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Elongational flows of some non-colloidal suspensions

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Abstract

The rheology of a system must be explored not only in viscometric flows, but also in other flow classes, and so, we present some results for the axisymmetric elongational flow of non-colloidal suspensions of spheres. We compare our results with data from shear flows using the same matrices and spheres. We have experimented with non-colloidal suspensions of 40-μm diameter polystyrene spheres with volume fractions (ϕ) varying from 0.3 to 0.5. Two matrix fluids were used—one was a near-Newtonian polydimethyl siloxane of 12 Pa-s viscosity and the other was a variant of the M1 Boger fluid sample of Sridhar which we call M1*. We did not find that the Trouton ratio for either of these fluids was 3; generally, the ratio was larger. We investigated the role of sphere roughness using spheres roughened to 5.3 % of the radius in a 50 % suspension in silicone oil and found an increase of elongational viscosity of about 65 % which is comparable with the 60 % increase in shear viscosity with roughness noted previously. For the silicone oil matrix, we found no rate effect, with very little strain-hardening. By contrast, the M1-type matrix suspensions showed strain-hardening and an increase of elongational viscosity with elongation rate.

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References

  • Barnes HA (2003) A review of the rheology of filled viscoelastic systems. In: Binding DM, Walters K (eds) Rheology reviews. British Society of Rheology, Aberystwyth, U.K., pp. 1–36

    Google Scholar 

  • Barnes HA, Roberts GP (1992) A simple empirical-model describing the steady-state shear and extensional viscosities of polymer melts. J. Non-Newt. Fluid Mech. 44:113–126

    Article  Google Scholar 

  • Batchelor GK, Green JT (1972) Determination of bulk stress in a suspension of spherical particles to order c2. J Fluid Mech 56:401–427

    Article  Google Scholar 

  • Cates ME, Wyart M (2014) Granulation and bistability in non-Brownian suspensions. Rheol Acta 53:755–768

    Article  Google Scholar 

  • Davis RH, Zhao Y, Galvin KP, Wilson HJ (2003) Solid-solid contacts due to surface roughness and their effects on suspension behaviour. Phil Trans R Soc Lond A361:871–894

    Article  Google Scholar 

  • Gallier S, Lemaire E, Peters LL (2014) Rheology of sheared suspensions of rough frictional particles. JFluid Mech 757:514–549

    Article  Google Scholar 

  • Greener J, Evans JRG (1998) Uniaxial elongational flow of particle-filled polymer melts. JRheol 42:697–709

    Google Scholar 

  • Housiadas KD (2015) An effective medium approach for the elongational viscosity of non-colloidal and non-Brownian hard-sphere suspensions. Phys. Fluids 27: art 083304

  • Kobayashi M, Takahashi T, Takimoto J, Koyama K (1996) Influence of glass beads on the elongational viscosity of polyethylene with anomalous strain rate dependence of the strain-hardening. Polymer 37:3745–3747

    Article  Google Scholar 

  • Le Meins JF, Moldenaers P, Mewis J (2003) Suspensions of monodisperse spheres in polymer melts: particle size effects in extensional flow. Rheol Acta 42:184–190

  • Lugt PM, Morales-Espejel GE (2011) A review of elasto-hydrodynamic lubrication theory. Tribol Trans 54:470–496

    Article  Google Scholar 

  • Metzner AB (1985) Rheology of suspensions in polymeric liquids. J Rheol 29:739–775

    Article  Google Scholar 

  • Moon JY, Dai S-C, Chang L, Lee JS, Tanner RI (2015) The effect of sphere roughness on the rheology of concentrated suspensions. J Non-Newt Fluid Mech 223:233–239

    Article  Google Scholar 

  • Moon JY, Lee SJ, Ahn KH, Lee SJ (2016) Filament thinning of silicon oil/PMMA suspensions under extensional flow. Rheol Acta 54:708–714

    Google Scholar 

  • Nguyen DA, Gupta RK, Sridhar T (1990) Experimental results and constitutive modelling of the extensional flow of ml. J Non-Newton Fluid Mech 35:207–214

    Article  Google Scholar 

  • Shenoy AV (1999) Rheology of filled polymer systems. Kluwer, Dordrecht

    Book  Google Scholar 

  • Sridhar T (1990) An overview of the project ml. J Non-Newton Fluid Mech 35:85–92

    Article  Google Scholar 

  • Takahashi T, Takimoto J, Koyama K (1999) Uniaxial elongation viscosity of various molten polymer composites. Polym Compos 20:357–366

    Article  Google Scholar 

  • Tanner RI (2000) Engineering rheology.2nd edition. Oxford Univ. Press, Oxford

    Google Scholar 

  • Tanner RI, Dai S-C (2016) Particle roughness and rheology in noncolloidal suspensions. J.Rheol 60:809–818

  • Tirtaatmadja V, Sridhar T (1993) A filament stretching device for measurement of extensional viscosity. JRheo 37:1081–1102

    Google Scholar 

  • Weinberger CB, Goddard JD (1974) Extensional flow behaviour of polymer solutions and particle suspensions in a spinning motion. Int. J. Multiphase Flow 1:465–486

    Article  Google Scholar 

  • Wilson HJ, Davis RH (2000) The viscosity of a dilute suspension of rough spheres. J Fluid Mech 421:339–367

    Article  Google Scholar 

Download references

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Authors and Affiliations

  1. School of Aerospace, Mechanical and Mechatronic Engineering, The University of Sydney, Sydney, NSW, 2006, Australia

    Shaocong Dai & Roger I. Tanner

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  1. Shaocong Dai
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  2. Roger I. Tanner
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Correspondence to Roger I. Tanner.

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Dai, S., Tanner, R.I. Elongational flows of some non-colloidal suspensions. Rheol Acta 56, 63–71 (2017). https://doi.org/10.1007/s00397-016-0984-x

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  • DOI: https://doi.org/10.1007/s00397-016-0984-x

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