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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