COM M U N ICAT I ON
Relative Importance of Viscosity and Oxygen Solubility on Oxygen Transfer Rates in Glucose Solutions James A. Muellerl and William C. Boyle Department of Civil Engineering, University of Wisconsin, Madison, Wis. 53706
Oxygen transfer rates have been used to determine oxygen solubilities in glucose solutions without taking into account the viscosity effect. This study was undertaken to evaluate the effects of both viscosity and oxygen solubility on oxygen transfer rate. To accomplish this, the viscosities and oxygen saturation concentrations for distilled water and glucose solutions were measured. The results indicate that viscosity change rather than oxygen solubility is the major cause for variation in oxygen transfer rate with varying glucose concentrations. Thus, estimation of oxygen solubility for dissolved oxygen probe calibration using oxygen transfer rate data is invalid.
A
method for calibrating a dissolved oxygen probe in a glucose-salts solution (Bennett and Kempe, 1964), consists of air-saturating a glucose-salts solution and using this to standardize the probe. The oxygen saturation value of this solution was calculated from data given by Solomons (1961). This method, however, is invalid, since Solomons’ data are misleading and cannot be used for this purpose. Solomons has presented a graph of solubility of oxygen expressed as oxygen transfer rate, OTR, GS. normality of glucose solutions. The manner of data presentation indicates that the ratio of the OTR at a given glucose concentration to the OTR in distilled water can be multiplied by the oxygen saturation value, ce, in distilled water to obtain the oxygen saturation value in the glucose solution. However, the following analysis shows that Solomons has not taken viscosity change into account. The oxygen transfer rate is given by Solomons as OTR
=
A 3.60 2 (c, 6
-
C)
where A I and 6 are, respectively, the interfacial area and liquid film thickness of the air bubbles, c is the oxygen concentration in the bulk liquid, and D is the diffusivity of oxygen in the solution. The ratio of the maximum oxygen transfer rates (c = 0) is given by 1 Present address, Regional Environmental Health Laboratory, Kelly Air Force Base, Tex. 78221
578 Environmental Science and Technology
where KLn is the oxygen transfer coefficient, and subscripts g and w refer to the glucose and distilled water solutions, respectively. Thus, to use Solomons’ OTR data directly, the values of KLa for distilled water and glucose solutions must be equal. If the assumption is made that the interfacial area and stationary film thickness are not affected by glucose concentration, the ratio of the KLnvalues is equal to the ratio of the diffusivities. As shown in the Stokes-Einstein equation (Bird, Stewart, et al., 1960). at a constant temperature, diffusivity is inversely proportional to the viscosity, k , of the solution. Substituting this relationship into Equation 2 yields (3)
From this equation, it is seen that the OTR ratio is a function of both the viscosity and oxygen saturation value of the solutions. Treybal (1955) states that the “diffusivity for concentrated solutions differs from that for dilute solutions because of changes in viscosity with concentration and also because of changes in the degree of ideality of the solution.” To determine which of the parameters in Equation 3 has the greater effect on OTR, the viscosities and oxygen saturation values of two glucose solutions were experimentally determined. F o r the viscosity determinations, a No. 100 CannonFenske calibrated viscometer was used. These determinations were made at 24.2” C. on a distilled water sample and two solutions having glucose concentrations of 50 and 188 grams per liter. The results (Figure 1) indicate that viscosity increases markedly with increasing glucose concentration in the range tested. Before measuring oxygen solubility values with a dissolved oxygen probe (Precision Scientific galvanic cell), it was necessary to determine the effect of various glucose concentrations on probe readings. This was accomplished by recording the probe reading of an air-saturated distilled water sample in an air-tight reactor, removing the probe and adding a known quantity of glucose to the reactor, immediately providing an air-tight seal by placing the probe back in the reactor, mixing the reactor contents with a magnetic stirring bar, and recording a probe reading after the glucose had dissolved.
n - II 22
0
i
i
‘I 2\
8
‘0
O o
0 8 “; ; I 0
0 MEASURED VISCOSITIES
A
2
M E A S U R E D OXYGEN SATURATION V A L U E S
0 2
04
06
1 ;’ 0
SOLOMONS OTR D A T A SOLOMONS’
0 8
I O
404
12
M O L A R I T Y OF GLUCOSE SOLUTIONS
Figure 1. Relation among glucose concentration and oxygen saturation value, oxygen transfer rate, and viscosity OTR curye calculated from Equation 3 using OTR of distilled water of 6.9 from Solomons
Since the reactor was open to the atmosphere for only a few seconds after glucose addition. insufficient time was available for the oxygen content of the glucose solution to equilibrate with the atmosphere. Therefore, the oxygen concentration in the glucose solution was substantially the same as that in the initial distilled water solution. Thus, a conversion factor, y, can be defined bq (4)
i+heie P,lu and P, are. respectively, the probe readings for a glucose sample and for distilled water at the same dissolved ouqgen concentrations The conversion factor (Table I) dect eased with increasing glucose concentrations.
Table I. Effect of Glucose Concentration on Probe Reading Probe Reading at Dissolved Oxygen Concn. Conversion Solution of 9 2 Mg / L Factor, y
Distilled water Glucose, 50 g ,1 Glucose. 188 g.,l
5 80 5 85 6 10
1 000 0 992 0 952
Table 11. Effect of Glucose Concentration on Viscosity and Oxygen Saturation Value Probe Reading, P, viscosity, after Aeration Time of Ce. -~ p, Cp. 0 hr. 1 hr. 2 hr. Mg./L. Solution Distilled water 0.92 1 . 1 0 5 7 5 5.80 9 . 2 0 Glucose, 50 g.,’l. 1.04 1.10 5 . 7 5 5.80 9.15 1 .39 1 10 5 . 6 7 5 75 8 . 6 6 Glucose, 188 g./l. (1
c, = 9.70 2 y p 2t r , 5.80
F o r the determination of the ce values, three 300-ml. flasks, each containing one of the solutions used in the viscosity determinations, were aerated a t 20°C. for 2 hours. The probe readings in the flasks increased markedly in the first hour and only slightly in the second hour of aeration. Thus, the flasks after 2 hours of aeration were assumed to be saturated. Using the conversion factors, y,from Table I, the oxygen saturation values were calculated (Table 11). The OTR curve in Figure 1 was calculated from Equation 3 using the value of O T R for distilled water given by Solomons. The slight deviation from Solomons’ data may be caused by a viscosity effect on the interfacial area and film thickness. I n Figure 1 there is a noticeable decrease in oxygen solubility with increasing glucose concentrations-about a 5.8 decrease in ce from distilled water to the 188 grams per liter glucose solution. However, the viscosity, varying linearly with glucose concentration, is 51 greater for the 188 grams per liter glucose solution than for distilled water. This proves that viscosity change rather than oxygen solubility is the major cause of variation in oxygen-transfer rate with varying glucose concentrations. Thus, Bennett and Kempe’s method for dissolved oxygen probe calibration using Solomons’ OTR data is invalid. However, since media used in most biological studies contain glucose concentrations well below 50 grams per liter, no measurable effect will be exhibited by the glucose on either oxygen solubility or probe reading. The glucose can therefore be excluded from the media and the standard Winkler method (American Public Health Association, 1965) used for probe calibration.
Literature Cited American Public Health Association, New York, “Standard Methods for Examination of Water and Waste Water.” 12th ed., 1965. Bennett, G. F., Kempe, L. L., Biotech. Bioeng. 6, 347-60 (1964). Bird, R . B., Stewart, W. E., Lightfoot, E. W., “Transport Phenomena,” Wiley, New York, 1960. Solomons, G . L., “Aeration and Agitation in Continuous Culture,” in Continuous Culture of Microorganisms, Monograph 12, pp. 233-53, Society of Chemical Industry, London, 1961. Treybal, R. E., “Mass Transfer Operations,” McGraw-Hill, New York, 1955. Receiced for reciew April 19, 1967. Accepted June 9, 1967. Volume 1, Number 7, July 1967
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