Skip to main content
SpringerLink
Log in

A mathematical model for the biosorption of copper on immobilized yeast in alginate

  • Modeling
  • Published:
Environmental Modeling & Assessment Aims and scope Submit manuscript

Abstract

Saccharomyces cerevisiae yeast was entrapped in alginate for the recovery of copper ions from aqueous solution, in which both yeast and alginate could take metal ions. The Freundlich isotherm had been shown to be successful in describing biosorption and a linear biosorption was assumed when the equilibrium copper ion concentration in the fluid was lower than 1 mg/l. The biosorption isotherm was found to be independent of the immobilized yeast densities ranging from 6 to 17 percent. A mathematical model describing the mass transport along with the biosorption was developed with the main assumptions that the inner diffusion with constant diffusivity was the rate limiting step of the biosorption process and the pore solution locally equilibrated with the adjacent biosorbent (both yeast and alginate). This model has theoretical advantages over the formerly proposed Shrinkage Core Model and Linear Adsorption Model. Effective diffusion coefficients of copper ion in immobilized yeast beads using the model developed were found to be independent of the immobilized yeast densities ranging from 6 to 17 percent. The average result was 2.22×10−5 cm2/s.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

Abbreviations

C :

Copper concentration in the pore of the bead (mg/l)

C 0 :

Initial concentration of copper ion in the reactor (mg/l)

C b :

Copper concentration in the bulk solution (mg/l)

C ∞ :

Final (equilibrium) concentration of free copper in solution (mg/l)

C 0 :

Average copper binding site density of immobilized yeast beads based on biosorption isotherm (mg/l)

D e :

Effective diffusivity of copper ion in the immobilized yeast bead (cm2/s)

i :

Grid point corresponding tor axis

j :

Grid point corresponding tot axis

m :

Grid dimension int axis

N :

Number of immobilized yeast beads in the reactor

n :

Grid dimension inr axis

Q :

Copper concentration in the biomass (mg/g dry mass)

R :

Average radius of the immobilized yeast beads (cm)

r :

Distance from the center of a bead (cm)

T :

Experiment period, (sec)

t :

Time (sec)

V :

Volume of copper ion solution except beads in the reactor (ml)

X :

Dimensionless concentration (C 0−C)/(C 0−C ∞)

∈:

Apparent immobilized yeast bead porosity

ρ:

Apparent biomass density (g dry mass/l)

References

  1. C.L. Brierley, Geomicrobiol. J. 8 (1991) 201.

    Google Scholar 

  2. T.H. Jeffers, C.R. Ferguson and P.G. Bennett, in:Mineral Processing, eds. R.W. Smith and M. Misra, The Minerals, Metal and Materials Society, Warrendale, PA, 1991, p. 289.

    Google Scholar 

  3. D. Brady and J.R. Duncan, in:Biohydrometallurgical Technologies, Proceedings of an International Biohydrometallurgy Symposium, Vol. 2, eds. A.E. Torma, M.L. Apel and C.L. Brierley, The Minerals, Metals and Materials Society, Wyoming, USA, 1993, p. 711.

    Google Scholar 

  4. D. Brady, A. Stoll and J.R. Duncan, Environ. Technol. 15 (1994) 429.

    Google Scholar 

  5. B. Mattuschka, K. Junghans and G. Straube, in:Biohydrometallurgical Technologies, Proceedings of an International Biohydrometallurgy Symposium, Vol. 2, eds. A.E. Torma, M.L. Apel and C.L. Brierley, The Minerals, Metals and Materials Society, Wyoming, USA, 1993, p. 125.

    Google Scholar 

  6. Y. Lu and E. Wilkins, J. Hazard. Mater. (1996), to appear.

  7. M. Tsezos, S.H. Noh and M.H.I. Baird, A batch reactor mass transfer kinetic model for immobilized biomass biosorption, Biotechnol. Bioeng. 32 (1988) 545–553.

    Google Scholar 

  8. L.K. Jang, W. Brand, M. Resong, W. Mainieri and G.G. Geesey, Environ. Prog. 9 (1990) 269.

    Google Scholar 

  9. L.K. Jang, S.L. Lopez and S.L. Eastman, Biotechnol. Bioeng. 37 (1991) 266.

    Google Scholar 

  10. L.K. Jang, D. Nguyen and G.G. Geesey, Water Res. 29 (1995) 307.

    Google Scholar 

  11. L.K. Jang, D. Nguyen and G.G. Geesey, Water Res. 29 (1995) 315.

    Google Scholar 

  12. F. Roe, Z. Lewandowski, D. Chen and R. Hughes, in:Biohydrometallurgical Technologies, Proceedings of an International Biohydrometallurgy Symposium, Vol. 2, eds. A.E. Torma, M.L. Apel and C.L. Brierley, The Minerals, Metals and Materials Society, Wyoming, USA, 1993, p. 145.

    Google Scholar 

  13. G.M. Gadd, in:Immobilization of Ions by Bio-sorption, eds. H. Eccles and S. Hunt, Ellis Horwood Ltd., West Sussex, England, 1986, p. 135.

    Google Scholar 

  14. J.E. Bailey and D.F. Ollis,Biochemical Engineering Fundamentals, McGraw-Hill, New York, USA, 1984.

    Google Scholar 

  15. M.G. Rao and A.K. Gupta, Chem. Eng. J. 24 (1982) 181.

    Google Scholar 

  16. M.L. Apel and A.E. Torma, Can. J. Chem. Eng. 71 (1993) 652.

    Google Scholar 

  17. H. Tanaka, M. Matsumura and I.A. Veliky, Biotechnol. Bioeng. 26 (1984) 53.

    Google Scholar 

  18. B.J.M. Hannous and G. Stephanopoulos, Biotechnol. Bioeng. 28 (1986) 829.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Chemical and Nuclear Engineering, University of New Mexico, 87131-1341, Albuquerque, NM, USA

    Yongming Lu & Ebtisam Wilkins

Authors
  1. Yongming Lu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Ebtisam Wilkins
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Lu, Y., Wilkins, E. A mathematical model for the biosorption of copper on immobilized yeast in alginate. Environ Model Assess 1, 159–169 (1996). https://doi.org/10.1007/BF01874903

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01874903

Keywords

Search

Navigation