A study on the mixing of flour in a motionless Sulzer (Koch) mixer using a radioactive tracer

i3

Powder Technology. 13 (1976) 73 - 83 @ Elsevier Sequoia S-A., Lausanne - Printed in the Netherlands

A Study on the Mixing of Flour in a Motionless F. S. LAI*

and L. T. FAN

Deporimenf

of Chemical

(Received Cctober

Engineering,

21.1971:

hFansas State University.

This work was concerned with the evaluation of the motionless Sulzer (Koch) mixer for radial mixing of flour. A radioactive tracer technique was employed. The tracer employed, “6Mn, was created by mainly radioisotope neutron activation with a neutron flux of 1.44 X lo’* n/cm* set_ The method has a high degree of accuracy and the advantage that no physical differences exist between the bulk and tracer materials_ The concentration distribution in the radial direction was measured, and the resulting degrees of mixedness of the mixture after passing through the miver for 1, 2, 3, 5 and 10 passes were determined. The degrees of mixedness in the radial direction increased with the number of passes. The experimental results were compared to the same mixture passing through an empty column without mixing elements inserted_ The comparison indicated that the mixing elements enhanced the mixing process in a predictable way. Finally, a mechanistic model was developed and verified by the experimental results. 1. INTRODUCTION

The technique of using radioactive tracers is well known in determining the mixing and transport characteristics of particulate solids [l - 53 _ The preferred method is radioactive isotopic labeling, which is implemented by neutron activation of a portion of the material itself for use as a tracer. The neutron-activated tracer technique is a method for qualitatively and quantitatively determining elemental composition by means of nuclear transmutations. The method begins with the exposure of tracers to a neutron flux, thus creating radioisotopes from elements present in the tracer. *Present address: U.S. Grain Marketing USDA

MLxer Using a FCadioactive Tracer

Manhattan.

h-an. 66506

(U_S.A.)

in revised form hlay 15, 1975)

SUhIhlARY

Center, ARS,

Sulzer (Koch)

Manhattan,

Research U.S.A.

Kansas 66502,

Isotopes formed in this manner are characteristic, in numbers and types, of the compositions of the original tracer and the irradiated conditions_ Assuming a uniform radiation source, and a uniform detection system, the only variable in radioisotope production for elemental analysis is concentration_ This method is possible when the material being mixed contains certain elements which can be readily activated to produce radioisotopes with suitable decay schemes and half-lives. While estensive investigation has been carried out in motionless mixers on the mixing of free-flowing solid particles [S] , viscous liquids [ 73 , and gases [S] , very little has been done in these mixers on the mixing of non-free-flowing powders. Flour, which is a non-free-flowing powder, can behave as a solid, liquid, or gas. When at rest, it resembles a solid; when aerated, a liquid; and when SUSpended, a gas. It is common knowledge that the mixing of flour is a frequently employed operation in food processing and cooking. For example, mixing of flour is a necessary step in production of the recently developed “composite flour”, which is a flour mixture designed for the production of bread, biscuits, and pasta t9] Most studies on the mixing of particulate solids in motionless mixers have concentrated on axial mixing [5,6, lo], except that by Chen ef al. [ 111, who considered radial miuing in a motionless Kenics mixer_ In n,ost mixing operations in use today, radial mixing appears to be more efficient than axial mixing in attaining a final homogeneous mixture. This is because the distance particles must travel in the radial direction is much shorter than that in the axial direction. The material to be mixed can be properly loaded in a feeder such that radial mixing can be _ _ exploited in continuous munng operation. Complete mixing can usually be achieved through continuous radial mixing in the

TABLE

1

Typical

mineral composition

8. THEORETICAL of flour, dry basis [ 13 1 p-p-m_ 0.105 0.126 O_O% 0.01s 9-s 7.6

10.6 6.5 I.7 0.23 0.003

steady state_ Hence, continuous mixing is thought to be the process more likely to be used in the future [ 12]_ The tracer technique was based on the activation of manganese, which is present in the flour in a very small amount. It is of general interest, but out of the scope of this study, to obtain information on the measurement errors of the neutron activation analysis technique_ Thus no esperiment was performed with the specific purpose of estimating the measurement errors. The main objective of this work was to study experimentally radial mhing of powder, or more specifically, flour, in -ihe Sulzer (or Koch) motionless mixer by measuring the radial dispersion of a radioactive tracer_ -4 portion of flour was irradiated in the KSI? nuclear reactor_ Since flour contains traces of manganese, which possesses favorable decay data (846 Kev gamma photons; half-life 2.58 hours), s6Mn was used as the tracer in this study- The content of manganese and other minerals in the flour are given in Table 2 [ 133 . When a naturally contained element is used as the tracer, the surface and physical properties of the flour will remain unchanged by its addition. A definite relation esists between the absorbed dose during activation and the quantity of the tracer produced. The absorbed dose in this study was too low to decompose the polysaccharides in the flour- Gamma-ray spectroscopy was used in sampling and assaying the final mixture_ Other objectives of this work were to establish a mathematical model of the radial dispersion process in the Sulzer (Koch) mixer and to examine the usefulness of the radioactive tracer technique as a sampling method.

In the mising of solid particles, the known mechanisms of the process are diffusion, convection and shear [ 14]_ Diffusion implies that particles are undergoing random motions, i.e. two or more components diffuse into one another. Convection is the bulk transportation of groups of particles. The shear mechanism is identified as the setting-up of slipping planes within the mass [14] - Note that it may be possible to reduce the number of different mechanisms of mixing to only the first two,

because shear forces are actually partial causes of both diffusive and convective mising-

_---

--

Fig_ l_ Schematic

diagram of the flow system.

Fig_ 2_ Diagrammatic representation (Koch) motionless mixer.

of the Sulzer

In a motionless mixer with radial load as shown in Fig. 1, the observed dispersion is a result of the particles acquiring a component of motion in the radial direction_ The

predominant mechanism of mixing in the motionless mixer is convection. J?igure 2 presents a schematic drawing of the geometric

75

Fig. 3. Operating principle of the Sulzer (Koch) motionless

mixer.

configuration

of a two-element

mixing unit.

This particular geometric arrangement results in a multitude of motions being imposed on the flowing stream-. The powder is split into several streams in the open, intersecting channels of the mixing element. At each intersection a partial quantity is sheared off into the crossing channel. Any inhomogeneity is spread two-dimensionally in the first mixing element and three-dimensionally in the following one turned 90 O_Because the powder is positively guided, the mixing process is independent of the flow pattern of the mixture (Fig. 3). The system under consideration is depicted in Fig. 4. The system consisted of a feeder, a mixer, and a collector_ The tracer loaded in the feeder is swept downstream (along the zdirection) and is dispersed radially in the mixer. If the motion of particles in the mixer is assumed to be sufficiently random, Fick’s second law of diffusion can be adoPted, by analogy, to describe the mixing process. By a mass balance on the tracer over the cylindrical ring shown in Fig. 1, we obtain the following Partial differential equations if the dispersion coefficient E is assumed to ‘be constant [ 151:

1 Fig. 1. Schematic experiments.

diagram of loading and miring

solved subject to the following boundary conditions: I.C.

t = 0,

l3.C r = r,

c = 1 c=o E>=O

The solution

OdrGr, ri d r =Grz

is [ 151

where (Y,, is the root of the first-order function:

(2) This partial differential equation is to be

Equation

(3) (4)

tko

Bessel (6)

51 (a,)=0 If we further assume that the concentration gradient in the z-direction is negligible as compared to that in the r-direction, eqn. (1) becomes

initial and

(5) can be rewritten

ln the form:

is the mean concentration in the mixture_ The variance of samples taken along the radial direction from a mixture blended by the motionless mixer is found by integrating the square of the deviation from the mean along the radial direction of the cylindrical container of the misture; thus,

or

For a long mixing time, the infinite series in eqn. (9) converges rapidly and can be tnmcated after the fn-st term. Thus, for large t:

Equation (IO) shows a linear relationship between the logarithm of the sample variance and the mising time. For the initial period, the higher terms in eqn. (9) must be retained_

3. ESPERI>IENTXL 3-l

Equipment and apparatus (1) 1lising system. The mixing system (Fig. 4) consisted of a feeder, two Sulzer motionless mixing eiements, a collector, and a vibrator. The designs of the feeder and the collector were identical so that they could be used interchangeably. The feeder and the collector were 4-m i-d. plexiglass pipes with lengths of ‘7% in_ in the axial direction. One end of the cylindrical pipe was sealed with plexiglass. The miser contained two Sulzer (Koch) motionless m;xing elements which were of the AY type_ The mixing elements had a layer height of % in. and a hydraulic diameter of 0.68 in. The elements were constructed fiorn 316 stainless steel.

[x~;eHU] Fig_ 5. -4 typicsi system [ 17]_

neutron

activation

analysis

detector

The miser was a plexiglass tube with an inside diameter of 4 in_ and a length of 4 in. and contained two mixing elements alternately mounted inside at right-angles to each other. Friction between the pipe wall and the edges of the mixing elements prevented slipping(2) Facilities for neutron activation analysis. Neutrons for the activation of the flour were supplied by the TRIGA MARK II nuclear reactor at Kansas State University_ The maximum pulse power allowed for this reactor under its federal license is 250 megawatts_ Maximum -teady-state operation results in 250 kilowatts of continuous power with a neutron flux of lOi neutrons/cm’ sec. The distribution of the neutron-activated flour was measured by the spectroscopy system shown in Fig. 5 [l’?] _ The detector used was an NaI(T1) scintillation crystal coupled to a photocathode powered by a high voltage source. The pulses from the photocathode were then amplified by a photomultiplier tube, preamplifier, and amplifier. A multichannel analyzer was then used to sort the pulses into several hundred channels to provide a complete spectrum for the gamma radiation originating from the sample. A standard ssMn sample was employed to identify the true peak of the gamma ray radiation_ The quantity of the tracer in a flour sample was determined by comparing the gamma ray activity to that of the true peak generated from the standard. Information stored ;a the memory of the multichannel analyzer was displayed on an oscilloscope, printed out in digital form by a paper tape printer, and stored on magnetic tapes for later computational analysis. A chamber was constructed on lead bricks (2 X 4 X 8 in-) to shield the detector from background radiation. and the 3 X 3 in. cylindrical scintillation detector was then placed inside the chamber.

77

Nuclear

Reoctcw

n

_z

Fig_ 6. Schematic

diagram of the overall experimental

system and operations. 3.2 Procedure end sampling method Figure 6 is a schematic representation of the experimental system and procedure. The experimental procedure consisted of four basic operations, namely, preparation of the tracer, mixing operation, preparation of samples, and measurement of sample radioactivities. Approximately 600 g of flour were used in each experiment. A portion of flour (14-O g) was irradiated in the nuclear reactor The power used was 200 kW with a flux of 1.44 X 1Or2 neutrons/cm’ set for a period of 2 minutes. The radiation time required was estimated based on the activity required, the neutron flux, and the amount of manganese in the flour. The whole mixing system was fiit placed in a hood for safety. The premixing section was then loaded with flour. In the premixing section, an empty cylindrical hole of 12 mm was created along the axis of the feeder and then filled with the irradiated tracer flour. The motionless mixer was placed on top of the premix section. A con’tainer which was identical to the premix section was then placed on top of the mixer. The mixer was made airtight with gaskets_ The mixing system was then

rotated 180” and placed on a vibrator. With the aid of gravitational and vibrational forces, the flour flowed through the mixer. This constituted one pass. Experiments with 1,2, 3, 5 and 10 passes were conducted. After each experiment the mixture was divided into five layers in the axial direction, each with a thickness of one inch. Nine samples were taken in each layer (Fig. 6). Quantitative determination of the radiation of the background, the blank value of the empty sample container, and each of the mised flour sampies completed the measurements necessary for analysis. Quantitative measurements were carried out by comparison of the photopeak area of the induced activity of s6Mn, in the sample, with that of the corresponding activated and counted standard sample at the same decaying time. The net area of a photopeak was obtained by adding up the counts in all the channels that comprised the peak, then subtracting the trapezoidal area (linear baselines) of the underlying Compton continuum. The counts to be subtracted are determined by averaging the counts in the channel put to the left of the photopeak and those in the channel put to the right of the peak and multiplying by the number of channels in the peak. The counting rates thus obtained, for samples, were then all corrected to the same decaying time, using the half-life of the 56Mn.

3.3

Treatment ofdata The percentage of tracer in each sample was calculated from the following equation: % tracer =

(11)

where S R b b, B CF W

= = = =

number of counts of the sample number of counts of the reference number of counts of the background number of counts of the background for the reference count = number of counts of the blank = calibration factor = sample weight

The background and the blank were ignored in this experiment, since they were very small fractions of the sample counts. Thus, the above equation was simplified to

iS

S

CF

% tracer = -

-

IV

R

(12)

Since only the relative magnitude of mising at each pass was of interest, the above percentages could be normalized_ The parcentagt of the tracer in each sample was considered as the average concentration for that sampie. The standard deviations or the variances of samples are the most frequently employed descriptions for the purpose of analysis_ In this work. the standard deviation was used_ The standard deviation from a mixture was computed by the equation: r s=

I

c i= 1

(x,

-

n-l

1)”

(13)

where -ri = average concentration of the tracer in a sample -?? = overall concentration of the tracer in the mixture R = number of samples taken from the mixture. In the present work, the degree of mixedness was defined in terms of the standard deviation as JZ = 1 -

” (14) s0 where s is the standard deviation of the total number of sampies taken from the mixture as defined by eqn. (13), and so is the initial standard deviation before mixing. For a mixture of two components, so is given by Lacey [is] as where -Y is the overall composition of the tracer in the mixture_ Xccording to Donald and Roseman 1191, only an index based on the variance can be theoretically independent of sample size; thus only this type of index gives rise to a consistently accurate value over the whole course of mixing- Furthermore. such an indes is more satisfactory statistically than indices based on other statisticaI terms, since the variance has additive properties. However, the definition of the degree of mixedness based on the variance approaches unity more rapidly than that based on the standard deviation- Therefore ‘&e latter definition is more sensitive than the former when the mixture is near the random state.

The mixing action number (MAN) can be defined as the product of the number of Sulzer mixing elements in the mixer and the number of passes of the misture through the mixer. For example, for a miser with two mixing elements and five passes, the MAN is equal to 10 (2 eiements X 5 passes = 10 IMAN)_ In this work, it was assumed that all the geometric characteristics of the mising elements were the same. The concentration distribution can be given as a function of the mixing action number, instead of the number of passes. This means that the same degree of mixedness can be reached with any combination of the number of passes and the number of mixing eIements inside the miser.

4. RESULTS

AND

DISCUSSION

Two sets of esperimental results were obtained_ One set was obtained by passing the mixture 1, 2, 3, 5 and 10 times through the mker, and the other by passing the mixture the same number of times through the empty column. Table 2 contains the esperimental conditions and normalized relative radiated flour concentrations in the mixtures for the former. Table 3 contains the same information for the latter. 4. I Concentration toe fficien t

distribution

and dispersion

Concentration distributions are functions of the number of mixing elements inside the mixer, the total number of passes through the miuer, the physical properties of the materiaI being mixed, and the mode of loading and feeding- In this study. the number of mixing elements, the mode of Ioadiig and feeding, and the material were fixed; hence the most important factor was the number of passes. Thus the number of passes was used as a parameter in the radial concentration distributions. Such concentration distributions provided detailed descriptions of the progress of mixing or segregation as a function of the number of passes through the mixer. Radial concentration distributions obtained from the experiments with mixing elements are shown in Fig. ‘7. Results using the empty column (without mixing elements) are presented in Fig. 8. As expected, the SuIzer mixing erements enhanced uniform distribu-

79

TABLE2 Normalized relative rediatedflour

concentration

distribution afterpassingthroughtwo Sulzermixing elements

No.of passes

Layer

1

2

3

4

5

6

7

8

9

1

1 2 3 1 5

0.048 0.055

0.0'78

0.095

0.052

0.135

0.096 0.092

0.036 0.032 0.063

0.263 0.136

0.011 0.049 0.041 0.061

0.471 0.308 0.301 0.253 0.22'7

0.054

0.136 0.092 0.064 0.123

0.100 0.141 0.101

0.056 0.106 0.062 0.053 0.13'7

0.051 0.063 0.053 0.055 O.OSS

I 2 3 4 5

0.019 0.059 0.131 0.092 0.055

0.080 0.018 0.16'7 0.173 0.21-l

0.092 0.172 0.094 0.096 0.061

0.039 0.106 0.041 0.051 0.078

0.186 0.116 0.231 0.255 0.195

0.059 0.089

0.188 0.138 0.092 0.075 0.080

0.13'7 0.17i 0.101 0.115 0.078

0.1'70 0.206 0.061 0.066 0.089

1 2 3 4 5

0.068 0.042 0.0'70

0.106 0.139 0.114 0.093 0.899

0.145 0.068

0.117 0.139 0.1'7'7 0.162

0.128

0.145 0.196 0.180 0.152 0.091

0.112 o.os1

0.0'72

0.089 0.155 0.162 0.159 0.169

0.116 0.101 0.064

0.064 0.052

0.100 o-077 0.110 o-151 0.119

5

I 2 3 4 5

0.119 0.140 o-111 0.092 0.099

0.111 0.133 O-138 0.112 0.094

0.096 0.118 O-106 0.118 0.107

0.129 0.141 0.138 0.125 0.139

0.107 0.085 0.083 0.101 0.116

0.142 0.105 0.136 0.110 0.116

0.110 0.095 0.07-I 0.108 0.105

10

1 2 3 4 5

0.091 0.091 0.120 O-120 0.102

0.112 0.112 0.115 O-101 0.127

0.11-l 0.116 0.115 o-124 0.116

0.111 0.101 0.101 0.110 0.111

0.121 0.123 0.117 0.099 0.117

0.119

0.092

0.10'7

0.097

0.09'7

0.112 0.121 0.106

2

3

0.23'7

tion of the tracer in the radial direction. The concentration distribution was less uniform and more erratic and scattered when the mixing elements were not used under equivalent conditions. However, wXh or without mixing elements, the radial concentration distribution essentially became uniform after five or more passes. The vibration provided in the experiments might have contributed partially to the mixing effect. The system under consideration was an ensemble of particles, which was contained in a collector or container. The state of mixing or mixing characteristics of the system were examined through the observations of relative displacement of the particles in the ensemble. Thus motionless mixing elements were considered as mechanical devices which provide the agitation needed to induce such relative displacement when the ensemble of particles was passed through the mixer. In other words, the mixing system under consideration is regarded as being of the batch type. When the theoretical model is applied to

0_05i

0.096 0.092 0.096 0.068 0.106 0.116 0-11s 0.133 0.114 0.097

0.118

0.1'72 0.092 0.088 0.12-1 0.128 0.10s 0.123 0.1-17 0.106 0.110 0.108

0.064 0.065 0.099 0.061

O.Oi7 0.077

0.150

O-OS9

0.118 0.09'7

0.015 0.081

0.072

a mixer operated in a batch process, the time of mixing can be considered to be proportional to an integral number of passes in the case of small end effects. Hence, t=aN and the concentration distribution, eqn. (5), can be rewritten as a function of the radial position and number of passes, Le. c(r,N)=~+Z

2 0

x

r2

where E’=arE Values of the dispersion coefficient, E’, were estimated by fitting [ZO] this expression to the experimental data. The calculations were based on the 45 measurements made in each

TABLE3 Normalized No. of

tetntive mdiated

ffour concentration

distribution

after pL2sing through an empty

c4umu

Layer

1

2

3

.I

5

G

7

a

9

1 2 3 4 5

0.319 0.051 0.031 0.043 0.053

0.023 0.063 0.019 0.013 o-025

0.020 0.137 O-d25 O-097 0.179

0.023 a030 o-012 0.018 O-036

0.025 0.294 0.037 0.532 OA84

0.087 0.261 0.018 0.243 0.092

0.044 0.039 O-417 0.021 0.039

0.041 0.053 0.028 0.014 0.056

0.419 0073 0:013 0.01s 0.028

1

0.063 0.025 0.00'1 0.053 o-O-t3

0.056 0053 Ok24 0.069 0.052

0.190 0.012 0.006 0.059 0.033

0.060 0.061 0.043 0.036 0.103

0.123 0.648 0011 0.317 0.249

0.091

0.128

0.085

3 4 5

0.172 0_074 0.035 0.116 0.029

0.031 0.016 0.05-t 0.091

0.026 0.015 0.076 0.255

0.066 0.093 O-201 O.lf5

1 2 3 -z 5

0.106 0.123 0.089 0.021 0.053

0.09s 0.113 0.03s 0.100 0.341

0.106 0.253 O_lS-i 0.397 0.020

0.092 O-126 O.&t8 0.164 0_394

0.105 0.114 0.012 0.048 0.040

O-333 0.036 0.047 0.057 0.034

0.147 0.144 0.014 0.093 O_lOO

0.116 0.012 0.02s 0.052 O.O-Il

O-100 0.079 0.13s 0.067 O.Oi5

5

I 2 3 4 5

0.120 0.107 0.102 0.095 0.095

O-124 0.119 0.129 0.150 0.123

0.106 0.111 0.111 0.095 0.112

0.116 0.132 0.096 0.116 0.131

O.ll7 0.121 0.126 O-117 O-120

0.100 0.101 0.117 0.114 0.111

0.106 0.097 0.114 0.097 Q-102

o.o-l5 0.101 0.101 0.120 0.09s

o.os3 O-103 0.101 0.091 0.109

10

1 2 3 -1 5

0. '09 0. '3 0. -20 0:)52 0.103

0.110 O_lO-i 0.113 0.132 O.lli

0.117 0.113 O.lli O-108 O-128

0.108 0.092 0.108 0.115 0.113

0.107 0.107 0.129 0.133 0.111

0.126 0.113 0.115 0.117 0.105

0.116 0.122 0.10-i 0.117 0.096

0.104 0.111 0.108 0.123 0.125

0.104 0.115 O-096 0.103 0.103

*asSCG 1

2

experiment_ The dispersion coefficients so obtained for each series of experiments are presented in TabIe 4. It can be seen that the dispersion coefficients for,the cases with mixing elements were consistently larger than the cases without mixing elements. The goodness of fit of the modeI with the concentration distribution data for the former is better than with that for the latter, as indicated by the standard deviation of the fit (also see Figs. ‘7 and 8). The data obtained indicated that the concentration profile in the mixture obfvained after passing through the empty column without mixing elements inserted fluctuated appreciabiy. It is very unlikely that the proposed model holds for this case_ We can probably assume that while the convective mixing mechanism still predominates in the empty column, the intensity is much smalIer than that of convective mixing mechanisms in the column with mixing elements inserted- If it were assumed *Ihatthe diffusive mechanism predominates in the empm column, the degree of mixedness of the empty cohmm mixture

would approach that from the column with m%xing elements inserted much more slowly than one can expect from the experimental data, Apparently the major mixing mechanism of the Sulzer (Koch) motionless mixer is convection, as mentioned previously. In the present. series of experiments, however, the numbers of splittings and recombinations of the particle streams through the mixer were very large and the size of each stream was smaII; these spMtings and recombinations gave rise to extensive and intensive interactions among the particles and between the particles and the wall_ In addition, irreguIar motion was imparted to the particles by the vibration. Since the combination of ali these phenomena shouid lead to the apparent diffusive mixing, a single parameter, the dispersion coefficient, was employed to characterize the radial mixing as expressed by eqn- (1). The theoretical degree of mixedness as given by eqn. (IO) is, therefore, applicable to the data (Table 2) obtained from the mixing of flour through the moticnless

Fig- 7. Nonnaiized radiated flour radial concentration distribution with motionkss mixer_

Fig. S. _Normalized radiated flour concentration distribution without motionless miser.

mixer. The results show that the proposed mechanistic model is in good agreement with the experimental data (Fig. 9). One objection to using the diffusion model in describing the mixing process is that the variance approaches zero as time approaches

usually defined as the dispersion coefficient rather than the diffusivity, D.

infinity,

Le.

(T~-+Oasf+=J

On the other hand, it is well known that any real mixture always has a ,C;*f& and limiting variance in the completely mixed state. This discrepancy is due to the fact that the diffusion equation assumes contiiuily of mass in the system. This assumption is only a gross approximation for a Farticulate matter involving mixing ]14,21] _ Lacey Cl43 pointed out that the apparent exponential relationship of the experimental data does not prove that diffusion is the controhing mechanism. Verification of the actual mechanism requires further study. For example, a detailed comparison of predicted and observed concentration profiles is needed- This is one reason why E is

4.2 Degree of mixedness versus number of passes and degree of mkedness versus mixing action number The degree of mixedness of the flour n%sture was determined from the standard deviation by eqn. (13). From eqns. (9) and (lo), the theoretical predictions of the degree of mixedness against the number of passes were also plotted in the figure. A plot of the degree of mixedness verws the number of passes provides an indication of the progress of mixing. Plots of the degree of mixedness uelsus the number of passes are shown in Fig. 9. Similar plots for the empty column are also shown in Fig. 9_ Such a figure can be used as a measure of the mixing efficiency, since it indicates the relative dispersion of irradiated flour in each case. The plots show that the rate of mixing was very rapid initially and decreased as the number of passes increased. After a sufficient number of passes

TABLE

A plot of the degree of mixedness against the mixing action number (MAN) provides a test of the assumption of negligible end effects. If the end effects are small, a good correlation between the degree of mixedness and the mixing action rumber can be expected_ The degree of mixedness is plotted against the mixing action number in Fig. 10, which indicates a good correlation. The plot also provides the design information. For a given desired degree of mixedness, the operation can be accomplished with the required mixing action number_ Any combination of passes and number of mixing elements can accomplish the desired mixing.

4

Dispersion coefficients

E' OF the theoretical

Dimensionless dispersion coefficients. E'h'ir$

Number of passes

model

Standard deviation

With mixing elements 1 2 3 5 LO

0.0925 0.149s 0.195-z 0.3130 0.4 169

Without

3.68 x 10-3 1.92 x 1o-3 829 X lo-’ is1 x IO+ 5.52 X 1O-4

mixing elements

I 2 3 5 10

x IO--’ x 10-3 x 10-3 '7.06X lo+ 6.19 X 1 o+

1.26 9.01 1.38

0.010 0.9953 0.9903 O_%-iS 0.372

CONCLUSION

I .t

___-_-2

__-i

*r I

g -,3<_i

/’

hl

i

_’

, _I’ ,=

I[

3

,(, c

O--u,-...

r[ ,li: ’ /

ez-z

E.R..-iC’--’

z-r,

-

.-

i

--

_-

I

--em_-_

-.*

-

e

-

‘/ z

.

z

I.

-_

-..eeer

i*

Fig_ 9_ Degree of mkednes

.

.

rc

SC%,”

L*S_number of passes.

The investigation of material transport and mixing can be advantageously performed using a neutron activation tracer technique which reduces considerably the amount of time and effort required for the investigation. The neutron activation tracer technique might also be useful for on-line process control of belts which handle solid material and pipes which handle liquid material. The technique developed in this work for the mixing of flour appears to be generally apphcable to mixing of powder. As Iong as plugging can be avoided by a proper choice of mixing elements and feeding mode, radial mixing by motionless mixers can be efficiently accomplished_ The results indicate that the proposed model for radial mixing is valid, and five passes are sufficient to attain a homogeneous mixture.

ACKNOWLEIXEMENTS

Fig. 10. Degree of mixednes number.

us. mixing action

(about five). the mixture appeared to attain the fmal equilibrium state, which is very close to a completely randomized state.

The authors wish to acknowledge the United States Department of Agriculture and NSF (Grant 40798) for partial financial support of this research. The authors also wish to express their gratitude to Dr. C. A. Watson of the Grain Marketing Research Center and Dr. N. D. Eckhoff of the Department of Nuclear Engineering at Kansas State University for assistance and helpful suggestions.

63 REFERENCES

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