Prediction of the performance of continuous mixers for particulate solids using residence time distributions

307

PowderTechology-ELwvicrSequoiaSA., Lausannc-Printed in theNetherIan&

Prediction of tbe Performance of Continuous Mixers for Particulate Solids using Residence Time Distributions Part IL Experimental J. C. WILLIAMS Posfgradume (Rtxeiwd

and M. A RAHMAN

School of Srudms m Powder Techoiog>.

May 6. 1971; in revised form October

C.+zirerm_~ of Bradford Bradjbrd (Cr. Brrraix)

25. 1971)

Swnmar_~ in an earlier paper a method was proposed to predict the performance of a continuous mixer for non-segregating particulate solids, using the residence tinre dtktribution for the mixer. 271ispaper reports experiments to test these predictions for a drum mixer- The results show satisfactory agreement between predicted and measured perfomrances, provided the tracer material med in the residence tbne tests does not show any appreciable segregation when mixed with the base material. It is contmted that the performance of the mixer is independent of changes in the variance of composition fluctuations in the input stream but depends heavily on its serial correlation coeflcient.

I.

IN-lRODUCl-ION

In Part I of this paper’ the authors proposed a method for predicting the performance of a continuous mixer for particulate solids from the residence time distribution for particles in the mixer. obtained by carrying out a stimulus response test_ The method consists of regarding the variations in composition in the input stream as a sequence of pulses. For each pulse the effect on the output is known and the composition of the output stream can be found by adding together the effects of the input pulses. This second part of the paper describes experiments carried out to test the method by determining the residence time distribution of a continuous mixer by a pulse input test, calculating the form of the output, and comparing this with the experimen’dy determined output under similar varying the mean proportion, the variance and the

Powder TetzImo~ 5 (1371/72)

correlation coeEcient of the tracer component in the input to the mixer was investigated.

L LITERATURE

StJXVEY

Although several workers have considered stimulus-response methods in connection with the -design of continuous reactors’-‘, distillation columns+, heat exchangers’ etc, a comprehensive experimental study of the phenomenon of mixing itself, particularly in the absence of other transfer operations, is not available. The literature show5 that all the work on residence time distributions is with fluids. In the past few years although many papers dealing with the batch mixing of particulate solids have appeared there seems to be iittle movement towards the study of continuous mixing systems involving particulate solids_ Poole, Taylor and Wall6 considered continuous mixing in a ribbon blender_ In their experiments they used feeders capable of giving very nearly constant feed rates so that there were no noticeable fluctuations in the input_ The problem was thus reduced to the mixing of the components in the direction perpendicular to that of the flow. They confined themselves mainly to investig$ng the homogeneity of the mixture by extractmg point samples from random positions in the mixer and also from various positions in the output, and concluded that in the continuous mixer a degree of homogeneity as good as in batch mixing’ could be achieved_ They ha\-e also found experimentally in the case of a Urania-thoria mixture that if the minor component is fed intermittently, maintaining the same overall rate as in continuous feeding the homogeneity of the mixture at the outlet is as good as in

308

3 C WILLIAMS,

the case of continuous feeding provided the batches are fed at a period of less than 02 times the mean residence time. For higher periods, however, the homogeneity of the mixture is worse in the case of intermittent feeding. In order to show that the consistency of the feeders (about 1 oA over a period of 1 min) was good compared to the spread of residence

time, they obtained

an F-diagram

in the case

of a urania-thoria

mixture. Nonetheless the phenomenon of back-mixing as depicted by the Fdiagrams wzs not experimentally investigatedSugimoto, Endoh and Tanaka* studied the phenomenon of segregation in a continuous horizontal drum mixer and found that segregating zones are formed in the drum. as in batch mixing These zones consist of (a) the large particles with the voids between them tilled with fines and (b) fine particles only. This arrangement occurred provided the tine particles were small enough to lit into the voids between the larger particles without destroying the packing arrangement of the larger particles, and provided the proportion of fine particles was more than could be accommodated in this way_ They

argued that the bulk density of zone (a) is higher than that of zone (b) and accordingly the discharge rate by weight fluctuates. From a knowledge of the packing arrangement of the large particles and the size ratio of the components they made an attempt to predict quantitatively the period and scale of the fluctuations in the discharge rate and also the composition of the zones. However, their experimental results do not generally support the prediction. On another occasion Sugimoto and his co-workersg argued that a continuously mixed drum may be thought to be composed of two parts: part I, where segregating zones have already been formed and no axial dispersion of particles takes place, and part II. where zones have not been formed and mixing takes place. They argued that a knowledge of the extent of the sesegating zones can be obtained from an axial dispersion coefficient and can be theoretically estimated from the residence time distribution. They found experimental!y that the axial dispersion increases with increasing proportion of the small particles but stopped when the segregating zones had been formed_ They also found that the axial dispersion increased with increasing mixer speed within the range of lO-30% of the critical speed of the drum. Sugimotoxo studied the mechanism of the axial transport of particles in a horizontal continuous drum mixer. During rotation the particles are carPOHdtT TechmL.

5 (1971f-n)

M. A RAHMAN

ried along by the wall of the drum (the “rotating path” of the particles), and when the dynamic angle of repose is reached the particles roll down in the “cascading path”. The distance moved forward by each particle during one rotation was estimated as a function of its depth below the surface during cascading, and from this an estimate was made of the residence time distribution. Although his experimental results approximately support the hypothesis, Sugimoto’s model for the axial transport of the particles is an over-simplification of the actual situation_ The objections to this model are: (i) The effect of collisions between particles during cascading was not considered. (ii) It was assumed that a given particle will follow the same rotating and cascading paths all the time and that all particles will take part in each cascading (iii) It was also assumed that the angle between the rotating and cascading paths of a particle which is at the free surface is the same as that for a particle deep in the bed. In the work of Sugimoto and his co-workers, there has been a consistent attempt to attack the problem by studying the mechanism of particle movement_ Although it is valuable to study the mechanisms leading to mixing it appears that an analytical solution of the problem based on such studies can be obtained only by making simplifying assumptions which raise doubts about the applicability of the solution to real situations_ The present authors have concentrated on the approach of studying the behaviour of a mixer from the results of stimulus response tests, the performance of the mixer being predicted from the results of such measurements.

3. EXPERIMEhlAL

3.1 Apparatus The apparatus used in these tests was the same as that described in an earlier paperr’. It consists of a cylindrical rotating steel drum, 100 mm i.d. and 200 mm long, with circular openings in the input and output end plates of diameter 20 mm and 60 mm repectively- The optimum operating conditions for thii mixer for the materials used were found to be as follows: Drum inclination to the horizontal: Drum speed: 80 rev min- ’ Feed rate: 30 g in 15 s

2”

PERFORMANCE

OF CONTINUOUS

MIXERS

FOR PARTICULATE

These conditions were used throughout the present series of tests. 3.2 Mcteriak In choosing the materials for the tests it was desired to use two materials whose properties were suffrcientlyy close that no appreciable segregation occurred in the mixer. At this stage of the work segregation of the components to be mixed was not being studied- The work described here was carried out using sand as the base material and salt (I.C.I. vacuum dried) as the tracer_ For both materials the sieve fraction between 355 and 420 JUZIwas used. It was found that at high concentrations of salt in the feed there was evidence of segregation, but that if the mean proportion of salt did not exceed 10% the effects of segregation were general!y small. The properties of the materials used aresummariscd in Table 1. 3.3 Input In feeding the mixer it was not possible to use a continuous feeder, since it would not be capable of introducing into the iced stream the fluctuations in composition required in this work Goldsmith” has shown that if the input is fed in a number of discrete batches and each output sample examined is of the same size as an input batch, the performance of the mixer is the same as if it were continuously fed and the output samples taken were of the same size_ This method was used in the present work as it provides great flexibility in introducing fluctuations into the input stream. Material to be fed into the mixer was first accurately weighed into SO-ml beakers to give a sequence of a large number of batches each of equal weight (30 g)_ To feed the rotating drum these batches were poured down a short chute at 15sec intervals_ For a pulse test one beaker contained the required amount of the tracer component_ TABLE

309

SOLIDS

3.4 Outlet A short chute was placed under the outlet from the mixer. In all experiments the whole of the outlet stream was collected in 1Isec batches, giving samples of approximately equal weight. This was done manually by exchanging the receiver every 15 sec. The overlapping of feedmg and sampling was avoided by placing the sample receiver in position 5 set before each feeding time This required a correction to be made to the results, as discussed in Part I of this paper’. 3.5 Zrnpdse tests To carry out an impulse test to measure a residence time distribution, the base material was sand and a pulse of salt was introduced. The feed material was prepared by placing 30 g of sand into each of a large number of beakers and in one beaker placing the required amount of the tracer and making up to 30 g with sand. Starting with the mixer empty, a sufficient number of batches containing sand only was fed in until steady-state hold-up and outflow were attained A preliminary experiment showed that 8 batches were sufficient to achieve this condition. In the 9th feeding position the batch containing the tracer was fed in and at the same time the collection of outflow sarnpies was begun. The experiment was continued until almost all the tracer material had left the mixer. The total weight ofeach outflow sample was measured and the batches were analysed to find the proportion of tracer element. 3.6. Verification runs According to the theory proposed in Part I of this paper’, the compositions of the outflow batches can be calculated for a general input having fluctuations in composition from batch to batch. Experiments were performed with inputs having different characteristics and the compositions of the

1

Phy.ical properties of the materiais

Sand (British Industrial Sand)

angular

355420

1.50

265

25

70

Salt (I CL

cubic

355420

130

217

23

67

Powder

Vacuum

Techml,

Dried)

5 (1971/72)

310

J. C WILLIAMS.

outflow batches were determined for comparison with the predicted values. Experiments of this type were designated “verification runs”_ Various types of input sequence were used, in which the fluctuations in composition were either serially random or correlated In selecting the input sequences it was ensured that the whole population of batch compositions was normal. The 108 batches prepared had the deviations from the mean composition shown in Table 2. TABLE

2

i’;umber

of batches and talus

of deviation from mean

Number ofbmhes

Dma!ion from mean

20

0

11 7 5 4 4 4 3 3 1

each of tb and -S AZ& -25 T-35 -3s +45 --4d -Ls -56 ~65 -65 s7s -75 286 -SC5 +96 -96

To obtain a random sequence all 108 values of the deviation were written on separate cards which were then thoroughly mixed and picked at random one at a time to give the required sequence. The process was repeated a number of times and in each case the serial correlation coefficient of the sequence was calculated using a computer pro,gram. The sequence having the lowest correlation coefficient was selected as a random sequence. Using mean percentage compositions of 5,10,20 and 30% and the selected sequence of deviations gave four sequences having the same variance and correlation coefficients but different means. To obtain a number of sequences having the same mean and correlation coefficient and different variances, all the deviations in the sequence were multiplied by a constant number. A number of non-random sequences of varying correlation coefficient, both positive and negative, were constructed by selecting the order of the cards to give the desired result. In this way a number of seque:*zs of different correlation coefficients was obtained_ To prepare for an experiment using any of the input sequences, the batches were fust prepared by PoHdet

Techml, 5 (1971/72)

M. A_ RAHMAN

weighing the required proportions of sand and tracer into each beaker, the total weight of each batch being 30 g. The batches were arranged in the specified order and fed at 15-set intervals into the drum, starting with the drum empty. When the 9th input batch was fed in, sampling of the outflow was commenced_ The material flowing out of the drum before sampling commenced and the contents of the drum at the end of the run were both analysed, to give a mass balance over the whole run. 3.7 Analysis of samples Outflow batches from all experiments were totally analysed to find the proportion of the soluble tracerThis was done by transferring each batch to a weighed Xl-ml sintered glass crucible. After weighing the crucibles were placed on a suction flask and the contents were washed until the water leaving the crucible contained no trace of the soluble component- The crucible and its contents were then dried for one hour at 110°C then cooled and weighed, giving the proportion of tracer in the batch. All the sand was washed before use to remove any soluble material. The analysis of prepared samples showed that the analytical variance was negligible compared with the composition variance ofthe outflow batches in all experiments.

?

RESULTS

AND

DISCUSSION

4.1 Linearity of response The method proposed for predicting the form of the output from a mixer is valid only if the response of the system is linear, that is if the proportion of the total amount of tracer appearing in any output sample is independent of the amount of tracer added_ This linearity has been tested in a series of pulse input tests in which the weight of salt added as a tracer was varied from 03 to 30 g. It is seen from the experimental results in Fig. 1 that, apart from scatter around the peak of the U-curves, in both cases the system is linear, so that the law of superposition is expected to hold The scatter of values around the peak is due to the fact that near the peak the values are very sensitive to both the duration and position of feeding and olutflow batches In the present experiment it was possible to feed an input batch and place a beaker in position for outflow sampling within +l set of the required time The time taken for the input batch

PERFORMANCE 1.5

OF CONTINUOUS

MIXERS

FOR

PARTICULATE

r

SOLIDS

311

4.2 Replicate pulse tests The results of replicate pulse tests are shown in Fig. 2 The same comments as made above apply to the scatter of results near the peak of the Ucurves The effect of the reproducibility of these results on the predicted values for the composition of the output of a verification run is discussed later. 43

Verijkation nms At the optimurp operating conditions for the drum, experiments were carried out by feeding into the drum sequences with varying batch composition so that a comparison could be made between experimental and predicted results. Although the ratio of input to output variance is of primary interest, both experimental and theoretical outputs have been character&d by their mean, variance and serial correlation. The results of the tests are given in the following paragraphs. More detailed results, giving the compositions of the outflow batches, in all runs. are provided by Rahman ’ 3_

1. Linearity of the system (effect of tram wet&t respouse to the impulse input). Puke test no. Symbol Weigh cftracer. Q (g) PSI9 0_3 Cl PS20 A 1J PS21 3.0 n PS22 45 x PS23 60 -IPS24 100 V PS25 I50 0 PS26 300 0 Fig

on the

1.5 r

_ __

Ftg 2 Reproduabtbty

of pulse tests

to run down the chute into the drum varied by 2 or 3 set The scatter iu the results is less marked in the cumulative F-curves, which are also shown in Fig 1. Ponder

Techrwl.,

5 (1971/72)

4.3.1 Reproducibility tests To examine the effect of variations in the results of the pulse test on -the predicted form of the output from a mixer, a nearly random input was selected and the corresponding output form was cakulated using each of the three measured residence time distributions. The input used had a mean salt content of loo/$ a variance of 16.71 and a serial correlation of O-10. The forms of the input and the three predicted outputs are shown in Fig 3. The three values for predicted variance reduction ratio are 9-9, 11.1 and 9-7, with a mean value of 10.2 The same form of input, shown iu Fig 3, was then fed into the mixer and the proportions of salt in the output batches determined experimentally. This test was carried out three times and the results are also shown in Fig 3, for comparison with the three predicted results. The experimental values of the variance reduction ratio are 8.8, 93 and 103. with a mean value of 95, compared with the predicted mean value of 10.2 The results of the reproducibility tests are summarised in Table 3. The results suggest that the reliability of predicted outputs based on a single pulse test is of the order of 1&20°% 4.32 The effect of input mean composition A series of verification runs was carried out in

312

J. C WILLIAMS. TABLE

M. k

RAHMAN

3

Results of rcproducibity

tests

Mean input concentrationloo/_ serial corrdation 0.10

input variance1671.

input

(i) Predicted ourput

% Mean

Variance

composition

1 2 3

10.1 10.1 10.1

1.73 1.53 176

090 088 OS8

% Mean

Varzance

StiUZ

correzation

COI?pXitiOn

correlnrron

102 10.1 10 1

1.94 I-S3

083 0x4

164

095

higher than the predicted variance if the input concentration is higher than loo/_ showing that there was poor mixing at the higher salt concentrations_ It has been shown earlier I1 that sand and salt differ slightly in flow properties, and when they are interchanged as the feed and tracer in a pulse test there is a change in response_ The present results confirm the earlier conclusion, that as the concentration of salt increases the properties of the mixture change in such a way as to give poor mixing. The results show that when the mixer contains a high proportion of salt the results of a pulse test no longer describe its performance. This fact was confirmed by carrying out step input tests using steps

which the mean concentration of salt in the input batches was varied from 5 to 30”/, In each case the observed properties of the output stream are compared with those predicted using the results of a pulse test. The results are shown in Table 4. The predicted output is independent of the input mean composition. The experimental results show that although the general form of the output is the same in each case, the observed output variance is

TABLE

Seriol

Puke rest no.

4

Efkct of input mean composxtlon

Run input

OUrpUt

IlO o/o

Mean

VLVlLI?ZCCSt?TiUl

composrrlon

vs4 vs9 vs7 vss vS6

so 100 IO-0 20_0 300

correlation

4 If3 4.18 II.55 1155 11.55

Powder TerzhnoL,5 (1971/72)

0.10 0 10 o-to 0.10 0.10

Expenmenral

Predzcied

0%M ea?l composition

vari5?lce

50 10.1 IO.1 20.1 30.1

0.43 0.43 I.20 I.54 214

S&l correlation

compontion

066 062 a92 075 071

5.1 10.0 10.1 2&l 30.1

%M-

VLVilRlCe

seriat correlarion

043 0.47 120 120 120

a92 094 O-90 0_9cl 0.90

PERFORMANCE TABLE

OF

FOR

PARTICULATE

313

SOLIDS

5

Results of steadystate Run. no.

Tracer

TSl TS2 Ts3 TS4

TABLE

MIXERS

CONTINUOUS

salt salt salt salt

tests Input c5ncentration

5 10 20 30

OUtpUt Mean composition

variance

sear

5-O 10-O 200 30-O

0017 0.043 0 148 0 17?

-023 0.15 -0 16 -0.13

valiance reducrron ratio

“/, Mean compozition

correlation

6

Effca of changing input variance Input mean composition lOY_ input correlation cocfiicient 0.10

% hieon composltron

V5lRXe

Serial correlarion

from 0 to 5,10,20 and 30% of salt in a feed of sand Increasingly poorer mixing was observed as the salt concentration increased. In these step input tests measurement of the output was continued after the transient effect was complete. As shown in Table 5, the steady-state variance increased with increasing concentration of salt in the input The steady-state variance is a measure of the amount of segregation between the sand and salt in the mixer. In an attempt to eliminate the effects of segregation of the tracer the steady-state variance was deducted from the observed variance in verification runs The resulting correction was generahy small. The results indicate that at mean concentrations higher than 10 “/, salt is not a reliable tracer, and in further tests the mean salt concentration was not allowed to exceed loo/, The general conclusion from the experiments in which the mean concentration of the tracer in the input batches was varied is that the variance reduction ratio is independent of concentration provided that no segregation between feed and tracer occurs in the mixer. Ponder

TechnoZ, 5 (1971f72)

~~arknce

Seripl

Il-mL7YKf?

correlation

redunion 3-CI~ZO

_4.3.3 Efid of input cariance Theoretically, the variance reduction ratio of a mixer for a given set of components is independent of the input variance provided the serial correlation coefficient of the input remains constant. For sand and salt mixtures verification runs have been carried out using input sequences having variances between 044 and 16.71. In all cases the mean and serial correlation were kept constant at 10% and 0.10 respectively_ The results of all the tests are summarised in Table 6. It is seen that within experimental error the observed value of the variance reduction ratio is constant, with a mean value of 9.75 cornTared with the predicted value of 9_9_ At the highest input variance used (16-71) the observed output variance is lZ”A higher than the predicted variance_ It is possible in this cast that the coucentiation of tracer in the input is at times sufftciently high for appreciable segregation to occur in the drum, leading to a performance poorer than predicted_ In Run VSlO the output variance is very small and the experimental error in its determination is, therefore, high.

J. C WILLIAMS,

-0

20

1

-2ucz.er

Fl_e 4 Comparison

L-r

5. C~mpan~ou

TABLE

of predIcted

bPic%ES

output For a random

a

20

oL

l-racer

s2lt

VSlZ

salt salt

and measured

output

for a correlated

loo

input (senal correlation

iO86).

Input serial correlation xl F c--wr_ Iz.1

403 086

lZ.55

0utplIr Predzcted

Experimenral Mean composi-

vmimrce

a4

Vwiance reduction

Mean composi-

flOIl

ratio

GO?8

723 428

4-06

120

139 092

salt

-a19

9.7

072

1.20

salt

-044

99

QOI

0.10

to3 101

S&III correla-

-0X

43-4 Efiect of input serd correbtion The predicted variance reduction ratio for a mixer varies with the serial correlation of the input. A series of tests was carried out in which the input serial correlation, Zz5 1 e--m r,, was varie4i from 4 to -0_44_ Ponder

19).

7

VSll

vs14

so

-0

Sat&es

r10Il

vs7 -vs13

input (serial correlation

60 cnrqmt

Effect of varying mput scnal correlation Input mean concentration 10% of tacer, input variance RUTI no

1cQ

RD

LO

.a-_~*

of predIcted and measured

I

Ftg

Of

M. A RAHMAN

Tecknol, 5 (1971/72)

13 27

9.8

8.4

103 10.1

Vticmce

727 4_05

130

15.6

9.7

069

1200

9.9

O-01

SerbZ correlarion 407 1.43

0% 125 -034

Varknce

r.sducticm

ratio

13 29

9.8 163 IL00

The compositions of the predicted and experimental output streams for some of the experiments are shown in Figs 4 and 5 Visual inspection shows that there is very good agreement between the observed and predicted outputs. The properties of the output stream are summarised in Table 7.

PERFORMANCE

OF CONTINUOUS

MIXERS

FOR

PARTICULATE

6 Comparison of responses to stepand step-demand (step from 0 to IO% salt; step demand from IO to 0% salt) Cl Step test. l step-demand testFig.

In general the experimental results for the variance and serial correlation of the output agree closely with the predicted values_ Run VS12, with a cyclic input. gives an output variance somewhat higher than the predicted value. This result was confirmed by a repeat test, the two output variances being 428 and 4.43 compared with a predicted value of 4.05. This discrepancy cannot be accounted for by the effect of input serial correlation on the predicted value, since the method of prediction makes no assumptions about the nature of the input. A probable reason for the discrepancy is that, due to the cyclic nature of the input, the situation is similar to an alternate step and step demand sequence; the responses of the system to step and step demand may not be the same. A step and step demand test using sand as the feed and saIt as the tracer was carried out in which the concentration of salt in input batches was increased from 0 to 10 o/mmaintained at that level until the steady state had been reached, then decreased to zero. The results are given in Fig 6, where it is seen that the effects of the step and the step demand on the output concentrations are not the same. These results arr presumed to be due to the small amount of segregation that occurs in the mixer between sand and salt

CONCLUSIONS

(i) Tests have shown that the method described in Part 1 of this paper for predicting the performance of a continuous mixer from a hcwledge of its residence time distribution gives results which agree with measured values for the variance and serial correlation of the output, provided the tracer used has the same properties as the feed material. Poeder

T&c%,

5 (1971/72)

SOLIDS

315

(ii) The response of the system to varying amounts of tracer in an impulse input test was linear within the range 0.3-30 g of tracer. (iii) Replicate tests gave reasonably reproducible results for an impulse input test. (iv) When the results of three replicate impulse tests were used to predict the performance of a mixer for a given input sequence, the reliability of the predicted variance reduction ratio of the mixer was of the order of IO-20%. (v) When the feed tc the mixer contained varying amounts of salt there was evidence of segregation between the sand and the salt in the mixer, particularly at high salt concentrations. Provided the measured output variance was corrected by deducting the output variance observed in the steady state for a fried salt concentration in the f-it was found that there was satisfactory agreement between observed and predicted output variances if the mean salt concentration in the output did not exceed 10 %(vi) Protided the limiting mean tracer concentration was not exceeded, the characteristics of the output stream were independent of :‘_= tracer concentration and agreed satisfactorily with lfie predicted values. (vii) The variance of the tracer concentration in the feed to the mixer was varied between 0-a and 16.71. The variance reduction ratio of the mixer was independent of input variance within this range. (viii) The serial correlation of composition fluctuations in the input stream was varied, havivlg both positive and negatix-e values. The measure output characteristics agreed satisfactory with the predicted values. For a regular cyclic input the agreement was less good than in the other cases, possibly due to segregation between the sand and salt in the mixer.

REFERENCES 1 J. C Williams and M. A_ Rahmar& Prediction of the pcrformana of continuous mixers for particulate solids usins rcsidcna time dtiributlonr Part L Theoretical, Powder TechnoL. 5 (1971/7?3 87. 2 P_ v_ Danckwerr& them Eng sci, 2 (1953) 1. 3 M_ SharZ Ai_ SC T&s& Unir _ of Bradford_ 1966. 4 P. H. Hammond and D. L X Barber. Truns Sot InmTechnol, 1: (1%5) 59. 5 J.D.Cumminr, Concentiun on Adrance in Au~omntzc C~nlroi Inn Mech. Engrs, Norringham, 5-9 A@, 1965. 6 K R Poole. R E Taylor and G. P_ Wall. Trans. Imz Chem Engrs 43 (1965) T26L

316

J. C. WILLIAMS,

7 IL R Poole

R F. Taylor and G. P. Wall, Trans

Eqrs, 42 (1964) T305. 8 M- Su@noto_ Ir_ Fndoh and T_ Tanaka, 4 (1966: 348. b M. Su_eimoto, K 31 (1967) 145.

Ponder

Endoh

TechnoZ, 5 (1971/72)

and T_ Tanaka,

INL Chon

Kagab

Kogah,

Kagaku

Kog&z,

M. A RAHMAN

10 M_ Sugimoto. Kagaku Kognku, 32 (1968) 291. 1 I J. C Williams and M A Rahrtta J_ Sot Cosmetic Chemkrs, 21 (1970) 3. 12 P_ I- Goldsmt~ Srutisri~ I3 M. A_ Rahman, Ph_D_ Thesis,

16 (1966) 1. Univ. of Bradford,

1970