Skip to main content
SpringerLink
Log in

Prediction of Permeate Flux During Ultrafiltration of Polysaccharide in a Stirred Batch Cell

  • Communication
  • Published:
Food and Bioprocess Technology Aims and scope Submit manuscript

Abstract

Ultrafiltration of polysaccharide macromolecule has been carried out in a stirred batch cell using a fully retentive membrane over a wide range of operating conditions. An unsteady state mass transfer model in conjunction with resistance-in-series model is developed using film theory. The proposed model is used to predict the transient permeate flux decline behavior in gel controlled ultrafiltration. This model is also able to quantify the variation of bulk volume as well as the bulk concentration of solute with time. The variation of viscosity as a function of solute concentration is included in the model. A model parameter is used in this model and is evaluated by optimizing the experimental flux profiles with calculated flux profiles. The model predictions are successfully compared with the experimental data. A parametric study has been performed to observe the effect of different process parameters on the filtration performance in terms of transient permeate flux decline behavior. The proposed model in general will provide a better understanding of gel controlled ultrafiltration.

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

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7

Abbreviations

A :

Effective membrane area, square meters

a :

Parameter used in Eq. 19, dimensionless

C :

Concentration of pectin, kilograms per cubic meter

d p :

Equivalent diameter, meters

D :

Diffusivity of pectin, square meters per second

K :

Boltzmann constant (1.38 × 10−23), joules per Kelvin

k :

Mass transfer coefficient, meters per second

L :

Gel layer thickness, meters

M ω :

Molecular weight, kilograms per kilogram-mole

N total :

Total number of data points, dimensionless

Pe w :

Water flux, dimensionless

\( Pe_{\mathrm{w}}^0 \) :

Pure water flux, dimensionless

R :

Radius of stirred cell, meters

R m :

Membrane hydraulic resistance, per meter

R g :

Gel layer resistance, per meter

Re :

Reynolds number at the bulk condition

Sc b :

Schmidt number at the bulk condition

Sh :

Sherrod number at the bulk condition

T :

Absolute temperature, degrees Kelvin

t :

Time of experiment, seconds

V :

Volume, cubic meters

J :

Permeate flux, cubic meters per square meter-second

J exp :

Experimental permeate flux, cubic meters per square meter-second

J cal :

Calculated permeate flux, cubic meters per square meter-second

y :

Coordinate from the membrane, meters

z :

Parameter in Eq. 13, kilograms per kilomole-cubic meter

ν :

Parameter used in Eq. 4, dimensionless

α 1 :

Specific gel layer resistance, meters per kilogram

ω :

Angular speed of stirring, radian per second

μ :

Viscosity of the solution, Pascal-second

δ g :

Gel layer thickness, meters

δ c :

Thickness of concentration boundary layer, meters

ε g :

Gel porosity, dimensionless

ΔP :

Transmembrane pressure, kilopascals

ρ g :

Gel density, kilograms per cubic meter

ρ :

Density, kilograms per cubic meter

τ total :

Total operation time, dimensionless

τ :

Operation time, dimensionless

0:

Initial condition

b:

Bulk condition

p:

Permeate

f:

Feed

g:

Gel

*:

Dimensionless

References

  • Azeredo, J., Oliveria, R., & Lazarova, V. (1998). A new method for extraction of exopolymer from activated sludges. Water Science and Technology, 37, 367–370.

    Article  CAS  Google Scholar 

  • Belfort, G., Davis, R. H., & Zydney, A. L. (1994). The behavior of suspensions and macromolecular solutions in cross-flow microfiltration. Journal of Membrane Science, 96, 1–58.

    Article  CAS  Google Scholar 

  • Belluci, F., Drioli, E., & Scardi, U. (1975). Protein ultrafiltration: An experimental study. Journal of Applied Polymer Science, 19, 1639–1647.

    Article  Google Scholar 

  • Bhattacharjee, S., Sharma, A., & Bhattacharya, P. K. (1996). A unified model for flux prediction during batch cell ultrafiltration. Journal of Membrane Science, 111, 243–258.

    Article  CAS  Google Scholar 

  • Blatt, W. F., Dravid, A., Michaels, A. S., & Nelson, L. (1970). Solute polarization and cake formation in membrane ultrafiltration: Causes, consequences and control techniques. In J. E. Flinn (Ed.), Membrane science and technology. New York: Plenum Press.

    Google Scholar 

  • Chakraborty, S., Bag, B. C., DasGupta, S., Basu, J. K., & De, S. (2004). Prediction of permeate flux and permeate concentration in nanofiltration of dye solution. Separation and Purification Technology, 35, 141–152.

    Article  CAS  Google Scholar 

  • Chang, I. S., Clech, P.-Le, Jefferson, B., & Judd, S. (2002). Membrane fouling in membrane bioreactors for wastewater treatment. Journal of Environmental Engineering, 128:1018–1029.

  • De, S., & Bhattacharya, P. K. (1997). Modeling of ultrafiltration process for a two-component aqueous solution of low and high (gel-forming) molecular weight solutes. Journal of Membrane Science, 136, 57–69.

    Article  CAS  Google Scholar 

  • Frank, B. F., & Belfort, G. (2003). Polysaccharides and sticky membrane surfaces: Critical ionic effects. Journal of Membrane Science, 212, 205–212.

    Article  CAS  Google Scholar 

  • Haber, A., & Runyon, R. (1977). General statistics (3rd ed.). Reading: Addison-Wesley Publishing Company.

    Google Scholar 

  • Kirk, D. E., Montgomery, M. W., & Kortekaas, M. G. (1983). Clarification of pear juice by hollow fiber ultrafiltration. Journal of Food Science, 48, 1663–1667.

    Article  Google Scholar 

  • Le Clech, P., Chan, V., & Fane, A. G. (2006). Review: Fouling in membrane bioreactors used in wastewater treatment. Journal of Membrane Science, 284, 17–53.

    Article  Google Scholar 

  • Le Clech, P., Marselina, Y., Ye, Y., Stuetz, R. M., & Chen, V. (2007). Visualisation of polysaccharide fouling on microporous membrane using different characterisation techniques. Journal of Membrane Science, 290, 36–45.

    Article  Google Scholar 

  • Nataraj, S., Schomäcker, R., Kraume, M., Mishra, I. M., & Drews, A. (2008). Analyses of polysaccharide fouling mechanisms during cross-flow membrane filtration. Journal of Membrane Science, 308, 152–161.

    Article  CAS  Google Scholar 

  • Pritchard, M., Howell, J. A., & Field, R. W. (1995). The ultrafiltration of viscous fluids. Journal of Membrane Science, 102, 223–235.

    Article  CAS  Google Scholar 

  • Rai, P., Majumdar, G. C., Dasgupta, S., & De, S. (2005a). Understanding ultrafiltration performance with mosambi juice in an unstirred batch cell. Journal of Food Process. Engineering, 28, 166–180.

    Article  Google Scholar 

  • Rai, P., Majumdar, G. C., DasGupta, S., & De, S. (2005b). Quantification of flux decline of depectinized mosambi (Citrus sinensis (L.) Osbeck) juice using unstirred batch ultrafiltration. Journal of Food Process Engineering, 28, 359–377.

    Article  Google Scholar 

  • Rai, P., Majumdar, G. C., DasGupta, S., & De, S. (2006a). Modeling of sucrose permeation through pectin gel during ultrafiltration of depectinized mosambi (Citrus sinensis (L.) Osbech) juice. Journal of Food Science, 71(2), E87–E94.

    Google Scholar 

  • Rai, P., Rai, C., Majumdar, G. C., DasGupta, S., & De, S. (2006b). Resistance in series model for ultrafiltration of mosambi (Citrus sinensis (L.) Osbeck) juice in a stirred continuous mode. Journal of Membrane Science, 283, 116–122.

    Google Scholar 

  • Rai, P., Majumdar, G. C., DasGupta, S., & De, S. (2007). Modeling of permeate flux of synthetic fruit juice and mosambi juice (Citrus sinensis (L.) Osbeck) in stirred continuous ultrafiltration. LWT, 40, 1765–1773.

    Article  CAS  Google Scholar 

  • Rai, C., Rai, P., Majumdar, G. C., De, S., & DasGupta, S. (2010). Mechanism of permeate flux decline during microfiltration of water melon (Citrullus lanatus) juice. Food and Bioprocess Technology, 3(4), 545–553.

    Google Scholar 

  • Rayessa El, Y., Albasia, C., Bacchinc, P., Taillandier, P., Mietton-Peuchote, M., & Devatinee, A. (2011). Cross-flow microfiltration of wine: Effect of colloids on critical fouling conditions. Journal of Membrane Science, 385–386, 177–186.

    Article  Google Scholar 

  • Sarkar, B., & De, S. (2012). A combined complete pore blocking and cake filtration model for steady state electric field assisted ultrafiltration. American Institute of Chemical Engineers, 58(5), 1435–1446.

    Article  CAS  Google Scholar 

  • Sarkar, B., Pal, S., Ghosh, T. B., De, S., & DasGupta, S. (2008). A study of electric field enhanced ultrafiltration of synthetic fruit juice and optical quantification of gel deposition. Journal of Membrane Science, 311, 112–120.

    Article  CAS  Google Scholar 

  • Stryer, L. (1998). Biochemistry. NewYork: Freeman.

    Google Scholar 

  • Tasselli, F., Cassano, A., & Drioli, E. (2007). Ultrafiltration of kiwifruit juice using modified poly (ether ketone) hollow fibre membranes. Separation and Purification Technology, 57, 94–102.

    Article  CAS  Google Scholar 

  • Thakur, B. R., Singh, R. K., & Handa, A. K. (1997). Chemistry and uses of pectin—A review. Critical Reviews in Food Science and Nutrition, 37(1), 47–73.

    Article  CAS  Google Scholar 

  • Todisco, S., Tallarico, P., & Drioli, E. (1998). Modeling and analysis of the effects of ultrafiltration on the quality of freshly squeezed orange juice. Italian Food and Beverage Technology, 12, 3–8.

    Google Scholar 

  • Vernhet, A., Pellerin, P., Belleville, M. P., Planque, J., & Moutounet, M. (1999). Relative impact of major wine polysaccharides on the performances of an organic microfiltration membrane. American Journal of Enology and Viticulture, 50, 51–56.

    CAS  Google Scholar 

  • Wu, M. L., Zall, R. R., & Tzeng, W. C. (1990). Microfiltration and ultrafiltration comparison of apple juices clarification. Journal of Food Engineering, 55, 1162–1163.

    Google Scholar 

  • Ye, Y., P-Le, C., Chen, V., Fane, A. G., & Jefferson, B. (2005). Fouling mechanisms of alginate solutions as model extracellular polymeric substances. Desalination, 175, 7–20.

    Article  CAS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. University School of Chemical Technology, GGS Indraprastha University, Delhi, 110006, India

    Pranshu Sharma & Biswajit Sarkar

Authors
  1. Pranshu Sharma
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Biswajit Sarkar
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Biswajit Sarkar.

Appendix

Appendix

Viscosity: Viscosity of various pectin solutions at normal pH and at 25 °C is experimentally measured and can be expressed by the following polynomial (correlation coefficient 0.997) as follows:

$$ \mu =0.9\left( {1+4.05\times {10^{-1 }}\mathrm{C}+1.128\times {10^{-2 }}{{\mathrm{C}}^2}+3.69\times {10^{-3 }}{{\mathrm{C}}^3}} \right)\times {10^{-3 }}. $$

Where, μ is in Pasacl-second and C is in kilograms per cubic meter.

Density: Density of pectin solution has been taken as 1,000 kg/m3.

Diffusivity: Diffusivity of pectin solution at feed concentration of 1, 3, and 5 kg/m3 are calculated using Eq. 12 and are found to be 7.25 × 10−11, 4.6 × 10−11, 3.2 × 10−11 m2/s, respectively.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Sharma, P., Sarkar, B. Prediction of Permeate Flux During Ultrafiltration of Polysaccharide in a Stirred Batch Cell. Food Bioprocess Technol 6, 3634–3643 (2013). https://doi.org/10.1007/s11947-012-0990-7

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11947-012-0990-7

Keywords

Search

Navigation