Flow and Functional Models for Rheological Properties of Fluid Foods

  • M. Anandha Rao
Part of the Food Engineering Series book series (FSES)


A flow model may be considered to be a mathematical equation that can describe rheological data, such as shear rate versus shear stress, in a basic shear diagram, and that provides a convenient and concise manner of describing the data. Occasionally, such as for the viscosity versus temperature data during starch gelatinization, more than one equation may be necessary to describe the rheological data. In addition to mathematical convenience, it is important to quantify how magnitudes of model parameters are affected by state variables, such as temperature, and the effect of structure/composition (e.g., concentration of solids) of foods and establish widely applicable relationships that may be called functional models.


Shear Rate Apparent Viscosity Cocoa Butter Relative Viscosity Whey Protein Isolate 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Abdel-Khalik, S. I., Hassager, O., and Bird, R. B. 1974. Prediction of melt elasticity from viscosity data. Polymer Eng. and Sci. 14: 859–867.CrossRefGoogle Scholar
  2. Agarwala, M. K., Patterson, B. R., and Clark, P. E. 1992. Rheological behavior of powder injection molding model slurries. J. Rheol. 36: 319–334.CrossRefGoogle Scholar
  3. Aguilera, J. M. and Kessler, H. G. 1989. Properties of mixed and filled dairy gels. J. Food Sci. 54: 1213–1217, 1221.CrossRefGoogle Scholar
  4. Al-Malah, K.-I.-M., Abu-Jdayil, B., Zaitoun, S., and Al-Majeed-Ghzawi, A. 2001. Application of WLF and Arrhenius kinetics to rheology of selected dark-colored honey. J. Food Process Eng. 24(5): 341–357.CrossRefGoogle Scholar
  5. Barnes, H. A. and Walters, K. 1989. The yield stress myth? Rheol. Acta 24: 323–326.CrossRefGoogle Scholar
  6. Barnes, H.A., Hutton, J. F., and Walters, K. 1989. An Introduction to Rheology, Elsevier Science Publishers B.V., Amsterdam, The Netherlands.Google Scholar
  7. Bird, R. B., Dai, G. C., and Yarusso, B. J. 1982. The rheology and flow of viscoplastic materials. Rev. Chem. Eng. 1: 1–70.Google Scholar
  8. Brodkey, R. S. 1967. The Phenomena of Fluid Motions, Addison-Wesley, Reading, MA.Google Scholar
  9. Casson, N. 1959. A flow equation for pigment-oil suspensions of the printing ink type, in Rheology of Disperse Systems, ed. C. C. Mill, pp. 82–104, Pergamon Press, New York.Google Scholar
  10. Choi, G. R. and Krieger, I. M. 1986. Rheological studies on sterically stabilized model dispersions of uniform colloidal spheres II. Steady-shear viscosity. J. Colloid Interface Sci. 113: 101–113.CrossRefGoogle Scholar
  11. Cross, M. M. 1965. Rheology of non-Newtonian fluids: a new flow equation for pseudoplastic systems. J. Colloid Sci. 20: 417–437.CrossRefGoogle Scholar
  12. Da Silva, P. M. S., Oliveira, J. C., and Rao, M. A. 1997. The effect of granule size distribution on the rheological behavior of heated modified and unmodified maize starch dispersions. J. Texture Stud. 28:123–138.CrossRefGoogle Scholar
  13. Demetriades, K., Coupland, J., and McClements, D. J. 1996. Investigation of emulsion stability using ultrasonic spectroscopy, in 1996 IFT Annual Meeting Book of Abstracts, pp. 109–110, Institute of Food Technologists, Chicago, IL.Google Scholar
  14. Demetriades, K., Coupland, J., and McClements, D. J. 1997. Physical properties of whey protein stabilized emulsions as related to pH and NaCl. J. Food Sci. 62: 342–347.CrossRefGoogle Scholar
  15. Dervisoglu, M. and Kokini, J. L. 1986. Steady shear rheology and fluid mechanics of four semi-solid foods.J. Food Sci. 51: 541–546, 625.CrossRefGoogle Scholar
  16. Dickinson, E. 1993. Towards more natural emulsifiers. Trends Food Sci. Technol. 4: 330–334.CrossRefGoogle Scholar
  17. Dickinson, E. and Pawlowsky, K. 1996. Effect of high-pressure treatment of protein on the rheology of flocculated emulsions containing protein and polysaccharide. J. Agric. Food Chem. 44: 2992–3000.CrossRefGoogle Scholar
  18. Dickinson, E. and Yamamoto, Y. 1996a. Viscoelastic properties of heat-set whey protein-stabilized emulsion gels with added lecithin. J. Food Sci. 61: 811–816.CrossRefGoogle Scholar
  19. Dickinson, E. and Yamamoto, Y. 1996b. Effect of lecithin on the viscoelastic properties of β-lactoglobulinstabilized emulsion gels. Food Hydrocollids 10: 301–307.CrossRefGoogle Scholar
  20. Dickinson, E., Hong, S.-T., and Yamamoto, Y. 1996. Rheology of heat-set emulsion gels containing beta-lactoglobulin and small-molecule surfactants. Neth. Milk Dairy J. 50: 199–207.Google Scholar
  21. Einstein, A. 1906. Eine neue bestimmung der molekuldimension. Ann. Physik 19: 289–306.CrossRefGoogle Scholar
  22. Einstein, A. 1911. Berichtigung zu meiner arbeit: Eine neue bestimmung der molekuldimension. Ann. Physik 34: 591–592.CrossRefGoogle Scholar
  23. Ellis, H. S., Ring, S. G., and Whittam, M. A. 1989. A comparison of the viscous behavior of wheat and maize starch pastes. J. Cereal Sci. 10: 33–44.CrossRefGoogle Scholar
  24. Fang, T. N., Tiu, C., Wu, X., and Dong, S. 1996. Rheological behaviour of cocoa dispersions. J. Texture Stud. 26: 203–215.CrossRefGoogle Scholar
  25. Fang, T., Zhang, H., Hsieh, T. T., and Tiu, C. 1997. Rheological behavior of cocoa dispersions with cocoa butter replacers. J. Texture Stud. 27: 11–26.CrossRefGoogle Scholar
  26. Ferry, J. D. 1980. Viscoelastic Properties of Polymers, John Wiley, New York.Google Scholar
  27. Genovese, D. B. and Rao, M. A. 2003. Role of starch granule characteristics (volume fraction, rigidity, and fractal dimension) on rheology of starch dispersions with and without amylose. Cereal Chem. 80: 350–355.CrossRefGoogle Scholar
  28. Giboreau, A., Cuvelier, G., and Launay, B. 1994. Rheological behavior of three biopolymer/water systems with emphasis on yield stress and viscoelastic properties. J. Texture Stud. 25: 119–137.CrossRefGoogle Scholar
  29. Hiemenz, P. C. and Rjagopalan, R. 1997. Principles of Colloid and Surface Chemistry, 3rd ed., Marcel Dekker, Inc., New York.Google Scholar
  30. Holdsworth, S. D. 1971. Applicability of rheological models to the interpretation of flow and processing behavior of fluid food products. J. Texture Stud. 4: 393–418.CrossRefGoogle Scholar
  31. Holdsworth, S.D.1993. Rheological models used for the prediction of the flow properties of food products: a literature review. Trans. Inst. Chem. Engineers 71, Part C: 139–179.Google Scholar
  32. Jacon, S. A., Rao, M. A., Cooley, H. J., and Walter, R. H. 1993. The isolation and characterization of a water extract of konjac flour gum. Carbohydr. Polym. 20: 35–41.CrossRefGoogle Scholar
  33. Jinescu, V. V. 1974. The rheology of suspensions. Int. Chem. Eng. 143: 397–420.Google Scholar
  34. Kimball, L. B. and Kertesz, Z. I. 1952. Practical determination of size distribution of suspended particles in macerated tomato products. Food Technol. 6: 68–71.Google Scholar
  35. Kitano, T., Kataoka, T., and Shirota, T. 1981. An empirical equation of the relative viscosity of polymer melts filled with various inorganic fillers. Rheol. Acta 20: 207–209.CrossRefGoogle Scholar
  36. Krieger, I. J. 1985. Rheology of polymer colloids, in Polymer Colloids, eds. R. Buscall, T. Corner, and J. F. Stageman, pp. 219–246, Elsevier Applied Science, New York.Google Scholar
  37. Krieger, I. M. and Dougherty, T. J. 1959. A mechanism for non-Newtonian flow in suspensions of rigid spheres. Trans. Soc. Rheol. 3: 137–152.CrossRefGoogle Scholar
  38. Launay, B., Doublier, J. L., and Cuvelier, G. 1986. Flow properties of aqueous solutions and dispersions of polysaccharides, in Functional Properties of Food Macromolecules, eds. J. R. Mitchell and D. A. Ledward, pp. 1–78, Elsevier Applied Science Publishers, London.Google Scholar
  39. Lopes da Silva, J. A. L., Gonçalves, M. P., and Rao, M. A. 1992. Rheological properties of high-methoxyl pectin and locust bean gum solutions in steady shear. J. Food Sci. 57: 443–448.CrossRefGoogle Scholar
  40. Lopes da Silva, J. A. L., Gonçalves, M. P., and Rao, M. A. 1993. Viscoelastic behavior of mixtures of locust bean gum and pectin dispersions. J. Food Eng. 18:211–228.CrossRefGoogle Scholar
  41. McClements, D. J., Monaham, F. J., and Kinsella, J. E. 1993. Effect of emulsion droplets on the rheology of whey protein isolate gels. J. Texture Stud. 24: 411–422.CrossRefGoogle Scholar
  42. Metz, B., Kossen, N. W. F., and van Suijdam, J. C. 1979. The rheology of mould suspensions, in Advances in Biochemical Engineering, eds. T. K. Ghose, A. Fiechter and N. Blakebrough, Vol. 2, p. 103, Springer Verlag, New York.Google Scholar
  43. Metzner, A. B. 1985. Rheology of suspensions in polymeric liquids. J. Rheol. 29: 739–775.CrossRefGoogle Scholar
  44. Mizrahi, S. and Berk, Z. 1972. Flow behaviour of concentrated orange juice: mathematical treatment. J. Texture Stud. 3: 69–79.CrossRefGoogle Scholar
  45. Moore, W. J. 1972. Physical Chemistry, 4th ed., Prentice Hall, Inc., Englewood Cliffs, New Jersey.Google Scholar
  46. Noel, T. R., Ring, S. G., and Whittam, M. A. 1993. Physical properties of starch products: structure and function, in Food Colloids and Polymers: Stability and Mechanical Properties, eds. E. Dickinson and P. Wolstra, pp. 126–137. Royal Soc. Chem., Cambridge, UK.Google Scholar
  47. Ofoli, R.Y., Morgan, R. G., and Steffe, J. F. 1987. A generalized rheological model for inelastic fluid foods. J. Texture Stud. 18:213–230.CrossRefGoogle Scholar
  48. Paredes, M. D. C., Rao, M. A., and Bourne, M. C. 1988. Rheological characterization of salad dressings. 1. Steady shear, thixotropy and effect of temperature. J. Texture Stud. 19: 247–258.CrossRefGoogle Scholar
  49. Parkinson, C., Matsumoto, S., and Sherman, P. 1970. The influence of particle-size distribution on the apparent viscosity of non-Newtonian dispersed system. J. Colloid Interface Sci. 33: 150–160.CrossRefGoogle Scholar
  50. Pham, K. N., Puertas, A. M., Bergenholtz, J., Egelhaaf, S. U., Moussaid, A., Pusey, P. N., Schofield, A. B., and Cates, M. E. 2002. Multiple glassy states in a simple model system. Science 296: 104–106.CrossRefGoogle Scholar
  51. Poslinski, A. J., Ryan, M. E., Gupta, R. K., Seshadri, S. G., and Frechette, F. J. 1988. Rheological behavior of filled polymeric systems I. Yield stress and shear-thinning effects. J. Rheol. 32: 703–735.CrossRefGoogle Scholar
  52. Quemada, D., Fland, P., and Jezequel, P. H. 1985. Rheological properties and flow of concentrated diperse media. Chem. Eng. Comm. 32: 61–83.CrossRefGoogle Scholar
  53. Rao, M. A. 2007. Influence of food microstructure on food rheology, in Understanding And Controlling the Microstructure of Complex Foods, ed. D. J. McClements, Woodhead Publishing Ltd., Cambridge, UK. (In Press).Google Scholar
  54. Rao, M. A. and Cooley, H. J. 1983. Applicability of flow models with yield for tomato concentrates. J. Food Process Eng. 6: 159–173.CrossRefGoogle Scholar
  55. Rao, M. A., Cooley, H. J., and Vitali, A. A. 1984. Flow properties of concentrated fruit juices at low temperatures. Food Technology 38(3): 113–119.Google Scholar
  56. Rao, M. A., Shallenberger, R. S., and Cooley, H. J. 1986. Effect of temperature on viscosity of fluid foods with high sugar content, in Engineering and Food, eds. M. LeMaguer and P. Jelen, Vol. 1, pp. 23–31, Elsevier Applied Science Publishers, New York.Google Scholar
  57. Rayment, P., Ross-Murphy, S. B., and Ellis, P. R. 1998. Rheological properties of guar galactomannan and rice starch mixtures. II. Creep measurements. Carbohydr. Polym. 35: 55–63.CrossRefGoogle Scholar
  58. Ross-Murphy, S.B. 1984. Rheological methods. In Biophysical Methods In Food Research, pp. 138–199, ed. H.W. Chan, Blackwell Scientific Publications, London.Google Scholar
  59. Saunders, F. L. 1961. Rheological properties of monodisperse latex systems I. Concentration dependence of relative viscosity. J. Colloid Sci. 16: 13–22.CrossRefGoogle Scholar
  60. Servais, C. Ranc, H., and Roberts, I. D. 2004. Determination of chocolate viscosity. J. Texture Stud. 34(5–6): 467–498.Google Scholar
  61. Shih, W.-H., Shih, W. Y, Kim, S.-I., Liu, J., and Aksay, I. A. 1990. Scaling behavior of the elastic properties of colloidal gels. Phys. Rev. A 42(8): 4112–4119.CrossRefGoogle Scholar
  62. Simoneau, C., McCarthy, M. J., and German, J. B. 1993. Magnetic resonance imaging and spectroscopy for food systems. Food Res. Intern. 26: 387–398.CrossRefGoogle Scholar
  63. Soesanto, T. and Williams, M.C. 1981. Volumetric interpretation of viscosity for concentrated and dilute sugar solutions. J. Phys. Chem. 85: 3338–3341.CrossRefGoogle Scholar
  64. Sopade, P.-A., Halley, P., Bhandari, B., D’Arcy, B., Doebler, C., and Caffin, N. 2003. Application of the Williams-Landel-Ferry model to the viscosity-temperature relationship of Australian honeys. J. Food Eng. 56(1): 67–75.CrossRefGoogle Scholar
  65. Sperling, L. H. 1986. Introduction to Physical Polymer Science, John Wiley, New York.Google Scholar
  66. Steiner, E. H. 1958. A new rheological relationship to express the flow properties of melted chocolate. Rev. Internationale de la Chocolatiére. 13: 290–295.Google Scholar
  67. Tattiyakul, J. 1997. Studies on granule growth kinetics and characteristics of tapioca starch dispersion during gelatinization using particle size analysis and rheological methods. M. S. thesis, Cornell University, Ithaca, NY.Google Scholar
  68. Tiu, C. and Boger, D. V. 1974. Complete rheological characterization of time-dependent food products. J. Texture Stud. 5:329–338.CrossRefGoogle Scholar
  69. Tiu, C., Podolsak, A. K., Fang, T. N., and Watkins, J. B. 1992. Rhelogical behavior of water-creosote and creosote-water emulsions. Rheol. Acta 31: 381–389.CrossRefGoogle Scholar
  70. Tsai, S. C. and Zammouri, K. 1988. Role of interparticular van der Waals force in rheology of concentrated suspensions. J. Rheol. 32: 737–750.CrossRefGoogle Scholar
  71. Vitali, A. A. and Rao, M. A. 1984a. Flow properties of low-pulp concentrated orange juice: effect of temperature and concentration. J. Food Sci. 49: 882–888.CrossRefGoogle Scholar
  72. Vitali, A. A. and Rao, M. A. 1984b. Flow properties of low-pulp concentrated orange juice: Serum viscosity and effect of pulp content. J. Food Sci. 49: 876–881.CrossRefGoogle Scholar
  73. Vocadlo, J. J. and Moo Young, M. 1969. Rheological properties of some commercially available fats. Can. Inst. Food Technol. J. 2: 137–140.Google Scholar
  74. Weltman, R. N. 1943. Breakdown of thixotropic structure as a function of time. J. Appl. Phys. 14: 343–350.CrossRefGoogle Scholar
  75. Wildemuth, C. R. and Williams, M. C. 1984. Viscosity of suspensions modeled with a shear-dependent maximum packing fraction. Rheol. Acta 23: 627–635.CrossRefGoogle Scholar
  76. Wu, H. and Morbidelli, M. 2001. A model relating structure of colloidal gels to their elastic properties. Langmuir 17: 1030–1036.CrossRefGoogle Scholar
  77. Yoo, B. and Rao, M. A. 1994. Effect of unimodal particle size and pulp content on rheological properties of tomato puree. J. Texture Stud. 25: 421–436.CrossRefGoogle Scholar
  78. Yoo, B. and Rao, M. A. 1996. Creep and dynamic rheological behavior of tomato concentrates: effect of concentration and finisher screen size. J. Texture Stud. 27: 451–459.CrossRefGoogle Scholar
  79. Yoo, B., Rao, M. A., and Steffe, J. F. 1995. Yield stress of food suspensions with the vane method at controlled shear rate and shear stress. J. Texture Stud. 26: 1–10.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2007

Authors and Affiliations

  • M. Anandha Rao
    • 1
  1. 1.Department of Food Science and Technology CornellUniversity GenevaNew York

Personalised recommendations