Ind. Eng. Chem. Res. 1996,34, 2485-2492
2486
Particle-Liquid Mass Transfer in Three-phase Mechanically Agitated Contactors: Power Law Fluids Kamlesh B. Kushalkar and V. G. Pangarkar* Department of Chemical Technology, University of Bombay, Matunga, Bombay 400 019, India
A systematic study of particle-liquid mass transfer coefficients in three-phase mechanically agitated contactors using non-Newtonian power law liquids is reported using the well-known physical dissolution technique. The system used is benzoic acidaqueous (carboxymethy1)cellulose solutions/air. A wide range of variables covering particle size, air flow rate, impeller type, and rheological characteristics has been employed. The results indicated a unique relationship between the particle-liquid mass transfer coefficient and the critical impeller speed for a solid suspension under aerated conditions. A conservative correlation for the particle-liquid mass transfer coefficient which makes allowance for the rheological complexity of the system is prgposed.
Introduction Mechanically agitated gas-liquid, solid-liquid, gasliquid-solid, and liquid-liquid reactors constitute a major class of multiphase reactors. These types of reactors are widely used in the chemical industry due to their reliability of operation and flexibility. Mechanically agitated contactors (MAC) are preferred over sparged contactors in specific situations where the superficial gas velocities are relatively low (10.01 d s ) , as in this range the sparged contactors are inefficient. For satisfactory design of these contactors, the knowledge of gas holdups, flow patterns, heat and mass transfer coefficients, and mixing characteristics is desired. In many applications the fluids encountered exhibit non-Newtonian behavior (froth floatation of mineral ores, fermentation reactions, waste water treatment, etc.). Therefore, particle-liquid mass transfer in non-Newtonian fluids is of industrial importance (Doraiswamy and Sharma, 1984). Over the past several years, extensive efforts have been made to investigate the behavior of rheologically complex fluids in mechanically agitated contactors. Nienow and Ulbrecht (1985) have presented a general review of the studies of gas dispersion in highly viscous and non-Newtonian liquids. Gas dispersion in such liquids occurs at much lower impeller Reynolds numbers because of high viscosities. Bruijn et al. (1974) found that the cavities formed in viscous liquids were very stable and remained attached t o the impeller blades even after the gas was turned off. For single phase mixing the shear thinning nature of the fluid reduces power consumption below that of a Newtonian fluid (Metzner and Otto, 1957; Metzner et al., 1961) in the transition region. As the turbulent mixing regime is approached the shear thinning nature of the fluid becomes unimportant. Machon et al. (1980) have provided data on the effects of shear thinning (carboxymethy1)cellulose (CMC) solutions on power consumption. Nienow et al. (1983) studied a variety of fluids including shear thinning and viscoelastic fluids with a yield point. In the turbulent regime (Re > goo), the power consumption in the rheologically complex solutions was not much different than that of water. Machon et al. (1980) studied the effects of the shear thinning nature of a liquid on the gas holdup. For CMC
* Author to whom correspondence should be addressed. 0888-5885/95/2634-2485$09.00/0
solutions the holdup varied between 1%and 8%. When the shear thinning nature of the liquid was increased, the holdup was decreased. This was attributed to an increase in the proportion of large bubbles which have a shorter residence time in the tank. At all CMC concentrations, two bubble sizes were observed: very tiny bubbles and large bubbles. The tiny bubbles remained in solution for considerably longer times than the larger bubbles. As CMC concentrations were increased, spherical cap bubbles were observed, which did not recirculate to the impeller but rose rapidly to the liquid surface. The large bubbles were present in the flow because of the inability of the impeller to disperse the gas and were not formed by coalescence. Apparently, CMC concentrations affected the nature of the gas cavities of the impeller. Ideally, mass transfer between a particle and a nonNewtonian fluid requires consideration of the nonNewtonian viscosity and elastic effects on flow regimes in the impeller region and the tank, liquid and gas circulation, liquid and gas phase mixing, particle size, and bubble size. The simplest approach used for correlating mass transfer coefficients is to begin with correlations for Newtonian fluids and to modify them to account for non-Newtonian effects mainly due to viscosity (Tatterson, 1991). Three-phase systems are more complex than twophase systems because the presence of the third phase affects the flow behavior existing in two-phase systems. In gas-liquid-solid systems the quantities of interest are the mass transfer, the flooding transition, the nature of gas recirculation, the critical impeller speed for complete gas dispersion, and solids suspension. Chapman et al. (1983b,c) and Nienow et al. (1985a,b) have presented detailed discussions on the design of gasliquid-solid agitated systems. Experimental studies reported in the literature are confined mainly to solid-liquid (two-phase) mass transfer in agitated Newtonian fluids (Jadhav and Pangarkar, 1991; Nienow, 1975; Chapman et al., 1983a; Hughmark, 1980; Harriott, 1962). However, studies on particle-liquid mass transfer in (two-phase)non-Newtonian fluids are scarce (La1et al., 1988). Astarita and Mashelkar (1977) have studied gas-liquid mass transfer in non-Newtonian liquids. Keey et al. (1970) have measured mass transfer rates for the dissolution of o-nitrophenol spheres suspended in pseudoplastic fluid 0 1995 American Chemical Society
2486 Ind. Eng. Chem. Res., Vol. 34, No. 7, 1995
in a batch mixer. La1 and Upadhyay (1981) and La1 et al. (1988) have reported mass transfer coefficients for benzoic acid spheres suspended in agitated CMC solutions. However, there is no information available on particle-liquid mass transfer in three-phase systems with non-Newtonian liquids in mechanically agitated contactors. It was therefore thought desirable to conduct a study of particle-liquid mass transfer to nonNewtonian liquids in three-phase MAC. An attempt is also made to study the effect of all the important variables on mass transfer and to find a simple correlation.
For the gas sparging controlled regime, Nishikawa et al. (1981) related the average shear rate t o the superficial gas velocity as yav = 5000Vg
(2)
This average shear rate was used to estimate the apparent viscosity due to gas sparging. Metzner and Otto (1957) proposed that in the agitation controlled regime the average shear rate in an agitated vessel is directly proportional to the speed of rotation. Yav
Theoretical Aspects
=a
- ~
(3)
Three-phase mechanically agitated systems are quite complex due to involvement of a multitude of variables such as operating parameters (vessel geometry, nature and number of baffles, type and size of impeller, and speed of rotation) and physical parameters (liquid density, viscosity, diffisivity, shape and size of particles, density of particles, etc.). Also, the flow patterns, velocity profiles, and turbulence in three-phase MAC are very complicated. Rheological properties of the fluid influence the power consumption and heat and mass transfer rates in MAC. Rheological Aspects of Shear Thinning (Power Law) Fluids. Shear thinning fluids show a decrease in viscosity with increasing shear rate. Polymeric solutions and melts and various greases exhibit pseudoplastic behavior. The present study deals with aqueous solutions of (carboxymethy1)cellulose(CMC)which are pseudoplastic in nature. Many fermentation broths in MAC are pseudoplastic in nature. The stress-strain relationship of such fluids can be explained by a simple twoparameter model, called the “Power Law” model, which is expressed as
The proportionality constant, a, was found to vary between 10 and 13 for turbines, propellers, and paddles. Equation 3 is acceptable only under creeping flow conditions. However, even under such conditions the constancy of a is doubtful. Equation 3 is not applicable for higher Reynolds numbers (Skelland, 1967). a is found to be a function of both the rheology of the fluids and the geometric parameters of the system, uiz,impeller type and size, tank size, impeller clearance, etc. The shear rate given by eq 2 can only characterize the flow near the impeller in the laminar region and is much smaller than the tip shear rates (van’t Reit and Smith, 1973). La1 et al. (1988) have correlated their data using dimensionless analysis and a modified Kolmogoroff s theory approach. The dimensionless groups used were as follows:
t = Ky”
The modified particle Reynolds number was defined as
(1)
For shear thinning fluids n is less than one and for shear thickening fluids n is greater than one. This model also explains Newtonian fluids when n = 1. Many models that are proposed to explain this behavior involve two or more parameters (Lal et al., 1988). Though most of these models are proposed for pipe flow, the same are also valid for the flow field established in mechanically agitated contactors. The shear rate and the shear stress are to be measured properly, and appropriate flow models must be used to estimate the apparent viscosity. It was observed that almost all the workers assumed the apparent viscosity to be proportional to W-l. The proportionality constant was different depending upon the fluid impeller system and the reference device selected. Either the reference device was a rotating cylinder of the same diameter as the impeller or the situation was assumed analogous to that of pipe flow. For shear thinning liquids the power law is assumed and the apparent viscosity is given as a function of some average shear rate. The operating regime in threephase MAC can be broadly divided into two regimes, an agitation controlled regime and a gas sparging controlled regime, depending upon whether the flow pattern in the MAC is dictated by the impeller or the gas sparger. For the agitation controlled regime in an agitated tank,the average shear rate is a constant times the impeller rotational speed (Metzner and Otto, 1957).
Sh, = k,,DJDm
(4)
Re, = nND2glp,
(5)
R&i = nNDD,gIp,
Re‘,= ND5’3D,4/3glH1/3e3pa
(7)
The apparent viscosity used by these workers was that defined for a cylinder having a diameter equivalent to the agitator diameter. pa = n1-nK(4nN)n-1
(8)
These workers reported that the effects of almost all the operating and physical variables (e.g., impeller type and diameter, vessel diameter, number of blades, blade width, particle size, solids loading, bottom clearance, speed of agitation, etc.) on the particle-liquid mass transfer coefficient in two-phase non-Newtonian systems were similar to the results obtained for Newtonian fluids. Their data for non-Newtonian fluids were found to satisfy their correlation for Newtonian systems within f30%. The correlation is as follows:
Sh, = 2
+ 0.474Re‘p2/3Sc1/3
(9)
Experimental Section The experimental program included a study of the influence of all important variables which affect the particle-liquid mass transfer rates. The system used was the dissolution of benzoic acid particles in aqueous non-Newtonian solutions of (carboxymethy1)cellulose
Ind. Eng. Chem. Res., Vol. 34, No. 7, 1995 2487 Table 1. Impeller Dimensions ~
impeller disc turbine DT1 pitched blade turbine (downflow) PTDl pitched blade turbine (upflow) PTUl
diameter, m 0.10 0.10 0.10
~~~
~~
no. of blades 4 4 4
blade width, m 0.02 0.02 0.02
Table 2
blade thickness, m 0.0019
hub diameter, m 0.05 0.05 0.05
0.0019
0.0019
20 1
A. Physical Properties of Non-Newtonian Fluids Used diffusivity, solubility, K, Pass" n kmol/m3 0.95 0.0348 0.0058 0.985 0.25 1000 1.00 1030 0.0440 0.750 0.82 0.0406 0.0452 0.75 1.50 1040 0.1350 0.633
concof density, CMC.wt% kdm3
~
B. Particle Characteristics average screen diameter, d,, 10+m 550 655 856 1100 surface area, m2kg 16.65 13.98 10.70 8.33 0.5 0.5 0.5 0.5 shape factor, 0 0.67 0.67 0.67 sphericity, ly 0.67 820 490 639 mean particle diameter 410 (d, $dv),1 W m ~~~
~
(CMC) (Jadhav and Pangarkar, 1988). An acrylic cylindrical vessel of diameter 0.3 m having a flat bottom was used. The clear liquid height was equal to the diameter of the tank. Disc turbines (DT),upflow pitched blade turbines PI"),and downflow pitched blade turbines (PTD) were used as per the details given in Table 1. The ratio of impeller diameter to vessel diameter was kept constant at 1/3. Benzoic acid granules of average particle sizes ranging from 550 to 1100 pm were used. The particle loading was kept constant at 0.5% (wt) in order t o avoid saturation of the liquid in the batch experiments. Air was sparged using a ring sparger. The ratio of the diameter of the ring sparger to the diameter of the impeller was fxed at 0.8 (Rewatkar et al., 1991). The superficial gas velocity was vaned from 0.015 to 0.03 m/s. Benzoic acid particles in aerated liquid are known t o impart a foaming tendency (Jadhav and Pangarkar, 1988). To avoid foaming during the experiment a known amount of tricresyl phosphate was added as an antifoaming agent. The antifoaming agent lowers the gas holdup by promoting coalescence of fine bubbles. However, it has a very insignificant effect on the mass transfer coefficient (Jadhav and Pangarkar, 1991). The densities of the non-Newtonian CMC solutions were experimentally determined. A Haake viscometer (model RV3) was used for determining rheological characteristics. Diffusivities of benzoic acid in Newtonian and non-Newtonian aqueous CMC solutions were obtained from the literature (Hansford and Litt, 1968). Table 2 gives the physical properties of the various experimental systems used.
Results and Discussions The initial and final concentrations of benzoic acid dissolved in CMC solutions were measured by titrating with dilute NaOH solutions. ~ S was L calculated by the following formula:
Critical SuspensionSpeed, Ne. Due to the specific nature of the experimental setup and system being
E
200
000
1000
1 200
PARTICLE SIZE, p m
Figure 1. Variation of critical impeller speed with particle size for disk turbine (DT). 25
I
I
K
0 15
d
W
a 5
0
l
600
,
l
l
000
l
l
l
l
1000
l
l
l
l
1200
l
l
l
1400
PARTICLE SIZE, p m
Figure 2. Variation of critical impeller speed with particle size for pitched blade downflow turbine VI").
studied, values of N , and Nsg were experimentally measured and the same were used later. The reproducibility of the critical speed values was also checked by repeating a few experiments and was found t o be within f2%. The Nsg values for DT and PTD were found to be much higher than N , as observed in the case of Newtonian liquids (Chapman, 1983a). The difference in N s and Nsgfor PTU was smaller relative to that for PTD and DT. Figures 1-3 show the Nsg and N , values for various impellers and particle sizes. The Nsg values were found to increase with the superficial gas velocity for all impellers. Rewatkar et al. (1991) and Chapman et al. (1983a) have made similar observations.
2488 Ind. Eng. Chem. Res., Vol. 34, No. 7, 1995 25
m
2 P
-
r
I
Vessel i . d . = 0.3m Particle size = 655 Fm lm eller = DT C f i = 1/3
Vessel i.d. = 0.3 -n bmp,ell;er,?je = PTU
-
C/T
- v,V,
= 1/3 = 0015 m / s
4'0
LT
0
w a Ln
m N , ,
LL&UN., -Nag,
l.k CMC l.B CMC
I
k
"
5 400
= 0 m/s = 0 m/s = 0 m/s
I
800
PARTICLE SIZE,
Qcd3L130.2- CMC. V, MMn 1.0% CMC, V, tkkt+1.5% CMC, V,
0.25% CMC
0.25s CMC
0.0
1200
3.0
5.0
pm
7.0
9.0
11.0
13.0
15.0
Speed of Agitation N, rev/s
Figure 3. Variation of critical impeller speed with particle size for pitched blade upflow turbine (PTU).
Effect of N on k S L . Particle-liquid mass transfer coefficients for 0.25%, 1.0%, and 1.5% aqueous CMC solutions were measured using DT, PTD, and PTU impellers. The impeller size was kept constant (DIT = 1/3). Figures 4-7 show the effect of the speed of agitation, N , on the particle-liquid mass transfer coefficient, KSL. The K s L values increased with an increase in N for all the impellers for a given particle size and superficial gas velocity. As observed in the case of DT and PTD the K S L values for two-phase (solid-liquid) systems were marginally higher than those for threephase (gas-liquid-solid) systems. It was also observed that the N , values were lower than Nsgvalues. It can be observed from Figures 4-7 that the K S L values for all the particle sizes are approximately similar at N = Nsg(marked with an asterisk). Similar observations were also made for unaerated conditions (Jadhav and Pangarkar, 1991; Nienow, 1969; Conti and Sicardi, 1982) and aerated conditions (Kushalkar 8z Pangarkar, 1994) with Newtonian liquids. The dependence of ksL on speed of agitation in the range of parameters and operating condition in this work can be expressed as KSL = N" where n varied between 0.95 and 1.2. Effect of d p on k S L . The particle-liquid mass transfer coefficient for benzoic acid particles of average sieve sizes of 655, 856, and 1100 pm were measured experimentally as shown in Figures 4-7. The values of K S L decreased as the particle size increased. This trend was observed with all the impellers similar to the observations made for Newtonian fluids. The average dependence of K s L on d, can be correlated as K s L = d,-0.45. This agrees well with the dependence, K S L = dp-0,5,as observed by Kuboi et al. (1974) and Jadhav and Pangarkar (1991) for unaerated systems and by Kushalkar and Pangarkar (1994)for aerated Newtonian systems. Mass Transfer Correlation The trend of the variation of mass transfer coefficients with the speed of agitation for non-Newtonian fluids is similar to that observed in the case of Newtonian fluids.
Particle size = 655 p m Im eller = DT = 1/3
Ch 4.0
I: v)
E
0
2.0
1711130.25% CMC V - 0.015 m/s CMC: V: 0.015 m/s
-1.0~ XXXM 1.5%
0.0
3.0
5.0
CMC, V,
= 0.015 m/s
7.0 9.0 11.0 13.0 15.0 17.0 19.0 Speed of Agitation N, rev/s
Figure 4. Variation of ksL with speed of agitation for disk turbine: V, = (a, top) 0 d s and (b, bottom) 0.015 d s .
Particularly important is the observation that KSL at Nsg is approximately the same for varying d,, impeller type, DIT, and CIT. The same was noted in the case of twophase and three-phase Newtonian systems (Jadhav and Pangarkar, 1991; Kushalkar and Pangarkar, 1994). Thus, Jadhav and Pangarkar's correlation for KSL based on this observation for a two-phase system was extended to three-phase systems. It is likely that such a correlation may have general applicability for particle-liquid mass transfer in MAC. The correlation developed for Newtonian liquids may also be applicable to nonNewtonian liquids provided that appropriate modifications are made to account for the non-Newtonian behavior (Tatterson, 1991). The mass transfer correlation obtained for Newtonian liquids in three-phase MAC (Kushalkar and and Pangarkar, 1994) is
ksL = 1.19 x 10-3(N/N~)1.15~/@~)-0.47 (11) In eq 11the Newtonian or non-Newtonian nature of the liquid affects only the viscosity, p, since all other properties are otherwise measured. The non-Newtonian
Ind. Eng. Chem. Res., Vol. 34,No. 7,1995 2489 4.0
I
3.0
I
Vessel id= 0.3m
Vessel i.d.= 0.3m Particle size = 856 pm Im eller = DT C,& = 1/3 D/T = 1/3
-
P
V, = 0.015 m/s Im eller = PTD C f i = 1/3
2.5 ffl
\
E
-
2.0
Ln
0 7-
X i
2
1.5
Q l l D 0 . 2 5 % CMC V = 0 m/s M1.0s CMC' V' o m/s 1.CMC: V: o m/s
u
-
i ."n
1
I
3.0
6.0 9.0 12.0 15.0 Speed of Agitation N, rev/s
18.0
3.0
6.0 9.0 12.0 15.0 Speed of Agitation
18.0 21.0 rev/s
24.0
N,
3.0
2.5
4
0.5 O
1
0.0
5.0
-
-0.2%
UCEOO.2S!a CMC V = 0.015 m/s $&$&?l.orS CMC: V: = 0.015 m/s XxxxX 1.5s CMC. V, = 0.015 m/s
20.0 10.0 15.0 Speed of Agitation N , rev/s
-1.0%
xxxxx 1.5%
25.0
5.0
10.0
CMC. 856 CMC, 856 CMC, 856
15.0
Speed of Agitation
N,
prn pm pm
20.0 rev/s
25.0
Figure 5. Variation of k S L with speed of agitation for disk turbine: Vg= (a, top) 0 d s and (b, bottom) 0.015 d s .
Figure 6. Variation of KSL with speed of agitation for pitched blade downflow turbine (FTD) for d, = (a, top) 655 pm and (b, bottom) 856 pm.
liquids used in the present work were pseudoplastic CMC solutions which obey the power law model (eq 1) over the operating range covered. The apparent viscosity for such liquids is given by the following expression:
particle-liquid mass transfer data using this apparent viscosity obtained. Figure 8 shows a parity plot of k s L with respect to eq 11. It is evident that the correlation developed for three-phase systems with Newtonian liquids shows large, systematic positive deviations from the experimental data for non-Newtonian liquids. This may be due to errors in the prediction of p a as otherwise there is very little change in the other physical properties, which, incidentally, were measured values. In order to investigate the validity of eq 13 for predicting the apparent viscosity, k s L data were generated for a two-phase (solid-liquid) system using the same compositions of aqueous CMC solutions as used for three-phase experiments. Figures 4 and 5 show the variation of k S L with N for the different particle sizes used. It was noted that for these data the k s L values were also approximately the same at N = N,. The nonNewtonian ~ S data L were found to be in agreement with the correlation of Jadhav and Pangarkar (1991)for Newtonian liquids, which is as follows:
pa=
(12)
For pseudoplastic fluids n is less than one. The correlation proposed by Metzner and Otto (1957)has been used extensively in the literature for estimating the apparent viscosity in MAC. The value of the proportionality constant in their correlation was found to vary between 10 and 13. Niranjan et al. (1990)have used the correlation of Metzner and Otto (1957)with the value of the constant as 13 for the treatment of their data of non-Newtonian fluids. pa = K(13N>"-1
(13)
Therefore, the same equation was employed for estimating the apparent viscosity of the CMC solutions used in this work and correlating the three-phase
kSL
= 1.72
(sc)-O.~~
(14)
2490 Ind. Eng. Chem. Res., Vol. 34,No. 7, 1995 4.0
I
I
t
Vessel i.d.= 0.3m V, = 0.015 m/s
Table 3. Measured Physical Properties of Non-Newtonian Fluids in MAC conc of CMC, wt % density, kg/m3 K,Pa*sn n A. Liquid Saturated with Benzoic Acid (Unaerated) 0.985 0.25 1000 0.0038 0.0875 0.750 1.00 1030 0.1750 0.657 1.50 1040 B. Liquid Saturated with Benzoic Acid (Aerated) 0.25 1000 0.004 0.985 1.00 1030 0.009 0.973 1.50 1040 0.015 0.965 51
/
QMX200.25~ CMC, 655 p m AM& 1.m CMC, 655 p m -ktkl+O.25% CMC, 856 pm URMU 1 . 0 % CMC, 856 p m 0.0 10.0
15.0
20.0
25.0
Speed of Agitation N, rev/s
Figure 7. Variation of k s with ~ speed of agitation for pitched blade upflow turbine (PTU). 51
A
I-
/I
A ”
0
1 2 3 KSL X lO’(EXPERIMENTAL),
4
5
m/s
Figure 9. Panty plot for eq 12 for three-phase non-Newtonian data.
Ksi X lO’(EXPERIMENTAL),
m/s
Figure 8. Parity plot for eq 11 using viscosity parameters for unaerated solutions.
For the calculation of the apparent viscosity to be used for processing the non-Newtonian data eq 13 was employed. At this stage it was thought that the presence of dissolved benzoic acid and dispersed gas may be causing a change in the rheological properties of the CMC solutions. In order t o find out whether such changes occur, the rheological characteristics were determined for two conditions as follows: (1) clear CMC solutions saturated with benzoic acid and (2) CMC solutions saturated with benzoic acid and aerated under agitation. Both these samples were removed from the MAC and studied with the Haake viscometer. The second type of samples were difficult t o handle as large gas bubbles escaped during sampling. However, it was observed that a large number of small bubbles still remained entrapped in the solution sample used for determination of rheological properties. The rheological characteristics of these two types of CMC solutions are given in Table 3 from which it is
evident that the mere presence of dissolved benzoic acid in CMC solutions does not cause significant changes in the rheological properties. However, the aerated CMC solutions clearly showed a distinct increase in the value of n (and a simultaneous decrease in K ) . This increase in the value of n to a value close to unity shows a shift from distinctly non-Newtonian behavior t o a behavior very similar to that for Newtonian liquids. It must be mentioned here that the values of K and n for aerated CMC solutions given in Table 3 are not measured under actual dynamic aerated conditions in the MAC but refer to a sample (devoid of large bubbles) removed from the MAC and tested elsewhere. It is thus apparent that the K and n values of Table 3 are not valid for the actual conditions but may be relatively close to them. In view of this observation, the viscosities were calculated using the rheological data of Table 3 and then used in eq 11. Figure 9 shows a panty plot for eq 11and the k S L data for non-Newtonian liquids which shows a much better agreement than that in Figure 8. It must be noted that this relatively better agreement of the data with eq 12 has been caused by a modification of the apparent viscosity used in eq 11. The agreement is still not satisfactory as shown by the standard deviation (25%), which is relatively high. It is possible that the apparent viscosity under actual conditions (which could not be measured) is different than that predicted from the data in Table 3. It is particularly relevant that the presence of small bubbles increases n values which indicates a clear shift from non-Newtonian behavior t o Newtonian behavior. The apparent viscosity of the dispersion is much lower than the single phase liquid viscosity.
Ind. Eng. Chem. Res., Vol. 34, No. 7, 1995 2491
Similar shifts in the rheological properties of emulsions of two polymeric fluids were reported (Han, 1981) supporting the above argument for a change in the rheological properties of the aerated CMC solutions.
Conclusion Particle-liquid mass transfer in three-phase MAC with non-Newtonian fluids has been studied. The effect of particle size, impeller type, and rheological characteristics on the particle-liquid mass transfer coefficient has been investigated. An attempt is made to extend the correlation developed for particle-liquid mass transfer in three-phase MAC with Newtonian fluids to the data obtained for non-Newtonian fluids. However, a systematic negative deviation is observed. In the present state of knowledge it is difficult to give a reason for the deviation of eq 11 and the non-Newtonian data. However, as pointed out above the presence of a dispersed gas phase in aqueous CMC causes significant changes in its rheological properties. It will be desirable to determine these rheological properties under actual conditions of operation of three-phase MAC so that the correct value of the apparent viscosity can be used in eq 11. In the absence of such information eq 11 may be used to yield a conservative estimate of K S L in threephase MAC with non-Newtonian liquids. Nomenclature Api = surface area of the particles, m2kg Apf = final surface area of the particles, m2Ag A, = surface area of solid particles, m2 C = clearance between the impeller and bottom of the tank, m C* = saturation concentration of solute, km0l/m3 Cf = final solute concentration, kmol/m3 Ci = initial solute concentration, km01/m3 D = diameter of the impeller, m Dm = diffusivity, m2.ss1 d, = average screen size of particle, m D , = equivalent particle diameter, m Dt = diameter of tank, m H = height of the liquid in the tank, m K = power law consistency index, Pa.sn KSL = particle liquid mass transfer, coefficient, ms-l kkL = ksL calculated as per eq 14 using eq 13 k i L = ksL calculated as per eq 11 using eq 13 k i L = ksL calculated as per eq 11 assuming Newtonian behavior for three-phase dispersion N = rotational speed of the impeller, N , = critical impeller speed for suspension of solid particles in unaerated liquid, revs-l Nsg= critical impeller speed for suspension of solid particle in aerated liquid, r e v - l n = flow index Re, = agitator Reynolds number Reg = particle Reynolds number Re, = modified particle Reynolds number Sc = Schmidt number QdeDm) Sh, = particle Sherwood number, ( K ~ ~ D M ) T = diameter of the tank, m t = batch time, s V = volume of the liquid in a batch, m3 V, = superficial velocity of gas, m*s-1 Wf = weight of the solids remaining in the batch, kg Greek Symbols eg = gas holdup, v/v y = shear rate, s-l
e = density of liquid, k g ~ n - ~ t = shear stress, Pa ,u = viscosity of liquid, Pa-s pa = apparent viscosity for non-Newtonian liquid, Pa.s
Literature Cited Astarita, G.; Mashelkar, R. A. Heat and mass transfer in nonNewtonian fluids. Chem. Eng. 1977,100-105. Bruijn, W.; van't Reit, K.; Smith, J. M. 1974,Power consumption with aerated Rushton turbines. Trans. Znst. Chem. Eng. 1974, 52,88-104. Chapman, C. M.; Nienow, A. W.; Cooke, M.; Middleton, J. C. Particle-gas-liquid mixing in stirred vessels - Part I: Particleliquid mixing. Chem. Eng. Res. Des. 1983a,61,71-81. Chapman, C. M.; Nienow, A. W.; Cooke, M.; Middleton, J . C. Particle-gas-liquid mixing in stirred vessels - Part 11: Gasliquid mixing. Chem. Eng. Res. Des. 198313,61,82-95. Chapman, C. M.; Nienow, A. W.; Cooke, M.; Middleton, J . C. Particle-gas-liquid mixing in stirred vessels. Part 111: Three phase mixing. Chem. Eng. Res. Des. 1983c,61,167-181. Conti, R.; Sicardi, S. Mass transfer from freely suspended particles in stirred tanks. Chem. Eng. Commun. 1982,14,91-95. Doraiswamy, L. K.; Sharma, M. M. Heterogeneous Reactions Analysis, Examples and Reactor Design - Vol. 2. Fluid-FluidSolid Reactions; John Wiley and Sons: New York, 1984. Han, C. D. Multiphase flow i n polymer processing; Academic Press: New York, 1981;Chapter 4,pp 149-220. Hansford, G. S.;Litt, M. Mass transfer from a rotating disc into power law fluids. Chem. Eng. Sci. 1968,23,849-864. Harriott, P. Mass transfer to particles - Part I: Suspended in agitated vessels. AZChE J . 1962,8 , 93-102. Hughmark, G. A. Heat and mass transfer for spherical particles in a fluid field. Ind. Eng. Chem. Fundam. 1980,19,198-201. Jadhav, S. V.;Pangarkar, V. G. Particle-liquid mass transfer in mechanically agitated contactors. Znd. Eng. Chem. Res. 1991, 30,2496-2501. Keey, R. B.; Mandeno, P.; Tuoc, T. K. Dissolution of freely suspended solid particles in an agitated non-Newtonian fluid - Rheology and mass transfer. Proceedings of Chemaca-70, Melbourne; 1970,pp 53-70. Kuboi, R.; Komasawa, I.; Otake, T.; Iwasa, M. Fluid and particle in turbulent dispersion - Part 3. Particle-liquid hydrodynamics and mass transfer in turbulent dispersion. Chem. Eng. Sci. 1974,29,659-668. Kushalkar, K. B.; Pangarkar, V. G. Particle-liquid mass transfer in three phase mechanically agitated contactors. Znd. Eng. Chem. Res 1994,33,1817-1820. Lal, P.; Upadhyay, S. N. Mass transfer from suspended solid spheres in agitated power law fluids. Chem. Eng. Sci. 1981, 36,1865-1866. Lal, P.; Kumar, S.; Upadhyay, S. N.; Upadhya, Y. D. Solid liquid mass transfer in agitated Newtonian and non-Newtonian fluids. Znd. Eng. Chem. Res. 1988,27,1246-1259. Machon, V.;Vlcek, A.; Nienow, A. W.; Solomon, J. Some effects of pseudoplasticity on holdup in aerated, agitated vessels. Chem. Eng. J . 1980,19,67. Metzner, A. B.; Otto, R. E. Agitation of non-Newtonian fluids. AZChE J . 1957,3,3-10. Metzner, A. B.; Feehs, R. H.; Ramos, H. L.; Otto, R. E.; Tuthill, J. D. Agitation of viscous Newtonian and non-Newtonian fluids. AZChE J . 1961,7,3-9. Nienow, A. W. Dissolution mass transfer in turbine agitated baffled vessel. Can. J . Chem. Eng. 1969,47,248-258. Nienow, A. W. Agitated vessel particle-liquid mass transfer: A comparison between theories and data. Chem. Eng. J . 1975, 9,153-160. Nienow, A. W.; Ulbrecht, J. J. Gas liquid mixing and mass transfer in high viscosity liquids. In Mixing of Liquids by Mechanical Agitation; Ulbrecht, J. J., Patterson, G. K., Eds.; Gordon and Breach: New York, 1985;Chapter 6. Neinow, A. W.; Konno, M.; Bujalski, W. Proceedings of the 5th European Conference on Mixing, Wurzburg, Germany; BHRA Fluid Eng.: Cranfield, England, 1985a;pp 1-17. Neinow, A. W.; Konno, M.; Warmoeskerken, M. M. C. G.; Smith, J . M. Proceedings of the 5th European Conference on Mixing, Wurzburg, Germany; BHRA Fluid Eng.: Cranfield, England, 198513;pp 143-161.
2492 Ind. Eng. Chem. Res., Vol. 34,No.7,1995 Niranjan, K.; Pandit, A. B.; Rielly, C. D.; Davidson, J. F.; Cumby, T. R.; Fonebi, J. F. Convex bladed mixed flow (CBMF) impeller: A high performance agitator for mixing slurries. J . Agric. Eng. Res. 1990,45,225-239. Nishikawa, M.; Nakamura, M.; Hashimoto, K. Gas absorption in aerated mixing vessels with non-Newtonian vessels. J . Chem. Eng. Jpn. 1981,14,227-232. Rewatkar, V. B.; Raghava Rao, K. S. M. S.; Joshi, J. B. Critical impeller speed for solid suspension in mechanically agitated three phase reactors. 1. Experimental part. Ind. Eng. Chem. Res. 1991,30,1770-1783. Skelland, A. H. P. Mixing and Agitation. In Non-Newtonian Flow and Heat Transfer; Wiley: New York, 1967;pp 308-357. Tatterson, G. B. Fluid Mixing and Gas Dispersion in Agitated Tanks; McGraw-Hill, Inc.: New York, 1991;Chapter 6.
van't Riet, K.; Smith, J. M. The behaviour of gas-liquid mixtures near Rushton turbine blades. Chem. Eng. Sci. 1973,28,10311037.
Received for review September 28, 1994 Revised manuscript received April 12,1995 Accepted April 26, 1995" IE940568E
Abstract published in Advance ACS Abstracts, June 1, 1995.
