Biotechnol. Prog. lQQ2,8, 233-239
233
Mixing of Highly Viscous Simulated Xanthan Fermentation Broths with the Lightnin A-315 Impeller Enrique Galindot and Alvin W. Nienow* SERC Centre for Biochemical Engineering, School of Chemical Engineering, The University of Birmingham, Edgbaston, Birmingham B15 2TT, England
The power characteristics of the Lightnin A-315 impeller have been evaluated in solutions of Xanthan and Carbopol of similar rheological properties, the latter being transparent to allow flow visualization. With the impeller pumping downward (forward mode), a t Re < 20, P o a Re-’; for 20 < Re < 300, P o a Re-1/2;and at Re > 600, P o was almost constant -1. In addition, for 20 IRe I250, higher values of P o were found a t equal Re, a t higher levels of elasticity in the fluids. In the reverse mode, the same trend was found although P o was lower a t the same Re. Upon aeration, no significant influence of the aeration rate (0.25-1.0 w m ) upon the gassed power was observed. In the forward mode, a decrease in the PodPo ratio was observed, reaching levels of about 0.5-0.6 a t the highest stirring speed (-7 s-l, Re = 200-800). During operation in the reverse mode, a minimum (or a plateau) Po,/Po value was observed and better gas dispersion was achieved. With the highest Xanthan concentration (35 kg m-3), high torque fluctuations were observed, though these were negligible in the inelastic Carbopol solutions of similar apparent viscosity. Video recordings made with transparent Carbopol solutions revealed very poor gas dispersion. Well-defined “cavernsn were also observed in the Carbopol solution. The reverse mode gave cavern volumes up to 60 % larger than the forward mode, if the modes are compared a t the same power drawn. The previously derived equations for cavern sizes which have been shown to predict well for a range of impellers were not found to be entirely satisfactory with this one in either pumping mode. Although the A-315 impeller may not be a suitable impeller for mixing highly concentrated Xanthan broths because of the drastic power drop and large torque instabilities, the reverse mode is an interesting possibility for moderately concentrated Xanthan broths giving better gas dispersion, less torque fluctuations, lower power drop, and larger cavern volumes than the forward, downward pumping mode.
Introduction Xanthan gum fermentation is probably the most complex fermentation process in terms of rheological property variations and associated mixing problems. The changes in viscosity during culture exceed 4 orders of magnitude, which is greater even than that found in high-viscosity polymerization processes in the chemical industry. The economics of Xanthan production is very dependent on the final gum concentration (1,2), and this, in turn, is a function of cultivation policies (e.g., fed-batch culture (3, 4 ) ) ,linked to the achievement of good mixing. Improvements have been reported in the bacterial strain (51, in the culture medium (61, and in feeding policies (7,8)in order to improve the production process of this gum. However, the limiting step is the ability to keep the highlyviscous broth well mixed, especially on the large scale. Variables such as the temperature (91, pH (IO), and dissolved oxygen (11)are critical, and bad mixing leads to poor control of them and, in turn, lower yields and/or lower Xanthan quality. The change in rheological properties of broths during the course of a batch fermentation leads also to increasing pseudoplasticity, viscoelasticity, and yield stress values. This last characteristic,the yield stress, makes it especially
* To whom correspondence should be addressed.
t Present address: Instituto de Biotecnologia, Universidad Nacional Aut6noma de MBxico, Apdo. Post. 510-3, Cuernavaca, Mor. 62271, MBxico.
8756-7938/92/3008-0233$03.0010
difficult to achieve good mixing because, beyond certain distance from the impeller, the fluid is stagnant. In these stagnant regions where only diffusional mass and heat transfer can occur, the productivity is practically reduced to zero. A series of papers (12-16) have studied the size of the well-mixed zone (the so-called “cavern”) in fluids having a yield stress when they are agitated by a number of impeller configurations. Agitation has traditionally been with the Rushton turbine, and it is probably still the most used impeller in the fermentation industry. However, the Rushton turbine has some disadvantages (17) including a high power number, high levels of shear stress in the vicinity of the impeller, a nonuniform spatial distribution of energy dissipation rate within the tank and a drastic drop in power on aeration, this latter phenomenon being particularly pronounced in viscous fluids. One approach to improving the mixing in a Xanthan fermentation is to replace the “standard”Rushton turbine with other impeller geometries, which might be expected to perform better (17). However, there is a lack of fundamental power data, especially in rheologicallycomplex fluids with almost all other impellers, including the recently-introduced hydrofoil type. Such impellers have been called by their manufacturers “high-efficiency hydrofoils”. They have large profiled blades and are designed to meet the needs of processes demanding high levels of gas dispersion, bulk blending, and mass transfer (asin viscous fermentations). Examples of these impellers
0 1992 American Chemical Society and American Institute of Chemical Engineers
Biotechnol. frog.., 1992, Vol. 8, NO. 3
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Table I. Rheological Properties of the Fluids fluid K,Pa.sn n A,Pa.sb b Xanthan, 15 kgm-3 19.2 0.12 19.1 0.34 Xanthan, 25 kgm-3 29.6 0.15 80.1 0.25 Xanthan, 35 kgm-3 34.8 0.18 192.2 0.19 Carbopol, 2 kg m-3 34.6 0.26
FORWARD ( D O W N 1
d
Figure 1. Lightnin A-315 impeller.
are the Prochem Maxflo T and the Lightnin A-315. The Maxflo T has been reported to give an improved performance in comparison to Rushton turbines in a mycelial fermentation (18). However, there are no reports documenting the mixing performance of this type of impeller in fluids with rheological properties similar to those of the broths in Xanthan fermentations. The aim of this work was to characterize, in terms of power consumption and well-mixed cavern development, the Lightnin A-315 impeller (Figure l ) , which the manufacturers claim (19,20)is able to disperse 86% more air than a disc turbine at the same power input. They also recommend that it be operated in the downward pumping mode. However, downward pumping impellers have been shown to create large flow instabilities in this mode upon aeration which in turn lead to torque fluctuations (21). Upward pumping pitched blade turbines eliminate this problem in water (22) and so both forward (downward) and reverse directions of rotation are tested here, the latter direction being used without inverting the impeller.
Experimental Procedures The experiments were performed in a flat-bottomed cylindrical vessel of diameter 0.45 m with an equal working liquid depth and with four 10% strip baffles. For ease of observation, the tank was constructed of transparent Perspex. The A-315 impeller had a diameter, defined as the diameter of the circle that encloses the projection of the impeller onto a plane, of 0.22 m (DIT = 0.49) and was positioned at a clearance of 0.21 m from the tank bottom. The temperature of the fluid was controlled at 25 f 1 “C by means of recirculating water through the jacket. Air was introduced through a centrally placed point sparger at rates up to 1 wm, monitored by a set of calibrated rotameters. The experimental fluids were (i) three solutions of a food-grade Xanthan (Rhodigel; Rh6ne-Poulenc, Paris, France) which were opaque and (ii) a solution of Carbopol 940 (B.F. Goodrich, Brecksville, OH) which has a similar shear stress-shear rate relationship and a yield stress and is also transparent and ideal therefore for flow visualization. The Carbopol solution was prepared as described elsewhere (23),but the pH was adjusted to 5.8. The highest concentration Xanthan solution (35 kg m-3) was prepared in the tank by means of a pair of A-315 impellers. In order to avoid microbial contamination in the Xanthan solutions, 5 kg m-3 of a sodium salt preservative (Nipasept; Nipa Lab., Llantwit, U.K.) was added. Lower concentrated solutions (25 and 15 kg m-3) were prepared by successive dilutions but the Nipasept concentration was kept constant. The actual Xanthan concentration was verified by precipitation with ethanol. Rheological properties of the fluids were measured at 25 O C in a Contraves 30 rheometer (Zurich, Switzerland)
ry,Pa
8.7 15.9 20.7 27.1
using a concentric cylinder system. Rheograms were obtained by means of a Rheoscan device in a range of 5-200 s-l. The rheological data were fitted to the Ostwald de Waele model (“power law”, 7 = K y n ) having high regression coefficients. Viscoelasticity was measured in a Model 19 Weissenberg rheogoniometer (SangamoWeston, Dorking, U.K.). The first normalstress data were also fitted to a power law equation ( N I =Arb). The yield stress was measured according to the stress relaxation technique proposed by Hannotte et al. (24). The power was measured by an accurate strain gauge-telemetry system (25). Cavern dimensions in the Carbopol solution were measured after injection of 10 mL of a 2% (w/v) methylene blue solution in the impeller zone and allowing5-10 min to clearly define the cavern boundaries. Video and photographs were taken, and the cavern dimensions were measured from the photographs by means of a calibrated scale placed within the fluid previous to the experiments. The addition of the dye did not change measurably the rheologicalproperties of the Carbopol solutions. It should also be noted that the cavern size remained unchanged over several hours if the agitation conditions were not changed. Thus, though it has been argued by rheologists that the concept of a true yield stress is a myth (411,this work strongly supports Elson’s contention (16) that, at least in the field of mixing, yield stresses are an engineering reality (42).
Results and Discussion Rheology. Table I presents a summary of the rheological properties of the fluids used in this study. The data for the Xanthan gum solutions agree very well with previous work (26) where the same batch of the polymer was used as well as the same preservative concentration. If compared with data in the literature, the viscoelasticities, in terms of the Weissenberg number (data not shown), are also similar to those reported recently (27,281. K and n values are within the range previously reported (see, for example, the survey in ref 29). ry values, determined by the same technique, are in agreement with those reported previously (24). The Carbopol solution showed shear stress-shear rate and yield stress values similar to those having the highest Xanthan gum concentration. However, no measurable elasticity was present which is in accord with other results which have also found it to be zero or very small (26). Of course, a precise fitting of rheological properties is not possible since it is the uniqueness of those properties which makes Xanthan a commercially important product. Ungassed Power (Forward, Downward-Pumping Mode). In order to define a Reynolds nuqber, the Metzner and Otto (30) approach was used, i.e., rev = k 3 giving Re =
1\12-D2
Kk;-’
However, because of the lack of a k, for this impeller, a value of 11.5 was taken which has been found to be suitable for many, high-speed, small impellers; and anyway, the particular value adopted does not change the trends in the power curves.
235
Blotechnol. Prog., 1992, Vol. 8, NO. 3 loo D
i
r
xanttlon I kg m - ’ l -
^.
-. 0
15 25 35
. 0
10
0
i?
J loo
1
I
10’
10’
10’
Re
Figure 2. Ungassed power number versus Reynolds number with agitation in the forward (downward) mode.
Figure 2 shows the power number (Po) versus Reynolds number (Re) plot which has three distinct zones. At Re below 20, Po a Re-’ as is usually found in the laminar region for the three Xanthan concentrations tested. In this Re region, higher values of Po were found for the more concentrated Xanthan solutions (25 and 35 kg m-3) compared with Po at the 15kg m-3. Thus, higher Po values correlate with higher levels of viscoelasticity (see Table I). At Re = 20, there seems to be an inflection point in the power curve. Above that value and up to Re = 300, Po a Re-1/2(exponents between -0.46 and -0.52). Again, the absolute power numbers were different in the fluids tested. Again at equal Re, higher levels of viscoelasticity give higher Po values. Similar results have been obtained in a previous work (26)using a Scaba 6SRGT impeller. These results further support previous findings (32-34) indicating that viscoelasticity generally tends to increase Po. A t Re > 500, the power data tend to converge to about 1. Because this is the first time that power curves are reported for the A-315 with very viscous (and viscoelastic) fluids, no comparisons can be made. However, the shape of the power curve of the A-315 was very similar to that reported (35)for a similar type of impeller (the A-320 with three blades). Using water, the only Po value for the A315 is given by Weetman and Oldshue (36) as 0.75. Unpublished results of Nienow (37) obtained in an industrial fermenter and McFarlane (31)in a 0.61-m tank give values of 0.75 and 0.77, respectively. Experiments carried out here in water showed Po remaining at about 1.0 in the turbulent regime (Re N lo5). Among the possible causes of the differences are the following: (a) the way the impeller diameter is defined, (b) the accuracy of the power measurement, (c) the differences in the DITratio, and (d) the scale of operation. Nevertheless, this discrepancy is somewhat surprising because the strain gauges were carefully calibrated and a Rushton turbine (DIT = 0.5) operating in water also a t Re N lo6gave a Po value of 5.7, which is typical for this impeller on this scale (38). Ungassed Power (Reverse “Upward-Pumping” Mode). Figure 3 shows the power curves when the impeller was operated in reverse. In all the Xanthan solutions over the whole Re range, Po values were lower when compared to the forward mode. The different “angles of attack” of the blades are the reason for this difference. In this mode, there are three different regions with Po related to Re as quoted in Table 11. At Re < 30, Po a Re-l; for 30 IRe I100, Po a Re-’/3; and for 100 IRe I300, Po a Re-1/2. As observed in the forward mode, in general, the higher the viscoelasticity, the higher the Po. Again for Re > 500, the Po values converge. Gassed Power (Downward-PumpingMode). Figure 4 is a plot of the ratio of aerated to unaerated power number
J loo
15
25 35
1
I
,
10’
102
io3
Re
Figure 3. Ungassed power number versus Reynolds number with agitation in the reverse mode. 1.2 -
1.0
-
0.8 -
$18 0.6 0.4
-
o’2
-
Forward mode
I
1
I
Re
Figure 4. Gassed to ungassed power ratio as a function of Reynolds number with agitation in the forward mode. Aeration rate = 1 Wm. Table 11. Constants Describing the Best Exponential Fit of Po versus Re Data for Xanthan Solutions Using the A-315 Impeller in Reverse Mode Xanthan, kg m-3 Re range 15 25 35 1-30 slope -0.99 -1.01 -1.01 intercept 81 87 106 r 0.999 0.999 0.999 30-100 slope -0.33 -0.31 -0.36 intercept 10 10 14 0.988 r 0.995 0.976 100-300 slope -0.47 -0.51 -0.52 18 24 30 intercept r 0.994 0.996 0.986
(PodPo) against Re for the Xanthan solutions. The data in Figure 4 were obtained at 1wm, but the values were independent of aeration rate between 0.25 and 1.0 w m (and this was also found for Carbopol; see Figure 7). Figure 4 shows a progressivedecrease in Po,/Po as Re is increased. In general, the higher the Xanthan concentration, the lower the value of the average PodPo at a given Re. High torque oscillations were observed in the highest Xanthan gum concentrations, their magnitude being indicated by the error bars shown in Figure 4 (and also Figure 6). Visual observations in the transparent Carbopol solutions revealed that very poor gas dispersion was achieved, even at high speeds, and that torque oscillations were less than about *7% at 1 w m and f12% at 1/4 wm. Given the similarity of the rheological properties apart from viscoelasticity and the equivalent Re range, it must be concluded that these increased torque fluctuations come
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;:I
Xanthan i k o m - ' l
15
i
25
i
35
r
Carbopol
12[
I Re
0.8
100
150
0 6 Xaithon I kg m - 3 1
20c 250
3
35 25
0
~5
0
0 4
R e v e r s e mode
20
10
30
Figure 5. Po,/Po as a function of the yield stress of Xanthan and Carbopol solutions agitated in the forward mode. from enhanced flow instabilities associated with the high level of elasticity in the Xanthan solutions. No exactly comparable Po,/Po data exist in the literature. However, the lower values of Po,/Po as Xanthan concentration increases have been observed with Rushton turbines (32,39)and the curved-blades of the Scaba 6SRGT impeller (26). Nevertheless, in the former cases a typical minimum in Po$Po is reached (321, a phenomenon that was not observed with the A-315 impeller operating in this mode. Different ways of correlating the data were tested, and yield stress was the parameter which best correlated the drop in power as shown in Figure 5, especially at higher Re. Yield stress has been shown to correlate successfullythe minimum PodPo value in Rushton turbines (39). These data suggest that the yield stress is playing a leading role in determining the drop in power, at least with this impeller geometry. Gassed Power (Reverse Mode). Figure 6 shows the power drop (Po,/Po) as a function of the Re number for the Xanthan solutions, and Figure 7 shows the data for Carbopol. The behavior was quite different from that observed in the forward mode saving only the fact that, the higher the Xanthan concentration, the lower the values of Po,/Po. As compared with the forward mode, the aeration level seemed to affect more the Po,/Po ratios in the reverse mode. Slightly lower Po,/Po values were obtained with the solutions containing 15 and 25 kg m-3 Xanthan when the aeration rate was higher (1 versus 0.25 wm). On the other hand, in the most concentrated Xanthan solution slightly higher average value in Po,/Po were obtained as the aeration rate was increased from 0.25 to 1 w m (data not shown). Different trends were observed for the fluids tested. The 15 kg m-3 Xanthan solution exhibited a mild decrease inPo,/Po over the whole Re range. The solution containing 25 kg m-3 Xanthan showed first a decrease (up to Re = loo), and then a plateau value of about 0.63 was obtained. The solution of the highest Xanthan concentration (35 kg m-3) showed very high torque instabilities and reached a minimum in PodPo, followed by an increase in this ratio at Re above 150. Po$Po values as low as 0.2 were reached in this condition. The behavior of the Carbopol solution (Figure 7) was similar to the highest Xanthan concentration but had considerably higher Po,/Po values and less than 3 95 torque vibrations at both aeration rates. As observed in this transparent fluid, the increase in Po,/Po at Re > -100 was coincident with better gas dispersion.
1000
100
10
r Y( P a )
Re
Figure 6. Gassed to ungassed power ratio as a function of Reynolds number with agitation in the reverse mode. Aeration rate = 1 wm.
"'061
Mode
0.2
1 I
m
Cyvm 25 1 0
Farword
A
Reverse
A
0
1
I
100
10
I
1000
Re
Figure 7. Gassed to ungassed power ratio as a function of Reynolds number for 0.2% Carbopol solution.
In this case, no single rheological parameter was able to correlate either the (Pog/Po),i, or the plateau Po,/Po values at a given Re. It is clear that this subject deserves more work. However, from the practical point of view, the reverse, upward mode seems to be an interesting possibility to deal with moderately concentrated Xanthan broths since both a lower drop in power and better gas dispersion are achieved than with the conventional forward, downward mode. Cavern Sizes. A number of papers (12-16) have established that when mixing fluids with a yield stress, a well-mixed, cylindrical cavern forms. For caverns of diameter less than that of the tank, its size has been shown to be given by (16)
where Pot is the power number in the turbulent region. However, strictly from the theory by which the equation was originally derived, based on a torque balance (12,131, the power number in the equation should be the power number for the actual operating conditions. Later, it was argued (14) that Pot was preferable, first, because the flow in the cavern is likely to be turbulent in nature even though the bulk of the fluid may be stagnant, and second, because Po, is constant and much more readily available in the literature. The aspect ratio of the cylindrical cavern HJ D, is known to vary with the type of impeller, ranging from 0.4 for radial-flow Rushton turbines to 0.75 for axialflow marine propellers (16).
Biotechnoi. Prog., 1992, Vol. 8, No. 3
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N (s-'1
I' I
5.3 2.7 Figure 8. Photographs and traced outlines of the caverns generated by the impeller operating in the forward (downward) mode, as a function of the stirring speed. Concentration of Carbopol = 2 kg m-3.
When the cavern reaches the vessel wall, the height of the cavern increases with the stirring speed such that
HJD, = N p (3) the exponent p being a function of the impeller type. Elson (16) quoted p values ranging from 0.76 (for marine propeller) to 0.88 (for Rushton turbines) while a value of 0.54 has been found for the Scaba 6SRGT (26). Figures 8 and 9 show photographs of typical results along with the traced outlines of the cavern boundaries (as seen from one side of the tank). Figure 8 shows the forward (downward) mode, and Figure 9 shows the reverse mode. Before the cavern touches the wall, the shape is ovoidal and shifted away from the direction of pumping as reported by Solomon et al. (12) for dual impeller systems, where one of them had an axial component of flow, and by Elson (16) for single impellers of that type. When the cavern reaches the vessel wall, the shape resembles more a doughnut with four protuberances between the baffles, but there is now some slight shift toward the direction of pumping. It is assumed as previously (16) that the cavern can be represented by a right circular cylinder. Although the shape is not exactly so, the error in estimating the cavern volume by making this assumption is low. Figure 10a relates the cavern diameter to agitation conditions and rheology on the basis of eq 2, taking Pot = 0.91 for the forward mode and 0.83 for the reverse. All the data are well correlated by a single line with a slope of about 0.25. This value is considerably less than l/3, as predicted by eq 2, which has been used successfully (16) for a Rushton turbine, a pitched blade turbine, a two-blade paddle, a marine propeller, and recently (23) for the Scaba 6SRGT impeller. On the other hand, if measured Po values equivalent to the relevant Reynolds number are used, Figure 10b is obtained. As can be seen, the direction of rotation now makes a big differencein the size of the cavern
1 2.7 5.3 Figure 9. Photographs and traced outlines of the caverns generated by the impeller operating in the reverse mode, as a function of the stirring speed. Concentration of Carbopol = 2 kg m-3.
3c
0
Forward Reverse
a slope
0 25
1
'r
b
o Reverse Forward
100
10 Pop N D 1 T y
Figure 10. Dimensionlesscavern diameter versus dimensionless
stress for the Carbopol solution: (a) using a constant turbulent power number Pot; (b) using Po at the relevant Re.
and its rate of increase. While the forward mode shows an almost linear relationship (exponent = 0.9), the reverse mode exhibits a square root dependence (exponent = 0.46). As a result of the change of Po, both of these exponents have become considerably higher than theory (eq 2) would suggest. At present, no decision can be made on which value of power number should be used. Perhaps LDA studies of flow in the cavern with the A-315 as has been carried out for Rushton turbines (40) will produce an explanation. Figure 11showsthat, before the cavern reaches the wall, the ratio HJD,is an average value of 0.58 regardless of the direction of rotation. This value is similar to the one reported by Elson (16) for a pitched blade turbine. After the cavern has reached the tank wall, the growth of the well-mixed region increases with agitation speed with an
-
Biotechnol. hog., 1992, Vol. 8, NO. 3
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1'OC
c Reverse 0 Farword
0 5 t
0.3
2
3
L
5
6
7
8
N (5-l)
A
1
Figure 12. (a) Well-mixedcavern volume as a function of power draw. (b) Volume of cavern produced per unit power drawn (VJP)as a function of the power input. Concentration of Carbopol = 2 kg m-3.
Reverse Forword
I
I
10
100
PIWI
Figure 11. Variation of cavern height to diameter ratio with impeller speed. Concentration of Carbopol = 2 kg m-3.
exponent between0.39 and 0.52 for the forward and reverse modes, respectively. This exponent is considerably lower than the ones quoted by Elson (16) for a number of impellers (ranging from 0.76 to 0.88) but was similar to the one observed for the Scaba 6SRGT (26) impeller. No explanation can be given for this discrepancy, but it could be an effect of scale,as most of the work reported previously concerned with caverns has been carried out in tanks much smaller than the one used on this work and that with the Scaba (26). The data in Figure 10 suggest that the reverse mode achieves larger caverns at the same power input. To confirm this, the data have been replotted in terms of the cavern volume as a function of the power input. This is shown in Figure 12a. Before the cavern reaches the vessel wall, the reverse mode yields 4040% larger cavern volumes than the forward mode. After the cavern has reached the wall, the difference between the two modes is less although the reverse one still gives higher values. Figure 12b compares the performance of the mode of operation in terms of the volume of cavern produced per unit of power input (V,/P). For D, < T, the V,lP ratio goes from 0.00116 to 0.00145 m3/W for the forward mode, whereas for the reverse mode this ratio ranged between 0.00184 and 0.00237 m31W. This means that the reverse mode is between 58 and 63% more effective than the forward mode in generating a well-mixed volume in this fluid. After the cavern has reached the tank wall, no significant differences were found between the modes of operation but the VJP ratio drops drastically as more power (Le., higher stirring speed) is applied to the fluid. This confirms that in order to maximize the power economy for achieving fluid motion throughout the tank large DIT impellers are best, with multiple arrangements in tall tanks (12).
Conclusions The power curves of the A-315 impeller in the mixing of non-Newtonian, highly viscous yield stress fluids have been reported for the first time. Po always decreased in the Re range tested (2-800) and for Re < -20, Po 0: Re-'. Forward rotation (pumping downward) gave higher Po than reverse rotation at the same Re. In either mode of rotation a t a given Re, Po was different for the three Xan-
than solutions tested, a phenomenon ascribable to the viscoelasticity level. The higher the first normal stress, the higher the Po. Aeration causes a drastic drop in Po, and in the most concentrated (35 kg m-3) Xanthan gum solution, severe torque oscillations were observed. As seen in the Carbopol solution, gas dispersion was bad, especially in the forward mode. For all except the 35 kg m-3 Xanthan solution, a lower power drop and better gas dispersion and less torque fluctuations were achieved in the reverse mode. The growth of the caverns before they touch the tank wall showed that the cavern diameter depends upon PoRe, to the power of about l for the forward mode and about l / 2 for the reverse mode. These exponents are higher than the ones reported previously and do not accord with an earlier-developedtheoretical relationship. On the other hand, if Pot is used, then the same correlation is found for both impellers with cavern growth a (p~tRe,)O.~~, Le., a lower exponent than the theoretical. At present, this anomaly cannot be resolved. When the cavern reaches the wall, its height increases with agitation speed to the 0.53 power for the forward mode and to the 0.39 power for the reverse. These values are lower than those quoted previously for a range of other impellers in smaller tanks but similar to those obtained for the Scaba GSRGT impeller at the same scale. The A-315 impeller is able to produce, in the forward mode, an average of 0.00125 m3/W wellmixed cavern (VJP) whereas the average of that index for the reverse mode was 0.00206. In either mode, V,IPdrops drastically with the power supplied when the cavern has reached the wall. The reverse mode is an attractive retrofitting possibility in order to improve mixing in Xanthan fermentation, provided the expected Xanthan concentration is not higher than about 25 kg m-3. A
b
Notation constant in normal force power law (NI = A i b ) , Pad exponent in normal force power law (N1= A i b ) , dimensionless impeller clearance bottom of tank, m impeller diameter, m well-mixed cavern diameter, m gravitational constant, m s - ~ liquid height, m height of well-mixed cavern, m shear rate constant (i,,= k&), dimensionless consistency index, Pa@ impeller speed, s-l first normal stress difference, Pa flow behavior index, dimensionless
Bbtechnol. Prog., 1992, Vol. 8,
P P Po QG
r Re Re,
T vc
Wi
230
No. 3
power drawn by impeller, W exponent (Hc a Np), dimensionless power number (P/pN3D5),dimensionless gassing rate, m3 s-1 (also expressed as wm, that is, volume of air per volume of liquid per minute) linear regression coefficient, dimensionless dimensionless Reynolds number (pW-nD2/Kk,n-1), yield stress Reynolds number (pWD2/rY), dimensionless vessel diameter, m well-mixed cavern volume, m3 ), Weissenberg number ( N ~ / Tdimensionless
Greek Letters Y shear rate, s-l P fluid density, kg m-3 7 shear stress, P a TY yield stress, Pa Subscripts g under aeration min minimum av average t in the turbulent region
Acknowledgment We are grateful to Mr. S. Chatwin, Mr. R. S. Badham, and Mr. L. G. Torres for their technical support and help; and to Dr.T. P. Elson for valuable discussions. The Xanthan gum sample was a courtesy of RhGne-Poulenc (France) and t h e A-315 impeller was kindly provided by the Lightnin Company. E.G. thanks the European Economic Community for the postdoctoral grant (Grant CI 1*/456, “International Scientific Co-operation MBxico”) which made possible his stay at Birmingham University. Literature Cited (1) Margaritis, A.; Pace, G. W. Chapter 49: Microbial polysaccharides. In ComprehensiveBiotechnology;Moo-Young, M., Ed.; Pergamon Press: Oxford, 1985; Vol. 3, pp 1005-1044. (2) Vincent, A. Chapter 5: Fermentation techniques in Xanthan gum production. Topics in Enzyme and Fermentation Biotechnology;Ellis Horwood Ltd.: Chichester, 1985;Vol. 10, pp 109-145.-(3) Funahashi, H.; Yoshida, T.; Taguchi, H. J . Ferment. Technol. 1987. 65 15). 603-606. (4) Zhao Xueming; Nienow, A. W.; Chatwin, S.; Kent, C. A.; Galindo, E. Improving Xanthan fermentation performance by changing agitators. Proceedings of the 7th European Mixing Conference,Brugge, _ _ Belgium; KVIV: Belgium, 1991; pp 277-283; (5) Marquet, M.; Mikolajczak, M.; Thorne, L.; Pollock, T. J. J. Ind. Microbiol. 1988, 4, 55-64. (6) Souw, P.; Demain, A. L. Appl. Environ. Microbiol. 1979,37, 1186-1192. (7) De Vuyst, L.; Van Loo, J.; Vandarme, E. J. J. Chem. Technol. Biotechnol. 1987, 39, 263-273. (8) Peters, H.-U.; Suh, 1.4.;Schumpe, A.; Deckwer, W.-D. Can. J. Chem. Eng., in press. (9) Shu, C.-H.; Yang, S.-T. Biotechnol. Bioeng. 1990, 35, 454468. (10) Moraine, R. A.: Rogovin, P. Biotechnol. Bioeng. - 1971,13, 381-391. (11) Suh, 1.4.; Herbst, J.; Schumpe, A.; Deckwer, W.-D. Biotechnol. Lett. 1990, 12 (3), 201-206. (12) Solomon,J.; Elson, T. P.; Nienow, A. W.; Pace, G. W. Chem. Eng. Commun. 1981,11, 143-164. (13) Elson, T. P.; Cheesman, D. J.; Nienow, A. W. Chem. Eng. Sci. 1986,41, 2555-2562.
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Accepted March 24, 1992.
