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Effect of impeller geometry on drop break-up in a stirred liquid—liquid contactor
Chemical
Engineering
Science,
1974, Vol. 29, pp. 345-348.
Pergamon Press.
Printed in Great Britain
EFFECT OF IMPELLER GEOMETRY ON DROP BREAK-UP IN A STIRRED LIQUID-LIQUID CONTACTOR D. E. BROWN and K. PITT? Department of Chemical Engineering, University of Manchester, Institute of Science and Technology, Manchester, England (Received 26 February 1973; accepted 16 May 1973) Abstract-Drop size measurements were made in the break-up zone at the tip of three 6 bladed disc turbines of different geometries in a 0.30 m dia. vessel. Three systems kerosene, methyl iso-butyl ketone (MIBK) and n-butanol at a volumetric fractional hold-up of 0.05 in water were examined. Power input and circulation time characteristics were determined and a new dimensionless group (e-“‘t,/P”) is proposed to account for the effect of geometric parameters in the correlation of the drop size. INTRODUCTION
EXPERIMENTALPROCEDURES
Some workers[I] have examined scale effect on drop size in stirred liquid-liquid contactors, but have maintained a constant impeller and vessel geometry. Several reports [2-4] have considered impeller-to-vessel diameter ratios in their experiments and the effect has been included in general drop-size correlations. The influence of the impeller size on mass transfer rates [5] and fluid velocities [6] highlight the significance of this particular aspect of contactor design. The choice of the disc turbine for liquid-liquid contact is widely accepted but no detailed information is available for the selection of its design relative to the vessel size. In a recent report [7] of drop break-up measurements, it was found that drop sizes measured at the impeller tip, for three different liquid-liquid systems, were identical at a given speed of rotation for two impellers of identical diameter but different blade widths. Arising from power input and circulation time measurements for these geometric systems it was found that the identical drop diameters resulted from identical turbulent head characteristics in the stream from each impeller. Drop-size measurements for break-up in the stream from a third impeller geometry are reported here, comparison of the various results indicates a useful relationship suitable for the correlation of the effects of geometry.
A 0.30 m dia. glass contactor was used in this study. Drop-size measurements were made in the break-up zone at the tip of the impeller using a previously calibrated photo-electric probe. The three systems kerosene, methyl iso-butyl ketone and n -butanol in water were examined at a volumetric hold-up ratio of 0.05. Three disc turbine impellers located midway between the bottom and top of the vessel were used in the study and their dimensions are listed in Table 1.
tPresent address: Department of Chemical Engineering, Teesside Polytechnic,
Middlesbrough,
England.
Table 1. Impeller dimensions Impeller No. D 1 2 3
0.10 0.10 0.15
W
~5,
0.025 0.0315 0.050 0.0315 0.0375 0.0475
W/D
D/T
Np
Nt,
0.25 0.50 0.25
0.33 0.33 0.50
5.8 9.3 5.8
12.3 7.8 3.1
Greater details of the experimental equipment and procedures, together with the physical properties of the systems at the operating temperature of 20°C have been previously reported [7-93. POWRRINPUT
power input characteristics of all three system geometries were obtained using a dynamometer unit constructed by mounting the stirrer motor in support bearings [7]. The results are expressed in terms of the power number (Np) and these are included in Table 1. The value of Np = S-8 for the impellers with blade width-to-diameter
345
The impeller
D. E. BROWN and K. PITT
346
ratios of 0.25 agrees identically with the value quoted for this geometry by Nienow and Miles [lo]. Although the impeller blade width effect was shown[7] to be of the form: Np (Y (W/D)*“, no effect of impeller-to-vessel diameter ratio was evident in these results.
of 0.05 were considered and are listed, together with results from impeller 3, for the three liquid-liquid systems in Table 3. Also included in Table 3 are the appropriate values of the circulation time and the energy input per unit mass (Z). The effect of dispersed phase hold-up on drop size has been previously discussed [7].
CIRCULATIONTIME
Circulation time (tJ data for impellers 1 and 2 were obtained using both flow follower and conductivity techniques (which were shown to give identical results) previously reported [7]. The flow follower method[l l] was used to determine circulation times for impeller 3 which are listed in Table 2. Table 2. Circulation time data for impeller 3 N
1.8
1.96
2.42
2.99
3.08
3.57
4.84
t,
1.95
1.35
1.29
0.92
l-02
0.84
0.65
Following the correlation procedure of Holmes et a1.[12], a constant value of Nt,= 3.1 was determined for this impeller and compared with the values for the other two impellers in Table 1. For this limited amounted of data the geometric effect was found to be correlated by: Nr, (%“‘($)“’
Table 3. Drop size measurements,
circulation times and
energy input Sauter mean diameter (mm) Speed Impeller (rpm)
t,
Z
kerosene
0.021 0.035 0.056 0.083 0.127
0.18 0.14 0.12 0.10 -
0.066 0.053 0.044 0,038 -
0026 0.020 0.017 0.014 -
0.066 0.053 0.044 0.038 -
0.026 0.020 0.017 0.014 -
1
2.50 300 350 400 450
2.95 2.46 2.10 1.85 164
2
250
1.87 0.033
300 350 400 450
1.56 1.34 1.17 1.04
0.056 0.091 0.135 0.189
0.18 0.14 0.12 0.10 0.087
125 150 175 200 250
1.49 1.24 1.06 0.93 0.74
0.020 0.035 0.056 0.081 0.152
0.30 0.24 0.19 0.16 0.12
3
M.I.B.K. n-butanol
-
0.040 0.033 0.027 0.023 0.018
=0.0122 DISCUSSION
For a constant blade width ratio, then, t, a (D/T)-2’67 which differs from the result that t, (Y (D/I’-*” obtained by Holmes et a1.[12]. This different result may possibly be explained by the ditference between the open air-liquid surfaceH21 and the filled closed vessel of this work. Mixing times, which are often measured in terms of a multiple of the circulation times, have been reported by Prochazka and Landau[l3] to be proportional to (D/T)-z~57 in close agreement with this work. Further, it is of interest to note that Oldshue1141 reported that the ratio of flow to turbulent head at constant power input (inversely proportional to the circulation time) could be considered to be proportional to (D/T)*‘66. DROP SIZE MEASUREMENTS
Drop size measurements for impellers 1 and 2 have been previously reported[7] for a range of volumetric dispersed phase hold-up fractions 8 and, at a given impeller speed and hold-up value, were shown to be identical. For the purpose of this investigation, only data for drop sizes at a hold-up value
A theoretical fines
analysis 5 &?)
and if the turbulent isotropic then
d,,
of drop break-up[l5] = constant
flow can be assumed
U2(d) = C( edmax)2/3
de(2) to be (3)
when d 2, d
l
= constant.
(4)
It has been shown [9] that a simple linear relationship exists between this predicted maximum drop size d,, and the experimentally measured Sauter mean diameter d3*.The energy dissipation per unit mass E refers to a point value in the turbulent stream. In the case of the break-up of drops in a stirred vessel, l is thus some maximum point value in the stream from the impeller. Point values of energy dissipation cannot easily be determined and it has been sometimes assumed that the average energy dissipation per unit mass Z, determined as
Drop break-up in a stirred liquid-liquid contactor the total power input to the vessel divided by the mass of fluid in the vessel, could replace the point value. However, if impeller geometry is altered, then for different impeller designs at a given average input Z, there could be quite different maximum point values of E in the stream from the impeller blade tip. Power input to the fluid from the impeller will dissipate [ 161as mass flow PQ and turbulent head: P=pQH and as Danckwerts[17]
Impeller
: 0
(5)
(6)
c
:
3
0
/ E /xe!Y~o~“” _ : 0.1_- .X/ i -0 -0 0”
-
E
-
has pointed out: Q=_Y
347
j
Kerosine
a/
MIBK
/LJso / /
v)
from which we can derive that: H=P=Pt,=~r PQ PV
I/
,s”
n - bu+a”o’
= 0.01
It has recently been shown[7] that the turbulent head, determined as g&, in the stream from impellers 1 and 2, rather than the average energy dissipation 3, controlled the drop size. Further confirmation of this observation is presented in Fig. 1 in which the Sauter mean drop sizes for the three systerns are plotted as functions of the turbulent head (I/$) for all three impellers. Very good agreement between the three impellers is indicated. A cross-plot of the results in Fig. 1 as a function of the system interfacial tensions (kerosene 0.050, M.I.B.K. 0.0105 and n-butanol OTlO19) confirmed the theoretical and well substantiated result that
I
1 1 1 ’ ’ 1
I
IO
tI/F;t,I,
kg/J
Fig. 1,Effect of impeller geometry. ^_ d32au”‘o.A further test of the data is shown in Fig. 2 in which the Sauter mean drop diameter is plotted as a function of ol&. The good correlation has a slope of 0.6 and as the density was constant in this work the results could be represented by: 03)
I
lo-’
[o/;tcl,
kg
m2
Fig. 2. General correlation.
D. E. BROWNand K. PITT
348 Rearranging gives:
Eq. (8) into the same form as Eq. (4)
d,,, H
(d$
ff Z’“)(C”‘tJ = constant.
It can be seen that the replacement of the point value of the energy dissipation E by the average value e is not complete. Some additional expression is necessary to describe the individual characteristics of the impellers of different geometry. A close examination of Eq. (9) reveals that the constant has the dimensions of (length)2” rather than being dimensionless as in Eq. (4). The obvious parameter which was not varied in this work but which would, no doubt, interact with the circulation time, is that of the vessel diameter. It is thus suggested that the more complete expression will be: (&f
$J3)($$)
= constant.
(10)
This auproach
introduces a new dimensionless which relates the circulation time to the average energy input and the scale of operation. No information is, however, available from this work to co&m the power of 1 on the vessel diameter.
V W
maximum drop diameter, m turbulent head, m impeller blade length, m impeller speed, set-’ impeller power number power input to vessel, J/set volume flow of fluid from impeller, m3/sec circulation time, set vessel diameter, m relative velocity between two points in fluid separated by distance d, m/set volume of liquid in vessel, m impeller blade width, m
Greek symbols E point energy dissipation
rate per unit mass, J/set kg rate per unit 1 average energy dissipation mass, J/set kg fractional volumetric hold-up P density of continuous phase, kg/m’ u interfacial tension, J/m’
group (&//T2/3)
CONCLUSION Drop sizes generated by disc turbines of different geometries have been shown to be controlled by the turbulent head contained in the flow from the impellers, rather than the average energy input per unit mass of fluid. Power input and circulation time data was obtained for the impellers and have been shown to be in good agreement with published results. A new dimensionless group (B1’3t,/T2’3)has been proposed which will take into account the turbulent head characteristics between impellers of different geometry and the changing scale of operation. Estimates of drop size can now be made from a knowledge of the readily measurable energy input and the circulation time. Work of this kind is needed at other scales of operation to conform this aspect of the correlation. NOTATION
C D dj2
constant in Eq. (3) impeller diameter, m Sauter mean drop diameter,
m
REFERENCES
[II VAN HEUVEN J. W. and BEEK W. J., Proc. I.S.E.C. Paper 51, Amsterdam, April 191. r21 RODGER W. A., TRICE V. G. and RUSHTON J. H., Chem. Engng Prog 1956, 52 515. [31 CHEN H. T. and MIDDLEMAN S., A.I.Ch.E.JI 1967 13 989. [41 MLYNEK Y. and RESNICK W., A.I.Ch.E..JI 1972 18 122. [51 SCHINDLER H. D. and TREYBAL R. E., Ind. Engng Chem. Fundls 1968 7 1. 161SCHWARTZBERG H. G. and TREYBAL R. E., Ind. Engng Chem. Fundls 1%8 7 1. [71 BROWN D. E. and PITT K., Proc. Chemeca ‘70, Melbourne and Sidney, August 1970. of Manchester 1968. [91 BROWN D. E. and PITT K., Chem. Engng Sci. 1972 27 577. t101 NIENOW A. W. and MILES D., Ind. Engng Chem. Proc. Des. Dev. 1971 10 41. r111 STEIDL H., Coil. Czech. Chem. Commun. 1958 23 1664. [I21 HOLMES D. B., VONCKEN R. M. and DEKKER J. A., Chem. Engng Sci. 1964 19 209. [I31 PROCHAZKA .I. and LANDAU J., Coil. Czech. Chem. Commun. l%l 26 2961. [I41 OLDSHUE J. Y., Proc. Biochem. 1969 4 51. t151 SHINNAR R. and CHURCH J. M., Ind. Engng Chem. 1960 52 253. [I61 RUSHTON J. H. and OLDSHUE J. Y., Chem. Engng Proc. 1953 49 161. [17] DANCKWERTS P. V., Chem. Engng Sci. 1952 2 1.
[81 PITT K., Ph.D. thesis, University
Engineering
Science,
1974, Vol. 29, pp. 345-348.
Pergamon Press.
Printed in Great Britain
EFFECT OF IMPELLER GEOMETRY ON DROP BREAK-UP IN A STIRRED LIQUID-LIQUID CONTACTOR D. E. BROWN and K. PITT? Department of Chemical Engineering, University of Manchester, Institute of Science and Technology, Manchester, England (Received 26 February 1973; accepted 16 May 1973) Abstract-Drop size measurements were made in the break-up zone at the tip of three 6 bladed disc turbines of different geometries in a 0.30 m dia. vessel. Three systems kerosene, methyl iso-butyl ketone (MIBK) and n-butanol at a volumetric fractional hold-up of 0.05 in water were examined. Power input and circulation time characteristics were determined and a new dimensionless group (e-“‘t,/P”) is proposed to account for the effect of geometric parameters in the correlation of the drop size. INTRODUCTION
EXPERIMENTALPROCEDURES
Some workers[I] have examined scale effect on drop size in stirred liquid-liquid contactors, but have maintained a constant impeller and vessel geometry. Several reports [2-4] have considered impeller-to-vessel diameter ratios in their experiments and the effect has been included in general drop-size correlations. The influence of the impeller size on mass transfer rates [5] and fluid velocities [6] highlight the significance of this particular aspect of contactor design. The choice of the disc turbine for liquid-liquid contact is widely accepted but no detailed information is available for the selection of its design relative to the vessel size. In a recent report [7] of drop break-up measurements, it was found that drop sizes measured at the impeller tip, for three different liquid-liquid systems, were identical at a given speed of rotation for two impellers of identical diameter but different blade widths. Arising from power input and circulation time measurements for these geometric systems it was found that the identical drop diameters resulted from identical turbulent head characteristics in the stream from each impeller. Drop-size measurements for break-up in the stream from a third impeller geometry are reported here, comparison of the various results indicates a useful relationship suitable for the correlation of the effects of geometry.
A 0.30 m dia. glass contactor was used in this study. Drop-size measurements were made in the break-up zone at the tip of the impeller using a previously calibrated photo-electric probe. The three systems kerosene, methyl iso-butyl ketone and n -butanol in water were examined at a volumetric hold-up ratio of 0.05. Three disc turbine impellers located midway between the bottom and top of the vessel were used in the study and their dimensions are listed in Table 1.
tPresent address: Department of Chemical Engineering, Teesside Polytechnic,
Middlesbrough,
England.
Table 1. Impeller dimensions Impeller No. D 1 2 3
0.10 0.10 0.15
W
~5,
0.025 0.0315 0.050 0.0315 0.0375 0.0475
W/D
D/T
Np
Nt,
0.25 0.50 0.25
0.33 0.33 0.50
5.8 9.3 5.8
12.3 7.8 3.1
Greater details of the experimental equipment and procedures, together with the physical properties of the systems at the operating temperature of 20°C have been previously reported [7-93. POWRRINPUT
power input characteristics of all three system geometries were obtained using a dynamometer unit constructed by mounting the stirrer motor in support bearings [7]. The results are expressed in terms of the power number (Np) and these are included in Table 1. The value of Np = S-8 for the impellers with blade width-to-diameter
345
The impeller
D. E. BROWN and K. PITT
346
ratios of 0.25 agrees identically with the value quoted for this geometry by Nienow and Miles [lo]. Although the impeller blade width effect was shown[7] to be of the form: Np (Y (W/D)*“, no effect of impeller-to-vessel diameter ratio was evident in these results.
of 0.05 were considered and are listed, together with results from impeller 3, for the three liquid-liquid systems in Table 3. Also included in Table 3 are the appropriate values of the circulation time and the energy input per unit mass (Z). The effect of dispersed phase hold-up on drop size has been previously discussed [7].
CIRCULATIONTIME
Circulation time (tJ data for impellers 1 and 2 were obtained using both flow follower and conductivity techniques (which were shown to give identical results) previously reported [7]. The flow follower method[l l] was used to determine circulation times for impeller 3 which are listed in Table 2. Table 2. Circulation time data for impeller 3 N
1.8
1.96
2.42
2.99
3.08
3.57
4.84
t,
1.95
1.35
1.29
0.92
l-02
0.84
0.65
Following the correlation procedure of Holmes et a1.[12], a constant value of Nt,= 3.1 was determined for this impeller and compared with the values for the other two impellers in Table 1. For this limited amounted of data the geometric effect was found to be correlated by: Nr, (%“‘($)“’
Table 3. Drop size measurements,
circulation times and
energy input Sauter mean diameter (mm) Speed Impeller (rpm)
t,
Z
kerosene
0.021 0.035 0.056 0.083 0.127
0.18 0.14 0.12 0.10 -
0.066 0.053 0.044 0,038 -
0026 0.020 0.017 0.014 -
0.066 0.053 0.044 0.038 -
0.026 0.020 0.017 0.014 -
1
2.50 300 350 400 450
2.95 2.46 2.10 1.85 164
2
250
1.87 0.033
300 350 400 450
1.56 1.34 1.17 1.04
0.056 0.091 0.135 0.189
0.18 0.14 0.12 0.10 0.087
125 150 175 200 250
1.49 1.24 1.06 0.93 0.74
0.020 0.035 0.056 0.081 0.152
0.30 0.24 0.19 0.16 0.12
3
M.I.B.K. n-butanol
-
0.040 0.033 0.027 0.023 0.018
=0.0122 DISCUSSION
For a constant blade width ratio, then, t, a (D/T)-2’67 which differs from the result that t, (Y (D/I’-*” obtained by Holmes et a1.[12]. This different result may possibly be explained by the ditference between the open air-liquid surfaceH21 and the filled closed vessel of this work. Mixing times, which are often measured in terms of a multiple of the circulation times, have been reported by Prochazka and Landau[l3] to be proportional to (D/T)-z~57 in close agreement with this work. Further, it is of interest to note that Oldshue1141 reported that the ratio of flow to turbulent head at constant power input (inversely proportional to the circulation time) could be considered to be proportional to (D/T)*‘66. DROP SIZE MEASUREMENTS
Drop size measurements for impellers 1 and 2 have been previously reported[7] for a range of volumetric dispersed phase hold-up fractions 8 and, at a given impeller speed and hold-up value, were shown to be identical. For the purpose of this investigation, only data for drop sizes at a hold-up value
A theoretical fines
analysis 5 &?)
and if the turbulent isotropic then
d,,
of drop break-up[l5] = constant
flow can be assumed
U2(d) = C( edmax)2/3
de(2) to be (3)
when d 2, d
l
= constant.
(4)
It has been shown [9] that a simple linear relationship exists between this predicted maximum drop size d,, and the experimentally measured Sauter mean diameter d3*.The energy dissipation per unit mass E refers to a point value in the turbulent stream. In the case of the break-up of drops in a stirred vessel, l is thus some maximum point value in the stream from the impeller. Point values of energy dissipation cannot easily be determined and it has been sometimes assumed that the average energy dissipation per unit mass Z, determined as
Drop break-up in a stirred liquid-liquid contactor the total power input to the vessel divided by the mass of fluid in the vessel, could replace the point value. However, if impeller geometry is altered, then for different impeller designs at a given average input Z, there could be quite different maximum point values of E in the stream from the impeller blade tip. Power input to the fluid from the impeller will dissipate [ 161as mass flow PQ and turbulent head: P=pQH and as Danckwerts[17]
Impeller
: 0
(5)
(6)
c
:
3
0
/ E /xe!Y~o~“” _ : 0.1_- .X/ i -0 -0 0”
-
E
-
has pointed out: Q=_Y
347
j
Kerosine
a/
MIBK
/LJso / /
v)
from which we can derive that: H=P=Pt,=~r PQ PV
I/
,s”
n - bu+a”o’
= 0.01
It has recently been shown[7] that the turbulent head, determined as g&, in the stream from impellers 1 and 2, rather than the average energy dissipation 3, controlled the drop size. Further confirmation of this observation is presented in Fig. 1 in which the Sauter mean drop sizes for the three systerns are plotted as functions of the turbulent head (I/$) for all three impellers. Very good agreement between the three impellers is indicated. A cross-plot of the results in Fig. 1 as a function of the system interfacial tensions (kerosene 0.050, M.I.B.K. 0.0105 and n-butanol OTlO19) confirmed the theoretical and well substantiated result that
I
1 1 1 ’ ’ 1
I
IO
tI/F;t,I,
kg/J
Fig. 1,Effect of impeller geometry. ^_ d32au”‘o.A further test of the data is shown in Fig. 2 in which the Sauter mean drop diameter is plotted as a function of ol&. The good correlation has a slope of 0.6 and as the density was constant in this work the results could be represented by: 03)
I
lo-’
[o/;tcl,
kg
m2
Fig. 2. General correlation.
D. E. BROWNand K. PITT
348 Rearranging gives:
Eq. (8) into the same form as Eq. (4)
d,,, H
(d$
ff Z’“)(C”‘tJ = constant.
It can be seen that the replacement of the point value of the energy dissipation E by the average value e is not complete. Some additional expression is necessary to describe the individual characteristics of the impellers of different geometry. A close examination of Eq. (9) reveals that the constant has the dimensions of (length)2” rather than being dimensionless as in Eq. (4). The obvious parameter which was not varied in this work but which would, no doubt, interact with the circulation time, is that of the vessel diameter. It is thus suggested that the more complete expression will be: (&f
$J3)($$)
= constant.
(10)
This auproach
introduces a new dimensionless which relates the circulation time to the average energy input and the scale of operation. No information is, however, available from this work to co&m the power of 1 on the vessel diameter.
V W
maximum drop diameter, m turbulent head, m impeller blade length, m impeller speed, set-’ impeller power number power input to vessel, J/set volume flow of fluid from impeller, m3/sec circulation time, set vessel diameter, m relative velocity between two points in fluid separated by distance d, m/set volume of liquid in vessel, m impeller blade width, m
Greek symbols E point energy dissipation
rate per unit mass, J/set kg rate per unit 1 average energy dissipation mass, J/set kg fractional volumetric hold-up P density of continuous phase, kg/m’ u interfacial tension, J/m’
group (&//T2/3)
CONCLUSION Drop sizes generated by disc turbines of different geometries have been shown to be controlled by the turbulent head contained in the flow from the impellers, rather than the average energy input per unit mass of fluid. Power input and circulation time data was obtained for the impellers and have been shown to be in good agreement with published results. A new dimensionless group (B1’3t,/T2’3)has been proposed which will take into account the turbulent head characteristics between impellers of different geometry and the changing scale of operation. Estimates of drop size can now be made from a knowledge of the readily measurable energy input and the circulation time. Work of this kind is needed at other scales of operation to conform this aspect of the correlation. NOTATION
C D dj2
constant in Eq. (3) impeller diameter, m Sauter mean drop diameter,
m
REFERENCES
[II VAN HEUVEN J. W. and BEEK W. J., Proc. I.S.E.C. Paper 51, Amsterdam, April 191. r21 RODGER W. A., TRICE V. G. and RUSHTON J. H., Chem. Engng Prog 1956, 52 515. [31 CHEN H. T. and MIDDLEMAN S., A.I.Ch.E.JI 1967 13 989. [41 MLYNEK Y. and RESNICK W., A.I.Ch.E..JI 1972 18 122. [51 SCHINDLER H. D. and TREYBAL R. E., Ind. Engng Chem. Fundls 1968 7 1. 161SCHWARTZBERG H. G. and TREYBAL R. E., Ind. Engng Chem. Fundls 1%8 7 1. [71 BROWN D. E. and PITT K., Proc. Chemeca ‘70, Melbourne and Sidney, August 1970. of Manchester 1968. [91 BROWN D. E. and PITT K., Chem. Engng Sci. 1972 27 577. t101 NIENOW A. W. and MILES D., Ind. Engng Chem. Proc. Des. Dev. 1971 10 41. r111 STEIDL H., Coil. Czech. Chem. Commun. 1958 23 1664. [I21 HOLMES D. B., VONCKEN R. M. and DEKKER J. A., Chem. Engng Sci. 1964 19 209. [I31 PROCHAZKA .I. and LANDAU J., Coil. Czech. Chem. Commun. l%l 26 2961. [I41 OLDSHUE J. Y., Proc. Biochem. 1969 4 51. t151 SHINNAR R. and CHURCH J. M., Ind. Engng Chem. 1960 52 253. [I61 RUSHTON J. H. and OLDSHUE J. Y., Chem. Engng Proc. 1953 49 161. [17] DANCKWERTS P. V., Chem. Engng Sci. 1952 2 1.
[81 PITT K., Ph.D. thesis, University