Biotechnol. Prog. 1995, 11, 221-223
221
NOTES Diffusion Behavior of Ammonium in Xanthan Gum Solutions E. Brito,*tt L. Torres: and E. Galindos Departamento de Alimentos y Biotecnologia, Facultad de Quimica, Universidad Nacional Autdnoma de Mexico, 045 10 MBxico, D.F., and Departamento de Bioingenieria, Instituto de Biotecnologia, Universidad Nacional Autdnoma de Mexico, Apdo. Postal 510-3, Cuernavaca, Morelos, 62271 Mexico
Ammonium diffusivity in xanthan solutions drastically decreases as xanthan concentration increases. The DA~IDAW ratio was practically independent of pH and a weak function of the ionic strength. This diffusional behavior is a typical case of the diffusion of a small molecule in a non-Newtonian macromolecular solution.
Introduction Xanthan gum fermentation is characterized by marked changes in rheological properties during the culture. The broth behaves as a Newtonian fluid at the beginning of the culture and as a high-viscosity, shear-thinning fluid a t the final stages. Thus, diffusion studies of nutrients such as ammonium and oxygen are needed for a better comprehension of mass transfer limitations during the culture. The purpose of this study, then, is to obtain the diffusion coefficient of ammonium in xanthan solutions under conditions similar to those occurring in a typical fermentation. Diffusivity results are analyzed and compared with predictions from models reported in the literature for non-Newtonian systems.
7
6
.
pn
8
9
0 5
1 1
n
Ammonium 7
5 mM
-
xonthon 1 25 r g / m 3
0 3 -
\
a
0
Materials and Methods Reagents. Food-grade xanthan gum (Keltrol, Kelco) and ammonium nitrate (J. T. Baker) were used. The pyruvic acid content and molecular weight for Keltrol were 4.30% and 4.4 x lo6, respectively (Torres et al., 1993). Xanthan and KC1 solutions were prepared and measured as described by Torrestiana et al. (1989). The conductivity of the solutions, measured in a conductivity meter (Copenaghe Beckman, CMD-2d JA-201,varied from 200 to 10000 pQ by adding KC1. Rheology. The steady shear viscosity function was evaluated in a Brookfield LVT viscometer by considering the case of Couette flow. Torque and rotational speed data then were transformed into shear stress, z, and shear rate, p, values. Diffusivity. Diffusion coefficients at 29 "C were obtained in a diaphragm cell identical to the one used by Torrestiana et al. (1989). A KC1 diffusivity value of 1.895 x m2/s a t 29 "C was considered for calibration purposes. Millipore filters, 0.45 pm in pore size, were used in this work.
Results and Discussion Experimental diffusivity results are expressed as the ratio of diffusivity in polymer solution, DAP, to the results diffusivity in water, DAW. Figure 1shows DA~IDAw for 7.5 mM ammonium diffusion in a semidilute xanthan
* Facultad de Quimica.
* Instituto de Biotecnologia. 8756-7938/95/3011-0221$09.00/0
..
0
50
100
150
200
K C I (mM)
Figure 1. Ionic strength and pH effects on the diffusivity ratio for 7.5 mM ammonium diffusion in a semidilute xanthan concentration.
solution (1.25kg/m3),as a function of the ionic strength. Although only one xanthan concentration was studied in this case, the results suggest that the dependence of DAPI DAW on the ionic strength is weak. These results may be explained by considering that normal polyelectrolytes show a viscosity-decreasing function with the addition of salts or increasing ionic strength. Nevertheless, for the case of the xanthan molecule, it is well-known that its viscosity is insensitive to salt concentration up to very high salt levels (Torres et al., 1993). Since diffusivity is inversely proportional to viscosity, and viscosity is independent of ionic strength for xanthan solutions, one may expect no significant changes of diffusivity with ionic strength. The effect of pH on the diffisivity ratio was also investigated, and the results are shown in Figure 1. can be considered essentially From this figure, DA~IDAW independent for values above pH 7. Although at pH 6 a value was observed, more experimental higher DA~IDAW data are needed in order to drawn definitive conclusions related to the microbial culture.
0 1995 American Chemical Society and American Institute of Chemical Engineers
Biotechnol. Prog., 1995, Vol. 11, No. 2
222
C
Oxvqen ; R e u s e !
01 19801 ( ~ = 3 L 4 5 , u = i 6863
v=O 578)
( a = l 764 ,
5
0
I; d
1 c -
C
2
3
4
5
6
7
8
5
'0
0 02
X a n t h a n concentration (kg/m3)
gum concentration changes. Comparison of experimental and literature data. The lines show the fitting of the Gorti and Ware model (eq 2).
Diffusivity results of ammonium as a function of xanthan concentration are shown in Figure 2. As may be noted, ammonium diffusivity drastically decreases as the xanthan concentration, Cp, increases. A similar tendency has been reported for various small diffusing solutes in xanthan solutions. Compared to the diffisivity of ammonium with no xanthan present (Cp = 0), the diffusivity of ammonium in a dilute xanthan concentration (0.5 kg/m3)is reduced by 80% according to the data shown in Figure 2. Regarding the effect of ammonium concentration on DAP,no significant differences in diffusivities were observed when either 7.5 or 10 mM ammonium was diffused. On the other hand, the experimental diffusivity of ammonium in water, DAW(m2/s),at 29 "C can be represented by
- 6.548 x lO-"(C,J
0 36
3 38
Figure 3. Diffusivity prediction of 7.5 mM ammonium from the Clough et al. model (eq 3). The limiting viscosity at high shear rates, qcp, is estimated from the Eyring-Powell-Ree model (eq 4).
viscosity have been used in the literature to explain the roles of polymer concentration and solution viscosity in diffusivity. However, most of these relationships do not have theoretical foundations, and consequently they cannot be generalized. On the basis of the general Eyring rate theory (Ree and Eyring, 19581, Clough et al. (1962) proposed a semitheoretical model to predict diffusivities in slurries and shear-thinning fluids, given by
(3) where qcpwill be equal to the limiting viscosity reached by the non-Newtonian system at very high shear rates, obtained from the Eyring-Powell-Ree model: y
lo-'
0 04
Limiting v i s c o s i t y o t high shear r a t e s , q C p (Pa s)
Figure 2. Ammonium diffusivity ratio dependence on xanthan
DAW= 2.331 x
i
I
0 00
(1)
where CA is the ammonium concentration (mM). The result from eq 1 compares quite well with the value reported by Cussler (19841, for whom DAW= 2.157 x m2/s at CA= 0 and 29 "C. The experimental diffusivity data of this study, as well as other results reported in the literature for the diffusion of small solutes in xanthan solutions, were fitted to the model of Gorti and Ware (19851, a scaling relationship specifically proposed to examine the dependence of the ratio DA~IDAwon polyelectrolyte concentration and ionic strength, given by
where a and v are fitting parameters dependent on the ionic strength. The results are shown in Figure 2, where only minor differences in the value of Y are observed but significant differences in a were found. Although it is very difficult to compare our results with those reported in the literature, mainly because the macromolecules and diffusing solutes studied are different, the values of v for xanthan solutions compare quite well with the values obtained by Gorti and Ware (1985) for other systems. Many empirical correlations that predict DAP to be inversely proportional to a variable power of solvent
xJ,sinh-' Pny
r=C-an
(4) PnY For a more detailed description of the Eyring rate theory and eq 3 and 4, the reader is referred to the original publications. In the case of this work, only the first two terms on the right-hand side of eq 4 were considered. The Newtonian viscosity at high shear rates, qcp, was estimated by using nonlinear regression techniques on the experimental viscosity data. On the other hand, X,, was chosen as 0.97, assuming solvation to triple the effective volume of the xanthan molecule in solution, and the ratio Utcp was chosen as 2.66, as suggested by Clough et al. (1962). The predictions from eq 3 are compared in Figure 3 with experimental data. As the results of this figure suggest, the choice of the limiting viscosity at high shear rates is a good alternative in the prediction of diffusivities, particularly at low xanthan concentrations. In conclusion, ammonium diffusivity in xanthan solutions drastically decreases as the xanthan concentration increases. The DApIDAw ratio was found to be essentially independent of pH and a weak function of the ionic strength. n=l
Literature Cited Clough, S. B.; Read, H. E.; Metzner, A. B.; Behn, V. C. Diffusion in slurries and in non-Newtonian fluids. AIChE. J . 1962, 8 (31, 346-350.
Biotechnol. Prog., 1995, Vol. 11, No. 2 Cussler, E. L. Diffusion: Mass transfer in fluid systems; Cambridge University Press: New York, 1984. Gorti, S.; Ware, B. R. Probe diffusion in an aqueous polyelectrolyte solution. J. Chem. Phys. 1985,83 (12), 6449-6456. Ree, T.; Eyring, H. The relaxation theory of transport phenomena. In Rheology; Eirich, F. R., Ed.; Academic Press: New York, 1958; Vol. 2, pp 83-144. Reuss, M.; Debus, D.; Niebelschutz, H. Oxygen transfer in viscous fermentation broths. In Colloque Societk Franqaise Microbiologie; INSA Tolouse, France, 1980; pp 49-70. Torres, L. G.; Brito, E.; Galindo, E.; Choplin, L. Viscous
223 behaviour of xanthan aqueous solutions from a variant strain ofxanthomonascampestris. J. Ferment. Bioeng. 1993,75 (11, 58-64. Torrestiana, B.; Galindo, E.; Brito, E. Diffusion of sucrose in xanthan gum solutions. Bioprocess Eng. 1989,4, 265-273. Accepted October 5, 1994.@ BP9400809 Abstract published in Advance ACS Abstracts, December 15, 1994. @
