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Mechanics of Time-Dependent Materials

, Volume 21, Issue 3, pp 455–479 | Cite as

Hyperbolic contraction measuring systems for extensional flow

  • M. Nyström
  • H. R. Tamaddon Jahromi
  • M. Stading
  • M. F. WebsterEmail author
Article

Abstract

In this paper an experimental method for extensional measurements on medium viscosity fluids in contraction flow is evaluated through numerical simulations and experimental measurements. This measuring technique measures the pressure drop over a hyperbolic contraction, caused by fluid extension and fluid shear, where the extensional component is assumed to dominate. The present evaluative work advances our previous studies on this experimental method by introducing several contraction ratios and addressing different constitutive models of varying shear and extensional response. The constitutive models included are those of the constant viscosity Oldroyd-B and FENE-CR models, and the shear-thinning LPTT model. Examining the results, the impact of shear and first normal stress difference on the measured pressure drop are studied through numerical pressure drop predictions. In addition, stream function patterns are investigated to detect vortex development and influence of contraction ratio. The numerical predictions are further related to experimental measurements for the flow through a 15:1 contraction ratio with three different test fluids. The measured pressure drops are observed to exhibit the same trends as predicted in the numerical simulations, offering close correlation and tight predictive windows for experimental data capture. This result has demonstrated that the hyperbolic contraction flow is well able to detect such elastic fluid properties and that this is matched by numerical predictions in evaluation of their flow response. The hyperbolical contraction flow technique is commended for its distinct benefits: it is straightforward and simple to perform, the Hencky strain can be set by changing contraction ratio, non-homogeneous fluids can be tested, and one can directly determine the degree of elastic fluid behaviour. Based on matching of viscometric extensional viscosity response for FENE-CR and LPTT models, a decline is predicted in pressure drop for the shear-thinning LPTT model. This would indicate a modest impact of shear in the flow since such a pressure drop decline is relatively small. It is particularly noteworthy that the increase in pressure drop gathered from the experimental measurements is relatively high despite the low Deborah number range explored.

Keywords

Hyperbolic contraction Pressure-drop Viscoelastic fluid Boger fluid Extensional flow Axisymmetric contraction–expansion 

References

  1. Aboubacar, M., Webster, M.F.: A cell-vertex finite volume/element method on triangles for abrupt contraction viscoelastic flows. J. Non-Newton. Fluid Mech. 98(2–3), 83–106 (2001) CrossRefzbMATHGoogle Scholar
  2. Aguayo, J.P., Tamaddon-Jahromi, H.R., Webster, M.F.: Excess pressure-drop estimation in contraction and expansion flows for constant shear-viscosity, extension strain-hardening fluids. J. Non-Newton. Fluid Mech. 153(2–3), 157–176 (2008) CrossRefzbMATHGoogle Scholar
  3. Andersson, H., Öhgren, C., Johansson, D., Kniola, M., Stading, M.: Extensional flow, viscoelasticity and baking performance of gluten-free zein–starch dough supplemented with hydrocolloids. Food Hydrocoll. 25, 1587–1595 (2011) (0268–005X) CrossRefGoogle Scholar
  4. Baaijens, F.P.T.: Mixed finite element methods for viscoelastic flow analysis: a review. J. Non-Newton. Fluid Mech. 79(2–3), 361–385 (1998) CrossRefzbMATHGoogle Scholar
  5. Baird, D.G., Huang, J.: Elongational viscosity measurements using a semi-hyperbolic die. Appl. Rheol. 16(6), 312–320 (2006) Google Scholar
  6. Baird, D.G., Tung, W.C., McGrady, C., Mazahir, S.M.: Evaluation of the use of a semi-hyperbolic die for measuring elongational viscosity of polymer melts. Appl. Rheol. 20, 34900 (2010) Google Scholar
  7. Binding, D.M.: An approximate analysis for contraction and converging flows. J. Non-Newton. Fluid Mech. 27(2), 173–189 (1988) CrossRefzbMATHGoogle Scholar
  8. Binding, D.M.: Further considerations of axisymmetric contraction flows. J. Non-Newton. Fluid Mech. 41, 27–42 (1991) CrossRefzbMATHGoogle Scholar
  9. Binding, D.M., Couch, M.A., Walters, K.: The pressure dependence of the shear and elongational properties of polymer melts. J. Non-Newton. Fluid Mech. 79(2–3), 137–155 (1998) CrossRefGoogle Scholar
  10. Binding, D.M., Phillips, P.M., Phillips, T.N.: Contraction–expansion flows: the pressure drop and related issues. J. Non-Newton. Fluid Mech. 137(1–3), 31–38 (2006) CrossRefzbMATHGoogle Scholar
  11. Boger, D.V.: A highly elastic constant-viscosity fluid. J. Non-Newton. Fluid Mech. 3(1), 87–91 (1977) CrossRefGoogle Scholar
  12. Boger, D.V.: Viscoelastic flows through contractions. Annu. Rev. Fluid Mech. 19, 157–182 (1987) CrossRefGoogle Scholar
  13. Campo-Deano, L., Galindo-Rosales, F.J., Pinho, F.T., Alves, M.A., Oliveira, M.S.N.: Flow of low viscosity Boger fluids through a microfluidic hyperbolic contraction. J. Non-Newton. Fluid Mech. 166(21–22), 1286–1296 (2011) CrossRefzbMATHGoogle Scholar
  14. Chen, J.S., Lolivret, L.: The determining role of bolus rheology in triggering a swallowing. Food Hydrocoll. 25(3), 325–332 (2011) CrossRefGoogle Scholar
  15. Chilcott, M.D., Rallison, J.M.: Creeping flow of dilute polymer solutions past cylinders and spheres. J. Non-Newton. Fluid Mech. 29, 381–432 (1988) CrossRefzbMATHGoogle Scholar
  16. Collier, J.R., Romanoschi, O., Petrovan, S.: Elongational rheology of polymer melts and solutions. J. Appl. Polym. Sci. 69(12), 2357–2367 (1998) CrossRefGoogle Scholar
  17. Davies, A.R., Devlin, J.: On corner flows of Oldroyd-b fluids. J. Non-Newton. Fluid Mech. 50(2–3), 173–191 (1993) CrossRefzbMATHGoogle Scholar
  18. Debbaut, B., Crochet, M.J.: Extensional effects in complex flows. J. Non-Newton. Fluid Mech. 30(2–3), 169–184 (1988) CrossRefGoogle Scholar
  19. Dobraszczyk, B.J., Morgenstern, M.: Rheology and the breadmaking process. J. Cereal Sci. 38(3), 229–245 (2003) CrossRefGoogle Scholar
  20. Entov, V.M., Hinch, E.J.: Effect of a spectrum of relaxation times on the capillary thinning of a filament of elastic liquid. J. Non-Newton. Fluid Mech. 72(1), 31–53 (1997) CrossRefGoogle Scholar
  21. Fuller, G.G., Cathey, C.A., Hubbard, B., Zebrowski, B.E.: Extensional viscosity measurements for low-viscosity fluids. J. Rheol. 31, 235–249 (1985) CrossRefGoogle Scholar
  22. Gillgren, T., Alven, T., Stading, M.: Impact of melt rheology on zein foam properties. J. Mater. Sci. 45(21), 5762–5768 (2010) CrossRefGoogle Scholar
  23. Gupta, R.K.: Polymer and Composite Rheology, 2nd edn. Dekker, Morgantown (2000) Google Scholar
  24. Hinch, E.J.: The flow of an Oldroyd fluid around a sharp corner. J. Non-Newton. Fluid Mech. 50(2–3), 161–171 (1993) CrossRefzbMATHGoogle Scholar
  25. Isaksson, P., Rigdahl, M., Flink, P., Forsberg, S.: Aspects of the elongational flow behavior of coating colors. J. Pulp Pap. Sci. 24(7), 204–209 (1998) Google Scholar
  26. James, D.F., Chandler, G.M., Armour, S.J.: A converging channel rheometer for the measurement of extensional viscosity. J. Non-Newton. Fluid Mech. 35(2–3), 421–443 (1990) CrossRefGoogle Scholar
  27. Kim, H.C., Pendse, A., Collier, J.R.: Polymer melt lubricated elongational flow. J. Rheol. 38(4), 831–845 (1994) CrossRefGoogle Scholar
  28. Koliandris, A.L., Rondeau, E., Hewson, L., Hort, J., Taylor, A.J., Cooper-White, J., Wolf, B.: Food grade Boger fluids for sensory studies. Appl. Rheol. 21(1), 13777 (2011) Google Scholar
  29. Meissner, J.: Development of a universal extensional rheometer for the uniaxial extension of polymer melts. Trans. Soc. Rheol. 16, 405–420 (1972) CrossRefGoogle Scholar
  30. Meissner, J., Hostettler, J.: A new elongational rheometer for polymer melts and other highly viscoelastic liquids. Rheol. Acta 33(1), 1–21 (1994) CrossRefGoogle Scholar
  31. Nigen, S., Walters, K.: Viscoelastic contraction flows: comparison of axisymmetric and planar configurations. J. Non-Newton. Fluid Mech. 102(2), 343–359 (2002) CrossRefzbMATHGoogle Scholar
  32. Nystrom, M., Tamaddon Jahromi, H.R., Stading, M., Webster, M.F.: Numerical simulations of Boger fluids through different contraction configurations for the development of a measuring system for extensional viscosity. Rheol. Acta 51(8), 713–727 (2012) CrossRefGoogle Scholar
  33. Ober, T.J., Haward, S.J., Pipe, C.J., Soulages, J., McKinley, G.H.: Microfluidic extensional rheometry using a hyperbolic contraction geometry. Rheol. Acta 52(6), 529–546 (2013) CrossRefGoogle Scholar
  34. Oliveira, M.S.N., Alves, M.A., Pinho, F.T., McKinley, G.H.: Viscous flow through microfabricated hyperbolic contractions. Exp. Fluids 43(2–3), 437–451 (2007) CrossRefGoogle Scholar
  35. Oom, A., Pettersson, A., Taylor, J.R.N., Stading, M.: Rheological properties of kafirin and zein prolamins. J. Cereal Sci. 47(1), 109–116 (2008) CrossRefGoogle Scholar
  36. Phan-Tien, N.: A nonlinear network viscoelastic model. J. Rheol. 22(3), 259–283 (1978) CrossRefzbMATHGoogle Scholar
  37. Phan-Tien, N., Tanner, R.I.: A new constitutive equation derived from network theory. J. Non-Newton. Fluid Mech. 2, 353–365 (1977) CrossRefzbMATHGoogle Scholar
  38. Renardy, M.: A matched solution for corner flow of the upper convected Maxwell fluid. J. Non-Newton. Fluid Mech. 58(1), 83–89 (1995) CrossRefGoogle Scholar
  39. Rothstein, J.P., McKinley, G.H.: Extensional flow of a polystyrene Boger fluid through a 4:1:4 axisymmetric contraction/expansion. J. Non-Newton. Fluid Mech. 86(1–2), 61–88 (1999) CrossRefzbMATHGoogle Scholar
  40. Rothstein, J.P., McKinley, G.H.: The axisymmetric contraction–expansion: the role of extensional rheology on vortex growth dynamics and the enhanced pressure drop. J. Non-Newton. Fluid Mech. 98(1), 33–63 (2001) CrossRefzbMATHGoogle Scholar
  41. Stading, M., Bohlin, L.: Measurements of extensional flow properties of semi-solid foods in contraction flow. In: Proceedings of the 2nd International Symposium on Food Rheology and Structure, vol. 2, pp. 117–120 (2000) Google Scholar
  42. Stading, M., Bohlin, L.: Contraction flow measurements of extensional properties. Annu. Trans. Nord. Rheol. Soc. 8–9, 147–150 (2001) Google Scholar
  43. Szabo, P., Rallison, J.M., Hinch, E.J.: Start-up of flow of a FENE-fluid through a 4:1:4 constriction in a tube. J. Non-Newton. Fluid Mech. 72(1), 73–86 (1997) CrossRefGoogle Scholar
  44. Tamaddon-Jahromi, H.R., Walters, K., Webster, M.F.: Predicting numerically the large increases in extra pressure drop when Boger fluids flow through axisymmetric contractions. Nat. Sci. 2(1), 1–11 (2010) Google Scholar
  45. Tamaddon-Jahromi, H.R., Webster, M.F., Williams, P.R.: Excess pressure drop and drag calculations for strain-hardening fluids with mild shear-thinning: contraction and falling sphere problems. J. Non-Newton. Fluid Mech. 166, 939–950 (2011) CrossRefGoogle Scholar
  46. Walters, K., Webster, M.F.: The distinctive CFD challenges of computational rheology. Int. J. Numer. Methods Fluids 43(5), 577–596 (2003) MathSciNetCrossRefzbMATHGoogle Scholar
  47. Walters, K., Tamaddon-Jahromi, H.R., Webster, M.F., Tome, M.F., McKee, S.: The competing roles of extensional viscosity and normal stress differences in complex flows of elastic liquids. Korea-Aust. Rheol. J. 21(4), 225–233 (2009a) Google Scholar
  48. Walters, K., Webster, M.F., Tamaddon-Jahromi, H.R.: The numerical simulation of some contraction flows of highly elastic liquids and their impact on the relevance of the Couette correction in extensional rheology. Chem. Eng. Sci. (2009b). doi: 10.1016/j.ces.2009.01.007 Google Scholar
  49. Wapperom, P., Webster, M.F.: A second-order hybrid finite-element/volume method for viscoelastic flows. J. Non-Newton. Fluid Mech. 79, 405–431 (1998) CrossRefzbMATHGoogle Scholar
  50. Wapperom, P., Webster, M.F.: Simulation for viscoelastic flow by a finite volume/element method. Comput. Methods Appl. Mech. Eng. 180, 281–304 (1999) CrossRefzbMATHGoogle Scholar
  51. Webster, M.F., Tamaddon-Jahromi, H.R., Aboubacar, M.: Time-dependent algorithm for viscoelastic flow-finite element/volume schemes. Numer. Methods Partial Differ. Equ. 21, 272–296 (2005) MathSciNetCrossRefzbMATHGoogle Scholar
  52. White, S.A., Gotsis, A.D., Baird, D.G.: Review of the entry flow problem: experimental and numerical. J. Non-Newton. Fluid Mech. 24(2), 121–160 (1987) CrossRefGoogle Scholar
  53. Wikström, K., Bohlin, L.: Extensional flow studies of wheat flour dough. 1. Experimental method for measurements in contraction flow geometry and application to flours varying in breadmaking performance. J. Cereal Sci. 29(3), 217–226 (1999) CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2017

Authors and Affiliations

  • M. Nyström
    • 1
  • H. R. Tamaddon Jahromi
    • 2
  • M. Stading
    • 1
    • 3
  • M. F. Webster
    • 2
    Email author
  1. 1.Food and BioscienceSP—Technical Research Institute of SwedenGöteborgSweden
  2. 2.Institute of Non-Newtonian Fluid Mechanics, College of EngineeringSwansea UniversitySwanseaUK
  3. 3.Department of Materials and Manufacturing TechnologyChalmers University of TechnologyGöteborgSweden

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