Ind. Eng. Chem. Res. 1994,33, 2364-2367
2364
Rheology of Shear Thinning Polymer Solutions Frans L. Muller7 and John F. Davidson' Department of Chemical Engineering, Pembroke Street, Cambridge CB2 3RA, England
A viscometer was used to measure power law parameters K and n for aqueous solutions of (carboxymethy1)cellulose(CMC), taken from a bubble column. The results were analyzed by plotting n as a function of Log K. Literature data and the present experiments show that dilution gives a slope of -0.147 on the Log K-n plot. Results with different molecular weights show, by contrast, a slope of -0.345. Results from the bubble column are consistent with (i) change of CMC molecular weight due to shear, the slope of the Log K-n plot being -0.345, and (ii) change of CMC molecular weight due to oxidation by hydrogen peroxide when this was added: the slope of the Log K-n plot was -0.223. That this was less than -0.345 is believed to be due to dilution. The effect of moderate temperature changes was also summarized. An important conclusion is that when CMC solutions are used in bubble columns or stirred tanks for mass or heat transfer studies, attention must be given to changes of properties due to shear, oxidation, dilution, and temperature.
Introduction Over the past 10 years much effort has been put into measuring gas-liquid mass and heat transfer coefficients in agitated tanks and bubble columns containing highly viscous aqueous polymer solutions, with effective viscosities between 0.1 and 3 Pa s. These liquids are usually shear thinning and have rheological properties similar to "real" industrial media like (i) fermentation broths and (ii) liquid suspensions of small particles (Shah, 1982).The hydrodynamical behavior of gas-liquid contactors containing highly viscous liquids is characterized by the presence of very large bubbles (up to 15 cm). This is because turbulence is strongly reduced, diminishing the bubble breakup rate (Philip et al., 1990). Many experiments are performed using (carboxymethy1)cellulose (CMC) solutions in water; see for instance Schumpe and Deckwer (1987). CMC is shear thinning and the rheological behavior is usually characterized by the Ostwald-deWaele (or power law) model: = -WYI *
7
n-1
*
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peff
= W+eftin-'
(1)
This empirical relationship describes the shear stress 7 as a function of the shear rate i. = aular, the consistency index K (Pa sn), and the flow behavior index n (dimensionless). The parameters of a gas-liquid contactor like mass and heat transfer coefficients are usually correlated with respect to viscosity by use of the effective viscosity (eq 1). The local shear rate in such systems cannot be calculated, and in the literature effective viscosity is calculated from a characteristic (effective) shear rate of the system; for a bubble column (tubular geometry) the effective shear rate is the ratio of the center line liquid velocity and the radius: qeff = uJR. The rheological properties of CMC are strongly related to the molecular weight and concentration. CMC is available in a low-, a medium-, and a high-viscosity form, viscosity increasingwith molecular weight. CMC solutions (0-8 % ) have in general effective viscosities peff between 1and 3000 mPa s. The physical properties of the CMC solutions differ only slightly from those of water: for the quoted range of peff, density varies from 1000 to 1004 kgJ m3 and the surface tension is between 0.065 and 0.072
* Author to whom correspondence should be addressed. + Departement de GBnie Chimique, Centre de Recherche de
Royallieu, B P 649, 60206 Compiegne, France.
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Figure 1. Consistency index K and flow behavior index n: plot of published data.The changes in K and n arose from changes in concentration of CMC and PAA. References for the plotted data are as follows: low-ukcosity CMC (A)from Buchholtz etal. (1978),Voigt et al. (1980), Deckwer et al. (1982), Schumpe and Deckwer (1982, 198'0, Vatai and Tekic (1986), Philip et al. (1990); high-viscosity CMC (0) from Godbole et al. (1982,1984), Kelkar and Shah (1985), Divine et al. (1986), Haque et al. (1986), Kawase and Moo-Young (1986),Kawase et al. (1987);polyacrylamide (PAA, 0)from Hecht et al. (1980), Nakanoh and Yoshida (1980), Kawase et al. (1987).
NJm (Godbole et al., 1984; Schumpe and Deckwer, 1987; Zhao, 1989). In mass transfer experiments, the viscosity parameters (K, n ) are often considered to be constant system properties, as system temperature and polymer concentration are assumed to vary only slightly (seefor instance Schumpe and Deckwer (1982, 1987). However, strong changes in the viscosity parameters were observed during mass transfer experiments in a bubble column (Muller and Davidson, 1992),which made a closer study of the viscosity parameters necessary. The effects on K and n of (i) molecular weight, (ii) concentration, (iii)temperature, and (iv) polymer degradation were evaluated using a new method of viscosity data analysis. The Log K-n Plot. In the literature, the polymer concentrations are often not given. To investigate the experimental parameters found in the literature, the flow behavior index n is plotted versus Log K (Figure 1). The three polymers plotted, low- and high-viscosity CMC and polyacrylamide (PAA), are frequently cited in mass transfer literature. The figure shows a linear dependence of the flow behavior index (n)on Log K, with a slope (-0.147) for all three polymers.
Ossa-5885/94/2633-2364~04.50JO 0 1994 American Chemical Society
Alternatively phrased: due to CMC concentration the viscosity parameters move over a line in the Log K-nplane with slope -0.147. The Log K-n plot is a powerful way of analyzing the effect of various parameters on the rheological behavior of power law solutions. The results in Figure 1show that the consistency index K is a useful indicator in considering changes in the viscosity of power law solutions, but not for comparing different types of liquid. A decrease in the (effective) viscosity of a CMC solution is caused by a decrease in the consistency index ( K ) and is always coupled to an increase of the flow behavior index (n);i.e., for a certain polymer, solutions of various concentrations and temperatures behave more Newtonian for lower consistency indices.
Experimental Section In this work only high-viscosity CMC was used. The CMC purchased (BHDProduct No. 27929) originated from three different production batches: CMC1, batch no. 2451460, CMC2, no. 4268280; and CMC3, no. 4498100. The CMC solutions used to analyze the effect of concentration were made in batches of 250 mL. Most of the CMC solutions were made in batches of 20-25 L by adding CMC to hot "Cambridge" tap water (-60 "C), while stirring vigorously. Using hot water speeded up the dissolving process considerably. The 25-L batches, characterized by their date of formation, are not necessarily made from CMC out of a single batch. The viscosity parameters were measured using a Haake Couette viscometer (VT-24). The effective viscosity of the solution was determined at six different shear rates between 10 and 400 s-l; K and n were obtained by plotting the logarithm of the measured peff against the logarithm of measured Teff;linear regression then gave K and n from eq 1. The correlation coefficient was usually 0.99, indicating a good fit of the power law model. Each run was usually repeated. The range of shear rates for the measurements corresponds with the shear rates expected in a bubble column (50-250 8-1). The temperature of the liquid analyzed was measured by immersing a thermocouple in the liquid immediately after the viscosity measurement. The viscosity parameters were converted to the parameters as for 20 "C using eqs 2 and 3 given below.
Rssults Effect of Concentration of CMC. The viscosity parameters of the different CMC batches (CMC1, CMC2, CMC3) are plotted at several concentrations on a Log K-n plot (Figure 2), which is similar to Figure 1. The dependence of the flow behavior index on K is fairly well described, for a given batch, by lines with a slope of -0.147, the value deduced from published data (Figure 1). Note that the three CMC batches have different characteristics. This is most likely caused by their different molecular weights, CMCl having the highest molecular weight and CMC 3 the lowest. The alternate plot is for solutions of equal concentration (1wt 7% ); i.e., changing the molecular weight. The viscosity parameters move in the Log K-n plane along a line of slope -0.345. Effect of Temperature. Increasing the temperature of a solution decreases its viscosity. The effect of temperature was investigated by changing the viscometer temperature (Tr) between 18 and 32 "C, a range corresponding to the change in "room temperature". Figure 3 shows the results for the three CMC batches. Within
Numbers next to the points
The consistency index
Figure 2. Effect of concentration from present experiments. Each set of points for a given batch of CMC are reasonably well correlated by a line of slope -0.147, the value deduced from published data, Figure 1. The alternate plot is for a fixed concentration of CMC (1 wt %) but for different batch numbers of decreasing molecular weight: the slope is-0.345. Data are for CMCl (A),CMC2 ( O ) ,CMC3 ( O ) ,and the initial values of K and p for 25-Lbatches of 1.0 wt % CMC solutions used for the bubble column experiments ( 0 ) .
this narrow temperature interval, Log K and n are linearly related to temperature, with proportionality constants independent of CMC concentration and batch numbers (i.e., molecular weight). It follows that due to temperature change, the viscosity parameters move in the Log K-n plane along a line with slope -0.294. The temperature a t which an experiment is performed, Te, is usually different from the temperature Tr at which the viscosity parameters are measured. From Figure 3 it follows that the measured viscosity parameters can be corrected for temperature to give (K,n) at the operating temperatures during the experiment: Log K(Te) = Log K(T,) - 0.0187(Te- T,)
(2)
n(Te) = n(T,) + 5.50 X 103(Te - T,) (3) The effects of the temperature corrections are considerable: if the temperature difference (T,- Tr) is 5 "C, the differences in experimental and measured viscosity parameters are up to 25% for K and up to 5% for n. An exponential decay of the viscosity (consistencyindex) with temperature is noted for many liquids. This can be explained by the theory of Eyring and co-workers, which shows that the relation between viscosity and temperature can be approximated by an Arrhenius equation (Glasstone et al., 1941; Bird et al., 1960): p = KoeEdRT Expanding the power of e to a series around Tr:
(4)
Applying eq 5 to K for a temperature Tr = 20 OC gives an activation energy of 13.4 kJ/mol for CMC solutions, Effect of CMC Degradation. The viscosity data, on which the following discussion is based, were obtained during a series of mass transfer experiments. The degradation occurred in a 14-cm-diameter bubble column, from which samples were taken, from time to time, for measurement in the viscometer. The changes of K and n were achieved over a total of about 20 h of bubbling air through the column. The superficial gas velocities ranged from 2 to 11cmls, and the liquid depth was between 1.51.8 m (see Muller and Davidson (1992) and also Muller
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2366 Ind. Eng. Chem. Res., Vol. 33, No. 10, 1994
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Figure 3. Influence of temperature on consistency index (K)and flow behavior index (n)for five CMC solutions. Note that, since both Log K and n are proportional to the temperature, the viscosity parameters in a Log K-n plot are related by a straight line (slope -0.294), as temperature varies. Data are for 2.0 wt % CMCl (A), 1.0 wt % (0) and 1.5 wt % ( 0 )CMC2, and 1.0 wt % (0) and 1.5 w t % (e) CMC3. 0 158
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3000 The consistency index: K (m Pas")
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Figure 4. Mechanical degradation by shear of CMC molecules due to residence of up to 20 h in the bubble column. The data follow lines of slope-0.345, similar to the effect of decreasingthe molecular weight at constant weight fraction polymer (Figure2). The data were obtained from severalbatches, characterized by date of formation (daylmonthi year): 19/09/91 (O),11/11/91 ( O ) , 13/11/91 (El), 20/11/91 (LP),and 28/11/91 ( 0 ) . 1
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31/10/91 11/11/91 13/11/91 20/11/91 28/11/91
A
05/12/91
0 0 0 E
0 40 80 120 160 200 Time peroxide is flowmg into the column (mm)
Figure 5. Degradation of viscosity of CMC solutions as function of the time hydrogen peroxide has been flowing into the column. The data were obtained from several batches, characterized by date of formation (day/month/year): 31/10/91 (a), 11/11/91 (a), 13/11/91 (El), 20/11/91 (a),28/11/91 ( O ) ,and 05/12/91 (A).
(1993)). Each data series is characterized by the date of formation of the 25-L batch of liquid in the column (see Figures 4-6). During the bubbling experiments it was noted that the viscosity of the CMC solutions decreased with time: K decreased and the flow behavior index (n)increased with time. Degradation of the CMC is the main cause of these
The consistency index: K (mPas")
Figure 6. Degradation of viscosity of CMC solutions, due to the presence of hydrogen peroxide, added by a steady feed, to the bubble column, of aqueous HzOz. The data were obtained from several batches, characterized by date of formation (day/month/year): 31/ 10/91 (a), 11/11/91 ( O ) , 13/11/91 (El), 20/11/91 ( 8 ) ,28/11/91 ( O ) , and 05/12/91 (A).
trends. If a polymer breaks down, the average chain length (molecularweight) is reduced therefore the chains become less entangled and/or are more easily disentangled by the shear forces; Le., the liquid has less resistance to shear and is thus less viscous. Chain breakup is caused by two main processes: mechanical breakdown of CMC chains by shear forces due to bubbling and chemical breakdown of the CMC by oxidation reactions due to dissolved oxygen, or peroxide if present. The mechanical degradation of CMC is relatively slow, and was most noticeable at high viscosities (K> 2000 m Pa sn) when the number of entanglements is high, and the viscous forces, due to a given shear rate, are large. The change of the viscosity parameters can be observed on a K-n plot (Figure 4). Note that there is no significance in the dates given in Figure 4;they are merely labels for the batches. Due to degradation the viscosity decreases; the Log K-n plot is a straight line with a slope of -0.345,similar to the effect of the molecular weight of CMC (see Figure 2). This validates the hypothesis that shear decreases the average CMC chain length. Chemical breakdown of the CMC was observed in longstanding batches of CMC solutions; oxygen concentrations corresponding to equilibrium gas phase concentrations below 21% (as low as 10 vol % oxygen) indicated that oxygen was consumed. This might explain why very old (months) batches of CMC have decreased viscosities. The chemical degradation of CMC solutions was speeded up
Ind. Eng. Chem. Res., Vol. 33, No. 10,1994 2367 considerably when hydrogen peroxide was added to the liquid. During steady state mass transfer experiments, a peroxide feed solution was continuously decomposed in the column. The feed solution (0.3 wt % H202 and 1 wt ?Ti CMC in water) decayed overnight from K = 2 P a sn to K = 0.003 Pa sn. Figure 5 shows that, during steady state experiments, K decays exponentially with the time peroxide solution was flowing into the column. The rate constant is about 3.92 X 103 min-1 and is independent of the batch number. The peroxide concentration in the column could not be measured. The data were obtained by sampling liquid from the column and making measurements in the viscometer. The same data plotted in a Log K-n plot (Figure 6 ) show that the viscosity decrease due to chemical degradation of CMC by peroxide is described by a line with slope -0.223. This value lies between that of mechanical degradation (chain breaking only, slope -0.345, Figure 4) and that of dilution of the CMC solution (concentration effect, -0.147, Figure 2), indicating that the effect of the peroxide addition must be attributed not only to (i) degradation of the CMC chain length but also to (ii) dilution of the solution or (iii) chemical modification of the polymer.
Conclusions For shear thinning power law liquids it is found that the flow behavior index (n)is strongly related to Log K (the consistency index). Changing various parameters showed the relation n-Log K to be linear, the slope of the line being an indication of the type of process that affects the polymer solutions. For CMC solutions, dilution gives rise to a slope of -0.147, whereas changes in molecular weight cause the slope to be -0.345 on the Log K-n plot. Effects on CMC solutions were observed as follows: (i) The plot of Log K-n, arising from temperature change, has a slope of -0.294. This may indicate the effect of increased mobility of the polymer chains. (ii) The plot of Log K-n, generated by shear due to bubbling, has a slope of -0.345. This is consistent with the slope due to the change of molecular weight, -0.345, and suggestsbreakdown of polymer molecules due to shear. (iii)Oxidation by hydrogen peroxide, with some dilution, gives a slope of -0.223 on the Log K-n plot, suggestive of polymer breakdown by oxidation allied to a dilution effect; as noted above, the dilution effect alone gives a smaller slope, -0.147 on the Log K-n plot. The analysis of viscosity data using a Log K-n plot gives a useful way of summarizing the data. The slope of a series of ( K , n) points gives an indication of the process affecting the system's rheological behavior. Further it allows the interpolation of the viscosity parameters ( K , n),which is necessary if for instance mass or heat transfer measurements are to be related to viscosity. In addition, the plot is very useful for a more complete comparison of the rheological behavior of polymer solutions. Finally, the results show that extreme care is needed when relating heat and mass transfer data for gas-liquid contactors containing polymer solutions to viscosity parameters, because these parameters may change during the experiment on account of (i) shear degradation of polymers, (ii) oxidation of polymers, (iii) temperature changes, and (iv) dilution.
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Kawase, Y. B.; Moo-Young, M. Influence of non-Newtonian flow behaviour on the masa transfer in bubble columns with and without draft tubes. Chem. Eng. Commun. 1986,40,67. Kawase, Y.; Halard, B.; Moo-Young, M. Theoretical predictions of volumetric mass transfer coefficients in bubble columns for nonNewtonian fluids. Chem. Eng. Sci. 1987,42, 1609. Kelkar, B. G.; Shah, Y. T. Gas hold up and back-mixing in bubble columns with polymer solutions. AIChE J. 1985,31, 700. Muller, F. L. Mass transfer to viscous liquids in bubble columns. Ph.D. Thesis, University of Cambridge, 1993. Muller, F. L.; Davidson, J. F. On the contribution of small bubbles to mass transfer in bubble columns containing highly viscous liquids. Chem. Eng. Sci. 1992,47, 3525. Nakanoh, M.; Yoshida, F. Gas absorption by Newtonian and nonNewtonian liquids in a bubble column. Znd. Eng. Chem. Process Des. Dev. 1980,19, 190. Philip, J.; Procter, J. M.; Niranjan, K.; Davidson, J. F. Gas hold-up and liquid circulation in internal loop reactors containing highly viscous Newtonian and non-Newtonian liquids. Chem. Eng. Sci. 1990,45,651.
Schumpe, A.; Deckwer, W.-D. Gas holdups; specific interfacial areas and mass transfer coefficientsof aerated CMC solutions in a bubble column. Ind. Eng. Chem. Process Des. Dev. 1982,21, 706. Schumpe, A.; Deckwer, W.-D. Viscous media in tower bio reactors: Hydrodynamic characteristics and mass transfer properties. Bioprocess Eng. 1987,2, 79. Shah, Y. T.; Kelkar, B. G.; Godbole, S. P.; Deckwer, W.-D. Design parameters estimation for bubble column reactors. AZChE.J. 1982, 28,353.
Vatai, G. Y.; Tekic, M. N. Gas hold up in bubble columns with nonNewtonian liquids. Chem. Eng. Sci. 1986,42,166. Voigt, J.; Hecht, V.; SchClgerl, K. Absorption of oxygen in countercurrent multistage bubble columns-II; aqueous solutions with high viscosity. Chem. Eng. Sci. 1980, 35, 1317. Zhao, M. Mass transfer to viscous liquids in bubble columns. PbD. Thesis, University of Cambridge, 1989. Received for review December 29, 1993 Revised manuscript received May 25, 1994 Accepted June 22, 1994. Abstract published in Advance ACS Abstracts, August 15, 1994.
