Skip to main content
Log in

A rheological model to predict viscosity of dispersions as a function of the modified Peclet number

  • Article
  • Published:
Korea-Australia Rheology Journal Aims and scope Submit manuscript

Abstract

The suspensions and emulsions are important products and raw materials for various industrial production and processing branches. The knowledge concerning the rheological properties of such substances is of key importance for many manufacturing processes. Many dependences can be found within the literature but there is lack of model that takes into account the influence of inner phase concentration, share rate, and diameters of the dispersed phase particles on a viscosity of these systems. The presented work goal was to obtain a rheological equation containing the modified form of Peclet number, which would provide the relation between the viscosity, the volume fraction, and the shear rate. The theory of Kozeny-Carman, which transforms the granular structure into a bunch of the torturous capillary tubes, was the base of this model. The proposed model has been verified for data available in the literature and for the data obtained in authors own experiments.

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

Access this article

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

References

  • Anvari, M. and H.S. Joyner, 2017, Effect of formulation on structure-function relationships of concentrated emulsions: Rheological, tribological, and microstructural characterization, Food Hydrocolloids 72, 11–26.

    Article  Google Scholar 

  • Aomari, N., R. Gaudu, F. Cabioc, and A. Omari, 1998, Rheology of water in crude oil emulsions, Colloid Surf. A-Physicochem. Eng. Asp. 139, 13–20.

    Article  Google Scholar 

  • Ariffin, T.S.T., E. Yahya, and H. Husin, 2016, The rheology of light crude oil and water-in-oil-emulsion, Procedia Eng. 148, 1149–1155.

    Article  Google Scholar 

  • Avazmohammadi, R. and P.P. Castaneda, 2016, Macroscopic rheological behavior of suspensions of soft solid particles in yield stress fluids, J. Non-Newton. Fluid Mech. 234, 139–161.

    Article  Google Scholar 

  • Böttcher, S., J.K. Keppler, and S. Drusch, 2017, Mixtures of Quillaja saponin and beta-lactoglobulin at the oil/water-interface: Adsorption, interfacial rheology and emulsion properties, Colloid Surf. A-Physicochem. Eng. Asp. 518, 46–56.

    Article  Google Scholar 

  • Carreau, P.J., D.C.R. De Kee, and R.P. Chhabra, 1997, Rheology of Polymeric Systems: Principles and Applications, Hanser, New York.

    Google Scholar 

  • Casson, N.A., 1959, A flow equation for pigment oil suspensions of the printing ink type, In: Mill, C.C., eds., Rheology of Disperse Systems, Pergamon Press, Oxford, 84–104.

    Google Scholar 

  • Castel, V., A.C. Rubiolo, and C.R. Carrara, 2017, Droplet size distribution, rheological behavior and stability of corn oil emulsions stabilized by a novel hydrocolloid (Brea gum) compared with gum arabic, Food Hydrocolloids 63, 170–177.

    Article  Google Scholar 

  • Ching, S.H., N. Bansal, and B. Bhandari, 2016, Rheology of emulsion-filled alginate microgel suspensions, Food Res. Int. 80, 50–60.

    Article  Google Scholar 

  • Cohen-Addad, S. and R. Höhler, 2014, Rheology of foams and highly concentrated emulsions, Curr. Opin. Colloid Interface Sci. 19, 536–548.

    Article  Google Scholar 

  • Cross, M.M., 1965, Rheology of non-Newtonian fluids: A new flow equation for pseudoplastic systems, J. Colloid Sci. 20, 417–437.

    Article  Google Scholar 

  • dos Santosa, R.G., A.C. Watson, and W. Loh, 2014, Phase segregation, shear thinning and rheological behavior of crude oil-in-water emulsions, Chem. Eng. Res. Des. 92, 1629–1636.

    Article  Google Scholar 

  • Herschel, W.H. and R. Bulkley, 1926, Konsistenzmessungen von Gummi-Benzollösungen, Colloid Polym. Sci. 39, 291–300.

    Google Scholar 

  • Huang, L. and M. Petermann, 2015, An experimental study on rheological behaviors of paraffin/water phase change emulsion, Int. J. Heat Mass Transf. 83, 479–486.

    Article  Google Scholar 

  • Kemblowski, Z., M. Dziubiński, and J.P. Sek, 1987, Flow of non-Newtonian fluids through granular media, In: Mashelkar, R.A., A.S. Mujumdar, and M.R. Kamal, eds., Advances in Transport Processes, Vol. 5, Wiley Eastern Ltd., New Delhi, 117–175.

    Google Scholar 

  • Krieger, I.M., 1972, Rheology of monodisperse latices, Adv. Colloid Interface Sci. 3, 111–136.

    Article  Google Scholar 

  • Krieger, I.M. and T.J. Dougherty, 1959, A mechanism for non-Newtonian flow in suspensions of rigid spheres, J. Rheol. 3, 137–152.

    Google Scholar 

  • Laba, D., 1993, Rheological Properties of Cosmetics and Toiletries, CRC Press, New York.

    Google Scholar 

  • Lorenzo, G., N. Zaritzky, and A. Califano, 2008, Modeling rheological properties of low-in-fat o/w emulsions stabilized with xanthan/guar mixtures, Food Res. Int. 41, 487–494.

    Article  Google Scholar 

  • Mader, H.M., E.W. Llewellin, and S.P. Mueller, 2013, The rheology of two-phase magmas: A review and analysis, J. Volca-nol. Geother. Res. 257, 135–158.

    Article  Google Scholar 

  • Meriem-Benziane, M., S.A. Abdul-Wahab, M. Benaicha, and M. Belhadri, 2012, Investigating the rheological properties of light crude oil and the characteristics of its emulsions in order to improve pipeline flow, Fuel 95, 97–107.

    Article  Google Scholar 

  • Mooney, M., 1951, The viscosity of a concentrated suspension of spherical particles, J. Colloid Sci. 6, 162–170.

    Article  Google Scholar 

  • Mougel, J., O. Alvarez, C. Baravian, F. Caton, P. Marchal, M.J. Stebe, and L. Choplin, 2006, Aging of an unstable w/o gel emulsion with a nonionic surfactant, Rheol. Acta 45, 555–560.

    Article  Google Scholar 

  • Mueller, S., E.W. Llewellin, and H.M. Mader, 2009, The rheology of suspensions of solid particles, Proc. R. Soc. A-Math. Phys. Eng. Sci. 466, 1201–1228.

    Article  Google Scholar 

  • Ostwald, W., 1929, Ueber die rechnerische Darstellung des Strukturgebietes der Viskosität, Colloid Polym. Sci. 47, 176–187.

    Google Scholar 

  • Pajouhandeh, A., A. Kavousi, M. Schaffie, and M. Ranjbar, 2017, Experimental measurement and modeling of nanoparticle-stabilized emulsion rheological behavior, Colloid Surf. A-Physicochem. Eng. Asp. 520, 597–611.

    Article  Google Scholar 

  • Princen, H.M. and A.D. Kiss, 1986, Rheology of foams and highly concentrated emulsions: III. Static shear modulus, J. Colloid Interface Sci. 112, 427–437.

    Article  Google Scholar 

  • Qiao, X., L. Wang, Z. Shao, K. Sun, and R. Miller, 2015, Stability and rheological behaviors of different oil/water emulsions stabilized by natural silk fibroin, Colloid Surf. A-Physicochem. Eng. Asp. 475, 84–93.

    Article  Google Scholar 

  • Savage, R.M., 2000, Effects of rheology modifiers on the flow curves of idealised and food suspensions, Food Hydrocolloids 14, 209–215.

    Article  Google Scholar 

  • Sharu, B.K., G.P. Simon, W. Cheng, J. Zank, and A.R. Bhattacharyya, 2017, Development of microstructure and evolution of rheological characteristics of a highly concentrated emulsion during emulsification, Colloid Surf. A-Physicochem. Eng. Asp. 532, 342–350.

    Article  Google Scholar 

  • Sisko, A.W., 1958, The flow of lubricating greases, Ind. Eng. Chem. 50, 1789–1792.

    Article  Google Scholar 

  • Sochi, T., 2009, Single-phase flow of non-Newtonian fluids in porous media, Technical Report arXiv: 0907.2399v1.

  • Taborda, E.A., C.A. Franco, S.H. Lopera, V. Alvarado, and F.B. Cortés, 2016, Effect of nanoparticles/nanofluids on the rheology of heavy crude oil and its mobility on porous media at reservoir conditions, Fuel 184, 222–232.

    Article  Google Scholar 

  • Tripathi, S., A. Bhattacharya, R. Singh, and R.F. Tabor, 2017, Rheological behavior of high internal phase water-in-oil emulsions: Effects of droplet size, phase mass fractions, salt concentration and aging, Chem. Eng. Sci. 174, 290–301.

    Article  Google Scholar 

  • Whitby, C.P. and P.C. Garcia, 2014, Time-dependent rheology of clay particle-stabilised emulsions, Appl. Clay Sci. 96, 56–59.

    Article  Google Scholar 

  • Zadymova, N.M., Z.N. Skvortsova, V.Y. Traskine, F.A. Kulikov-Kostyushko, V.G. Kulichikhin, and A.Y. Malkin, 2017, Rheological properties of heavy oil emulsions with different morphologies, J. Pet. Sci. Eng. 149, 522–530.

    Article  Google Scholar 

  • Zhang, X., J.Y. Wu, and J. Niu, 2016, PCM-in-water emulsion for solar thermal applications: The effects of emulsifiers and emulsification conditions on thermal performance, stability and rheology characteristics, Sol. Energy Mater. Sol. Cells 147, 211–224.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Łukasz Przybysz.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Sęk, J.P., Błaszczyk, M.M. & Przybysz, Ł. A rheological model to predict viscosity of dispersions as a function of the modified Peclet number. Korea-Aust. Rheol. J. 31, 81–88 (2019). https://doi.org/10.1007/s13367-019-0009-2

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s13367-019-0009-2

Keywords

Navigation