

180

125

70

60

50

35

30

25

90

63

45

38

40

35

30

25

20

17

15

12

The recommended test sample weight (g) is calculated by multiplying

the volume quantity (cm3) in column 3 by the apparent bulk density (g/cm3)

of the material to be sieved. To avoid overloading the sieve, the test sample

will have to be divided into two or more charges if the quantity of material

remaining on the sieve at the end of the sieve process exceeds the quantity

stated in column 4.

Sieve tests can be carried out by the hand or on machine designed to

impart the necessary shaking, rotating, vibrating or jolting motion to the

material on the screens. In general, the mechanical method of testing has

many advantages over the hand method. Reproducible results are usually

obtained in a much shorter time. Mechanically, with much lower expenditure

of human effort.

Procedure:

The chosen nest of sieves is assembling with the coarsest mesh at the

top the finest at the bottom and the bottom have measured on a receiver

pan. The weighted sample is transferred to the top sieve, and the nest is

shaken with a rotating section and continually tapped by hand of a 10

minutes. When dusty samples are being handled, the top sieve should be

fitted with a lid. The top sieve is then removed from the nest and inverted

over sieve piece of glossy paper. All the material is discharged from it, first

by gently tapping the frame and then by brushing the gauge with a special

brush. The material is then transferred back to the cleaned sieves which is

now material on another receiver pan, and screened to an “end-point” as

follows.

The sieve is shaken for 2 minutes, and the material which passes into

the collector pan during this period is weighed. This procedure is repeated

until the weight of material passing through the sieve in 2 minutes is less

than 0.2 percent of the original test sample weight. Weighing should be

made to ±0.1 percent (analytical balance). Greater accuracy than this is not

generally warranted

The procedure described above relates to the sieving of particles

smaller than 4mm. above the size it is not usual for use nests of sieves fresh

charges are best. Sieved through each sieve turn, for particles larger than

about 25mm the test sieves serves essentially as a gauge. The appropriate

charges may be screened gently and the particles remaining on the sieve are

then checked, one by one, by presenting them in favourable attitudes to the

sieve apertures. Those that do not pass through the apertures are rejected

and become the sieve residue.

Cleaning of test sieves:

Sieves should be used with care, cleaned, regularly and stored in a dry

safe place. It should always be remembered that a sieve is a measuring

instrument and should not be maltreated. Particles should not be forced

through a test sieve. Even the gentle brushing of material through the liner

or finer meshes is undesirable, but this procedure is occasionally unavailable

for certain materials that are otherwise difficult to sieve. If brushing is found

necessary, care should be taken to avoid particle breakdown. In any case,

the brush pressure must never be allowed to distort the mesh. Sieves which

are in constant use should be inspected regularly for mesh defects. A

defective sieve is useless.

After each analysis the sieve should be cleaned and replaced in its

storage container. Mesh of the near-mesh particles, which block the sieve

openings, can usually be removed by inverting the sieve and gently tapping

the frame with a piece of woods. In failing this, the undesirable or nylon

brush. For sieve liner than about 100 mesh a soft hair brush should be used.

A jet of compressed air applied to the back of the gauge may also prove

successful.

Tabulation of data:

There are several ways in which the results of a sieve test can be

tabulated. The 2 mesh convince methods are indicated together in table 2

where a typical size analysis carried out with B. S. sieves is recorded. First

the fractions retained on each of the sieves used in the test can be listed as

percentages of the original less sample weight. This is probably the most

widely used (but not necessarily the best) method or recording sieve test

data. A brief glance at the relevant column of table 2 brings out such facts as

the sieves and the bulk f the material was confined to the 1200-300 microns

range.

In the second and third tubular methods, the cumulative percentage (i.

e. running totals) of oversize and undersize material are listed. Either of

these methods can be used to provide information not readily gathered from

the fractional tables. The percentages of materials larger, or a smaller than a

certain mesh size can be roughly estimated from cumulative tables. For

example, referring to table 2 it can be seen that 70.7 percent of the material

was liner than 850 microns and 88.9 percent was coarser than 300 microns.

It can also be roughly estimated that the quantity that would have passed

through a 5oo microns sieve, is about 37 percent (arithmetic mean of 46.3

and 27.8: the quantities referring to the 600 and 420 microns aperture

respectively).

Table2: Tabulating of Sieve Test Data

BS mesh

number

Sieves

Aperture

(microns)

Weights Percentages

Retained Cumulative

Oversize

Cumulative

Undesirable

10

14

18

25

36

52

72

100

150

-150

1680

1200

830

600

420

300

210

130

105

1.1

5.6

20.6

36.4

18.5

10.8

5.9

3.9

2.7

4.5

1.1

6.7

27.3

53.7

72.2

83.0

88.9

92.8

95.5

98.9

93.3

72.7

46.3

27.8

17.0

11.1

7.2

4.5

Graphical Methods:

The full significance of a sieve test can most readily be assessed when

the data are recorded in graphical form. Trends which are frequently

obscured in mass of figures in a table are easily seen in a graph. The extra-

effort involved in graphical plotting is usually rewarded by the additional

amount of useful information obtained. Graphical techniques are very useful

aids for routine test sieving. It is much easier, for instance, to compare the

data from several tests one graph than it is by trying to compare tables of

figures. Again, by the use of certain graphical techniques, described sieves

used in a test to 2 or 3, with a subsequent and valuable saving in time and

labour.

There are literally dozens of different graphical methods and are used,

or have been suggested for use, in sieve test data analysis. The actual

method to be chosen in any given case will, of course, depend on the

characteristics of the data and the sort of information that is required. Only

few of the more common methods will be discussed here, and these involve

the use of 3 different types of graph paper.

In Ordinary or Arithmetic Paper:

This is this most common graph paper of all. Both sieves are

marked off in a series of equal intervals; either name for this type of paper is

squared, linear and rectilinear co-ordinate.

Semi-Log Paper:

On semi-logarithmic paper and scale is marked off in equal intervals

(arithmetic or linear scale) and the other on a logarithmic scale. On this

latter scale the spacing between 1 and 10, 10 and 100, 100 and 1000 are the

same. These intervals are called “cycles” and usually 2 cycle paper sill

suffice for most tests. However, to cover the entire fine-mesh range 3 cycle

paper would be required.

Log-Log Paper:

In this type of graph paper both scales are marked off

logarithmically. For most sieves test work 2x2 cycle paper is used, but again

if the full fine-mesh size range is to be covered one cycle scale is necessary.

Some of the uses of the above types of graph paper will now be described

briefly. For illustration purpose the same sieve test data (Table 2) are used in

every case. It must be understood, however, that all the methods described

here will not necessary be applicable to any given set of data. Experience

will determine the best graphical method for any particular case.

Fractional Percentage Graphs:

The retained fractional listed in table 2 may be plotted on ordinary

(arithmetic) or semi-log graph paper, either in the form of histograms (bar

charts) or as frequency curves. With any of these methods an immediately

picture 2 and 3. This case, a sharp peak is seen in the 850-600 macrons

region, and the extent of the size spread be clearly visualized.

The vertical columns of the histogram extend between the various

adjacent sieves used in the test. The points on the frequency curve (the

dotted line) may be plotted in between two sieve sizes. For example for the

peak fraction, which passed through an 850 microns sieve and was retained

on a 6oo microns sieve, the mean particle size could be taken as the average

of 850 and 600-725 microns.

The main virtue of the arithmetic plot (Figure 2) is simplicity; no special

graph paper is required. The main advantage is that points in the region of

the finer meshes tend to become congested. For instances, the data in table

2 were obtained from alternate sieves in the B. S. ranges, but it consecutive

sieves had been used, some of this points would have crowded into one

another on the graph.

Congestion is avoided on the semi-logarithmic plot (in the figure 3).

The points in the fine mesh region are spread out and those in the coarse

mesh region closed in, with the result that the points are approximately

equidistant and the columns are approximately of equal widths.

Cumulative Percentage Graphs:

Cumulative percentage of oversize material plotted against aperture

size give graphs of wide applicability. Figure 4 demonstrate the use of both

ordinary and semi-log graphs for this purpose. In both cases it can be seen

that the oversize and undersize curves are actually mirror images of one

another. For most practical purposes, only one these curves need be plotted.

As described above for the fractional percentage graphs, the main

advantage of the semi-log plot is the avoidance of congestion of the points in

the line-mesh region. One of the principal uses of graphs such as those

shown in figures 4a and 45 is for predicting values that were not measured

experimentally, I.e. for interpretation between the recorded points.

For example although a 250 microns aperture sieve was not used in

the test (Table 2) it is easily ascertained from figure 4b that 13.8 per cent of

the sample would have passed through such a screen. Again, suppose the

test data obtained on B.S. sieves had to be translated into values for sieves

14, 25, 45 and 80 mesh of the U.S. (ASTM) Standard series. The

corresponding apertures are 1410, 707, 354 and 177 microns, so it is an

easy matter o read off values on either figures 4a or 4b to give the results 14

(97%), 25 (59%), 45 (21%), 80 (80%).

Another valuable quantity readily obtained from graphs such as those

shown in figure 4 is the median size of the sample. This defines the mid-point

in the size distribution, half the particles are smaller than the median size

and half are larger. The median size, therefore, is read off either graphs

corresponding to 50 percent oversize or undersize. In this case the median

size is 8-10 microns.

See Graph (page 14 and 15)

Approximately useful cumulative plot can be made on log-log graph

paper. Cumulative undersize data are plotted against sieve aperture in figure

5. The over-size curve is of no value; it is not mirror image of the undersize

curve.

See the graph at the last page

The interesting point here is that a log-log cumulative undersize plot

very frequently results in a straight line over a wide size range, particularly

over the smaller sizes. In a figure 5 for examples the straight line extends

over the region 850 to 105 microns. Interpolation is much easier from a

straight line that is from curve, thus, if it is known that data obtained from

the material of routine analysis can be greatly eased. For example for the

case shown in figure 5 only 2 sieves need have been used (e.g. 600 and 150

microns sieves) to check essential features of the size distribution. The

median sizes of the material (640 microns) can be read off at 50percent

undesirable on a log-log plotting the same manner as described for the semi-

log plot.

Precision of Weighing:

The fraction quantities retained on the sieves and the undesirable

should be weighed with a precision of ±0.1 percent of the charge. The area

of these weights should not differ by more than 2 percent from that of the

test sample weight. The losses are to be recorded separately. The fraction

weights should be converted into percentages of the sum total of the fraction

weights, not of the original test sample weight.

V. Bulk Density and Angle of Repose

Experiment:

To determine the bulk density and natural angle of repose of the two

granular material provided.

The bulk density is measured by pouring the material into a granulated

measuring cylinder and then weighing the given material. The weight at a

given volume thus gave the density (bulk). Two readings for each material

should be taken and average values calculated. The angle of repose is

measured in the axially mounted cylinder, which can be rotated at 90

degree. The actual angle rotation being indicated by a protractor granular

material is introduced into the container metal. It was approximately half

bulk. The 3 surface is made level by shaking the container and the cylinder is

rotated. The particles must begin to slide and the angle at which bulk being

measure. The container is then rotated in the opposite direction until the 3

surface appear horizontal. From the reading in the position, the angle

between the horizontal and justified sharpen surface can be found. This is

the natural angle of repose. This procedure is repeated several times in

order to obtain average values for the two materials. As it is different to as

certain accurately when the surface is horizontal, a further set of runs should

be made in which the angle is altered until the particles just begin to slide,

and then the cylinder is rotated in the opposite direction until the particles

just begin to slip the other way. Half of the angle through which the cylinder

rotated is taken as the angle of repose.

VI. Flow from a Hopper

In order to understand the theory of flow of solids through an orifice, it

is necessary to examine the grain movement paths. The particles tend to roll

in layers over slower moving layers underneath. This is illustrated in figure 6.

Particles on the surface over B: B in turn is sliding over k which remains

stationary. The angle at which the layers B and E meet its approximately

equal to the angle of repose. Particles from regions A and B move into the

centre region C because the layer angles are greater than the angle of

repose. From the region C the particles move rapidly downwards and inwards

through the region D and then through the orifice.

In a narrow container the wall takes place of the region E and in the

upper part paling. The central zone C of faster moving material occupies,

most of the tube, with the result that the free surface of the material

becomes a large cone (inverted).

Most workers investigating this subject have related the discharge rate to

the orifice diameter. Linear plots were obtained for graphs of log Q and log D

usually with slope of 3 (i.e. Q=kD3).

The most recent work published is that of Crown and Richards who

round that their results could be represented by Q= 2.24 D2.5 ø where Q is

measured in ton/hr, D in inches, and ø is the dimensionless group V/(GH½).

Where (V=Q/2A); Q being known as flow rate.

H is known as the perimetral diameter, which equalled the area of the

aperture times four over the perimeter in cm.

It is the purpose of this experiment to attempt to correlate data for

flow through orifice in a similar way to the above expressions, and also to

determine whether or not the head of material over the orifice has any effect

on the flow rate.

Experimental:

The apparatus consists of a vertical, cylindrical hopper and removable

orifice plate at the base.

A movable plate is fitted under the orifice in order to stop and start the

flow of material. The vessel should be about 2/3 fitted with fine grain sand,

and shaken until the surface is plane. The initial height and the material

allowed is flow into a collecting tray for a measured period of time. The flow

is then stopped and the collected material weighed. The surface of the

material in the vessel is re-showed, and its height repeated until no more

material can be collected.

The same orifice is then used again and the rates of efflux for

convenient periods of the time again measured as above. However, in this

experiment no attempt is made to level the surface from its inverted cone

shape( caused by the flow of material), the measured height being that of

base of the cone above the orifice. Again, no orifice or head on efflux rate

should be detected.

In order to investigate the effect of orifice diameter on the efflux rate,

alternative orifice is used separately, and an each series the same line

material should be used. Two runs for any one orifice can be carried out over

a convenient period of time (down to collect about 800g), and average efflux

rates calculated. These should then be plotted against orifice diameter on a

log-log basis.

VII. Mixing of Solids Particles

In the mixing of solids particles, 3 mechanisms may be involved:

1. Convective mixing - in which groups of particles are moved from alone

position to another.

2. Diffusion mixing – where the particles are distributed over a freshly

developed interface.

3. Shear mixing – where slipping planes are formed.

These three mechanisms will occur to varying extents in different kinds

of mixers and with different kinds of particles. A trough mixer with a ribbon

spiral will give almost pure convective mixing, but a simple barrel mixer will

give mainly a form of diffusion mixing.

Degree of Mixing:

It is difficult to express the degree of mixing, but any index should be

related to the properties of the required ix, should be say to measured, and

should be suitable for a variety of different mixers. When dealing with solid

particles, the statistical variation in composition among samples withdrawn

at any time from a mixing commonly used as measure of the degree of

mixing. The standard deviation is square root of the mean of the angles of

the individual deviation on the variants as generally used. A particulate

material cannot obtain the perfect mixing that is possible with two fluids. For

the best that can be obtained will be at a degree of randomness on which

two similar particles may well be side by side. No amount of mixing will lend

to the formation of a uniform modal but only to a condition where there is an

overall uniformity but not point uniformity. For a completely random mix of

uniform particles distinguishable, say only by colour, it has shown that;

Sr2 = p(1-p)/n

Where sr2 is the variance for the mixture, p is the overall proportion of

particles in each sample.

This at once brings out the importance of the size of the sample in

radiation to the size of the particles. In a completely unmixed system

(indicated by suffix o) it can be shown that:

So2=p(1-p)

Which is independent of the number of particles? Only a definite

number of samples. In practice be taken from a mixture, and hence will itself

be subject to random errors.

When a material is partly mixed, then the degree of mixing can be

represented by some term M, and several methods have been suggested for

expressing M in terms of measurable quantities. It is obtained from

examination or a large number of samples, and then we can define M.

M=So-Sr/(So x Sr)

Where So is the value of s for the unmixed material. This form of

expression is useful in that M = 0 for an unmixed material and L for a

completely randomized material (L=S-Sr). If we use s2 instead of s, then we

can rearrange above expression to give;

M=S2o-S2/(S2o x S2r)

L-M= S2o-S2/(S2o x S2r)

For diffusive mixing, M will be independent of ample size provided the

sample is small. For convective mixing has suggested that we have groups of

particles randomly distributed, each group behaving as a unit containing a

particle. As mixing proceeds Ng becomes smaller.

The number of groups will then be N/Ng, where n is the number of

particles in each samples. Applying the equation above;

S2=p(1-p)/(N/Ng)=NgxSr2

And this gives;

L-M=(Ng)(Sr2)-Sr2/(NSr2-Sr2)=Ng-1/N-1

Thus, with congestive mixing, L-M will depend on the sample size. The

rate of mixing expressions for the rate of mixing can be developed for any on

of the possible mechanism since mixing involves obtaining an equilibrium

condition of uniform randomness, we may expect the relation between them

to be a general form;

M=L-e-eL

Where e is some constant depending on the nature of the particles and

the physical action of the mixer. The process of mixing consists of making

some of A enter the space occupied by B, and some B enter the lower

section originally filled by A. We may consider this as the diffusion of A

across the initial boundary into B, and of B into A. We can imagine his

process to continue till there is a maximum degree of dispersion, and a

maximum interfacial area between the two materials. This type of process is

somewhat a kind to diffusion, and we may tentatively apply the relationship

given by Fick’s Law in the following way.

Let A be the area of the interface per unit volume of the mix, and Am be the

maximum interfacial surface per unit volume that can be obtained.

Then dA/dT= c(Am-A)

And A=Am(1-e-et)

Suppose that, after any time t, a number of samples are removed from

the mix, and are examined to see how many contains both components. If a

sample contains both components, it will contain an element of the

interfacial surface. If Y is the fraction of the samples containing the two

materials in approximately the proportion in the whole mix, we can then

write;

Y=1- e-et

COULSON AND MAITRA have examined the mixing of the number of

pairs in the materials in a sample drum mixer, and have expressed their

results in the form of a plot of

In 100/x vs n, where X is the percentage of the samples that are

mixed, i.e. Y=1-x/100. They are able to show that the constant e

depends on.

(1) The total volume of the material.

(2) The inclination of a drum.

(3) The speed of rotation of the drum.

Whilst the precise values of e are only of value for the particular mixer

under examination. They do bring out the effect of these variables. Thus, fig.

shows the effect of speed rotation, and the best results are obtained when

the mixture is just not taken round by centrifugal action. I fine particles are

put in at the bottom and coarse of the top, then on rotation no mixing

occurs, the coarse remaining on top. If the coarse particles are put at the

bottom and the fine on top then on rotation mixing occurs to an appreciable

extent but on further rotation y, and the coarse particles settle out on the

top. This is shown in these, which shows maximum degrees of among the

same size but single down to the vessel migrate to the bottom and the

lighter to the top. Thus, the lighter particles are inverted of the drum give

improved to a defining value after which the measure particles with actual to

the bottom.

VIII. Non-Standard Electrical Supplies

Where equipment has been supplied for operation from a non-

standard, single phase supply (other than 220/240 volts, 50Hz) a

transformer of appropriate current rating will have been fitted. In the case of

small, bench u units this may be supplied as a separate item.

The transformer supplied is of the “Auto” type with eight (8)

alternative voltage tapping and will have been connected to the equipment

in accordance with the frequency specified on the arm field technical

Education Company acceptance of order. The supply cable to the

transformer will have been installed and the equipment tested in accordance

with the voltage specified on the Arm field technical education Company

acceptance of order.

The Voltage and Frequency of the laboratory supply should be checked

for compatibility against the equipment as supplied. If any doubt or

discrepancy exists the top cover of the transformer should be removed

(retained by four (4) screws around the periphery) and the connections

confirmed. Input and output connections to the transformer terminate on two

(2) independent terminal blocks, inside the transformer case, with

identification legends. Connections to those terminal blocks should be as

follows:

Electrical Input Supply Cable:

Irrespective of 50 or 60 Hz supply, the following connections should be

made to the INPUT terminal blocks:

Earth Wire (Green/Yellow) : To E-A Input Connector

Neutral Wire : To Common Input Connector

Haze Wire : To Relevant Input Voltage

Connection to match laboratory

supply

(E.g. 100 volts)

Equipment Instrumentation Supply Cable:

Irrespective of 50 or 60 Hz supply, the following connections should be made

to the OUTPUT terminal blocks and should not require modification:

Earth Wire (Green/Yellow) : To E- output connection

Neutral Wire (Blue) : To COMMON output connection

Live Wire (Brown) : INST. Output connection

Pump/Motor Supply Cable:

For 50 Hz operation only, the following connections should be made to the

OUTPUT terminal blocks:

Earth Wire (Green/Yellow) : To E- Output connection

Neutral Wire (Blue) : To COMMON output connection

Live Wire (Brown) : 60 Hz PUMP/MOTOR connection

NOTE:

Certain pumps require the impeller to be reduced in diameter for

satisfactory operation at 60 Hz. Where equipment has been supplied for

operations 60 Hz, this modification will have been incorporated.

Where an operation at the alternative frequency is necessary, Arm

field Technical education Company should be contracted for advice relating

to possible impeller modification.

IX. Graphical Representation