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Bioprocess Engineering

, Volume 4, Issue 6, pp 265–273 | Cite as

Diffusion of sucrose in xanthan gum solutions

  • B. Torrestiana
  • E. Galindo
  • E. Brito
Originals

Abstract

Molecular diffusion of solutes, like sucrose in the xanthan gum fermentation, is important in order to understand the complex behavior of mass transfer mechanisms during the process. This work was focused to determine the diffusion coefficient of sucrose, a carbon source for xanthan production, using similar sucrose and xanthan concentrations to those occurring in a typical fermentation. The diaphragm cell method was used in experimental determinations. The data showed that diffusion coefficient of sucrose significantly decreases when xanthan gum concentration increases. Theoretical and semiempirical models were used to predict sucrose diffusivity in xanthan solutions. Molecular properties and rheological behavior of the system were considered in the modeling. The models tested fitted well the behavior of experimental data and that reported for oxygen in the same system.

Keywords

Sucrose Fermentation Molecular Diffusion Semiempirical Model Mass Transfer Mechanism 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

List of Symbols

A

constant in eq. (5)

Cpg cm−3

polymer concentration

D cm2 s−1

diffusivity

DABcm2 s−1

diffusivity of A through liquid solvent

DAPcm2 s−1

diffusivity of A in polymer solution

DAWcm2 s−1

diffusivity of A in water

DPcm2 s−1

diffusivity of polymer in liquid solvent

ΔED

gradient of the activation energy for diffusion

HP

hydratation factor of the polymer in water (g of bound water/g of polymer)

K dyn sn cm−2

consistency index

K1

constant in eq. (5)

KP

overall binding coefficient [g of bound solute/cm3 of solution]/[g of free solute/cm3 of polymer free solution]

n

flow behavior index

MBg g mol−1

molucular weight of liquid solvent

MPg g mol−1

molecular weight of the polymer

MSg g mol−1

Molecular weight of polymer solution (= MBXB+MPXP)

R cm3 atm g mol−1 K−1

ideal gas law constant

T K

absolute temperature

VBcm3 g mol−1

molar volume of liquid solvent

VPcm3 g mol−1

molar volume of polymer

VScm3 g mol−1

molar volume of polymer solution

XB

solvent molar fraction

XP

polymer molar fraction

α

polymer blockage shape factor

φP

volume fraction of polymer in polymer solution

η g cm−1 s−1

viscosity

ηag cm−1 s−1

apparent viscosity of the polymer solution

ηicm3 g−1

intrinsic viscosity

η0 g cm−1 s−1

solvent viscosity

ηPg cm−1 s−1

polymer solution viscosity

ηR

relative viscosity (= η/η0)

ηγ=0 g cm−1 s−1

viscosity of polymer solution obtained at zero shear rate

ϱ0 g cm−3

water density

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References

  1. 1.
    Whithcomb, P. J.; Ek, B. J.; Macosko, C. W.: Rheology of xanthan gum solutions. In: Sandford, A.; Laskin, A. I. (Eds.): Extracellular Microbial Polysaccharides, A. C. S. Symposium series Vol. 45, pp. 160–173. Washington D. C. (1977)Google Scholar
  2. 2.
    Jamieson, A. M.; Southwick, J. G.; Blackwell, J.: Dynamical behavior of xanthan polysaccharide in solution. J. Polym. Sci. 20 (1982) 1513–1524Google Scholar
  3. 3.
    Galindo, E.; Torrestiana, B.; García Rejón, A.: Rheological characterization of xanthan fermentation broths and their reconstitued solutions. Biopr. Eng. 4 (1989) 113–118Google Scholar
  4. 4.
    Lim, T.; Uhl, J. T.; Prud'homme, R. K.: Rheology of self associating concentrated xanthan solutions. J. Rheol. 28 (1984) 367–379CrossRefGoogle Scholar
  5. 5.
    Torrestiana, B.; Galindo, E.; Brito, E.: Cooperative binding of sucrose in xanthan gum solutions. Biotech. Prog. 4 (1988) 14–18Google Scholar
  6. 6.
    Osmers, H. R.; Metzner, A.: Diffusion in dilute polymeric solutions. Ind. Eng. Chem. Fundam. 11 (1972) 161–169Google Scholar
  7. 7.
    Li, S. U.; Gainer, J. L.: Diffusion in polymer solutions. Ind. Eng. Chem. Fundam. 7 (1968) 433–440Google Scholar
  8. 8.
    Geankoplis, C. J.; Okos, M. R.; Grulke, E. A.: Diffusion of urea and potassium chloride in albumin solution. J. Chem. Eng. Data 23 (1978) 40–44Google Scholar
  9. 9.
    Nystrom, B.; Roots, J.: Diffusion transport of sucrose, β-alanine and bovine serum albumin in aqueous solutions of hydroxypropyl cellulose. Europ. Polym. J. 16 (1980) 201–204CrossRefGoogle Scholar
  10. 10.
    Oosting, E. M.; Gray, J. I.; Grulke, E. A.: Correlating diffusion coefficients in concentrated carbohydrate solutions. AIChE J. 31 (1985) 773–780CrossRefGoogle Scholar
  11. 11.
    Reuss, M.; Debus, D.; Niebelschutz, H.: Oxygen transfer in viscous fermentation broths. Colloque Soc. Fr. Microbiol., Tolouse/France, pp. 49–70. INSA Tolouse: Société Française de Microbiologie 1980Google Scholar
  12. 12.
    Navari, R. M.; Gainer, J. L.; Hall, K. R.: A predictive theory for diffusion in polymer and protein solutions. AIChE J. 17 (1971) 1028–1033CrossRefGoogle Scholar
  13. 13.
    Zandi, I.; Turner, C. D.: The absorption of oxygen by diluted polymeric solutions. Molecular diffusivity measurements. Chem. Eng. Sci. 25 (1970) 517–528CrossRefGoogle Scholar
  14. 14.
    Secor, R. M.: The effect of concentration on diffusion coefficient in polymer solutions. AIChE J. 11 (1965) 452–456CrossRefGoogle Scholar
  15. 15.
    Chester, S. H.; Lu-Kwang, J.; Baddour, R. F.: The anomaly of oxygen diffusion in aqueous xanthan solutions. Biotechnol. Bioeng. 32 (1988) 8–17Google Scholar
  16. 16.
    Astarita, G.; Mashelkar, R. A.: Heat and mass transfer in non-Newtonian fluids. Chem. Eng. 2 (1977) 100–105Google Scholar
  17. 17.
    Niebelschutz, H.; Reuss, M.: Measurements of oxygen diffusivities in polysaccharide solutions. Third European Congress on Biotechnology, Vol. 2, pp. 579–584. Munich: Verlag Chemie (1984)Google Scholar
  18. 18.
    Colton, C. K.; Smith, K. A.; Merrill, G. W.; Reece, J. M.: Diffusion of organic solutes in stagnant plasma and red cell suspensions. Chem. Eng. Prog. Symp. Ser. 66 (1970) 85–100Google Scholar
  19. 19.
    Goldstick, T. K.; Fatt, I.: Diffusion of oxygen in solutions of blood proteins. Chem. Eng. Prog. Symp. Ser. 66 (1970) 101–113Google Scholar
  20. 20.
    Brito, E.: Diffusion of sucrose and glucose in protein solutions with blockage and binding effects present. M Sc. Thesis. The Ohio State University, Columbus, Ohio, U.S.A. 1982Google Scholar
  21. 21.
    Perkins, L. R.; Geankoplis, C. J.: Molecular diffusion in a ternary liquid system with the diffusing dilute. Chem. Eng. Sci. 24 (1969), 1035–1041CrossRefGoogle Scholar
  22. 22.
    Hayduk, W.; Chang, S. C.: Review of relation between diffusivity and solvent viscosity in diluted liquid solutions. Chem. Eng. Sci., 26 (1971) 635–639CrossRefGoogle Scholar
  23. 23.
    Hiss, G. T.; Cussler, E. L.: Diffusion in high viscosity liquids. AIChE J. 19 (1973) 698–703CrossRefGoogle Scholar
  24. 24.
    Lohse, M.; Alper, E.; Quicker, G.; Decker, W. D.: Diffusivity and solubility of carbondioxide in diluted polymer solution. AIChE J. 27 (1981) 626–631CrossRefGoogle Scholar
  25. 25.
    Perez, J. F.; Sandall, O. C.: Diffusivity measurements for gases in power-law non-Newtonian liquids. AIChE J. 19 (1973) 1073–1075CrossRefGoogle Scholar
  26. 26.
    Summer, J. B.; Howell, S. F.: A method for determination of saccharase activity. J. Biol. Chem. 108 (1935) 51–53Google Scholar
  27. 27.
    Brito, E.: Reología de Fluidos, Ley de la potencia; software. Departamento de Alimentos, Facultad de Química, Universidad Nacional Autónoma de México. México, D. F. 1988Google Scholar

Copyright information

© Springer-Verlag 1989

Authors and Affiliations

  • B. Torrestiana
    • 1
  • E. Galindo
    • 1
  • E. Brito
    • 2
  1. 1.Depto. de Bioingenieria Centro de Investigaciones sobre Ingenieria Genética y BiotecnologíaUniversidad Nacional Autónoma de MéxicoCuernavacaMéxico
  2. 2.Departamento de Alimentos Facultad de QuímicaUniversidad Nacional Autónoma de MéxicoMéxico D. F.México

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