Skip to main content
SpringerLink
Log in

Nonlinear oscillating-cup viscometry

  • Original Contribution
  • Published:
Rheologica Acta Aims and scope Submit manuscript

Abstract

The general algorithm of calculations for oscillating-cup viscometry of fluids with viscous, elastic and plastic components is developed for damped and forced modes. The working equations efficient for practical applications are presented and related problems of data processing are analyzed. The case of forced oscillations of viscometer filled with rheostable fluids is treated in detail.

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

Similar content being viewed by others

References

  • Abramowitz M, Stegun IA, eds (1972) Handbook of mathematical functions with formulas, graphs and mathematical tables. New York

  • Beckwith DA, Newell GF (1957) Theory of oscillating type viscometers: the oscillating cup. Part II. Z Angew Math Phys 8:450–465

    Article  CAS  Google Scholar 

  • Bercovier M, Engelman M (1980) A finite-element method for incompressible non-Newtonian flows. J Comp Phys 36:313–326

    Article  Google Scholar 

  • Berg RF, Moldover MR (1986) Viscometer for low frequency, low shear rate measurements. Rev Sci Instrum 57:1667–1673

    Article  CAS  Google Scholar 

  • Berstad DA, Knapstad B, Lamvik M, Skjolsvik PA, Torklep K, Oye HA (1988) Accurate measurements of the viscosity of water in the temperature range 19.5°C–25.5°C. Phys A 151:246–280

    Article  CAS  Google Scholar 

  • Beverly CR, Tanner RI (1992) Numerical analysis of three-dimensional Bingham plastic flow. J Non-Newton Fluid Mech 42:85–115

    Article  CAS  Google Scholar 

  • Bingham EC (1922) Fluidity and plasticity. McGraw-Hill, New York

    Google Scholar 

  • Brooks RF, Dinsdale AT, Quested PN (2005) The measurement of viscosity of alloys—a review of methods, data and models. Meas Sci Technol 16:354–362

    Article  CAS  Google Scholar 

  • Burgos GR, Alexandrou AN, Entov V (1999) On the determination of yield surfaces in Herschel–Bulkley fluids. J Rheol 43:463–483

    Article  CAS  Google Scholar 

  • De Waele A (1923) Viscometry and plastometry. J Oil Colour Chem Assoc 6:33–88

    Google Scholar 

  • Elyukhina IV (2006) Johnson–Segalman fluid behavior in a oscillating-cup system. R J Phys Chem 5:819–822

    Article  Google Scholar 

  • Elyukhina IV (2009) Theoretical foundation of oscillating-cup viscometry for viscoplastic fluids. High Temp 47:562–567

    Article  Google Scholar 

  • Elyukhina I, Vyatkin G (2008) Software for oscillating-cup viscometry: verification of data reasonableness and parametric identification of rheological model. J Phys: Conf Ser 98

  • Elyukhina I, Apakashev R, Vyatkin G, Kholpanov L (2009) Vibrodiagnostics of non-Newtonian properties of high-temperature melts by oscillating-cup and inertial viscometers; 13th Asia Pacific Vibration Conference, Canterbury of NZ, p 10

  • Grouvel JM, Kestin J (1978) Working equations for the oscillating-cup viscometer. Appl Sci Res 34:427–443

    Article  Google Scholar 

  • Herschel WH, Bulkley R (1926) Konsistenzmessungen von Gummi–Benzollösungen. Kolloid-Z 39:291–300

    Article  Google Scholar 

  • Iida T, Guthrie RIL (1988) The physical properties of liquid metals. Clarendon, Oxford

    Google Scholar 

  • Johnson M, Segalman D (1977) A model for viscoelastic fluid behavior which allows nonaffine deformation. J Non-Newton Fluid Mech 2:255–270

    Article  Google Scholar 

  • Keentok M, Georgescu AG, Sherwood AA, Tanner RI (1980) The measurement of the second normal stress difference for some polymer solutions. J Non-Newton Fluid Mech 6:303–324

    Article  CAS  Google Scholar 

  • Kehr M, Hoyer W, Egry I (2007) A new high-temperature oscillating cup viscometer. Int J Thermophys 28:1017–1025

    Article  CAS  Google Scholar 

  • Kestin J, Newell GF (1957) Theory of oscillating type viscometers: the oscillating cup. Part I. Z Angew Math Phys 8:433–449

    Article  CAS  Google Scholar 

  • Kholpanov LP, Elyukhina IV (2009) Identification of the complex nonlinear processes. Theor Found Chem Eng 43:869–880

    Article  CAS  Google Scholar 

  • Kleiman RN (1987) Analysis of the oscillating-cup viscometer for the measurement of viscoelastic properties. Phys Rev 35:261–275

    Article  CAS  Google Scholar 

  • Krall AH, Sengers JV (2003) Simultaneous measurement of viscosity and density with an oscillating-disk instrument. Int J Thermophys 24:337–359

    Article  CAS  Google Scholar 

  • Macosko CW (1994) Rheology: principles, measurements and applications. Wiley/VCH, New York

    Google Scholar 

  • Malik MM, Jeyakumar M, Hamed MS, Walker MJ, Shankar S (2010) Rotational rheometry of liquid metal systems: measurement geometry selection and flow curve analysis. J Non-Newton Fluid Mech 165:733–742

    Article  CAS  Google Scholar 

  • Nieuwoudt JC (1990) An extension of the theory of oscillating cup viscometers. Int J Thermophys 11:525–535

    Article  CAS  Google Scholar 

  • Nieuwoudt JC, Sengers JV, Kestin J (1988) On the theory of oscillating-cup viscometers. Phys A 149:107–122

    Article  Google Scholar 

  • Nunes VMB, Santos FJV, Nieto de Castro CA (1998) A high-temperature viscometer for molten materials. Int J Thermophys 19:427–435

    Article  CAS  Google Scholar 

  • Oldroyd JG (1950) On the formulation of rheological equations of state. Proc R Soc Lond A 200:523–541

    Article  CAS  Google Scholar 

  • Ostwald W (1925) About the rate function of the viscosity of dispersed systems. Kolloid-Z 36:99–117

    Article  CAS  Google Scholar 

  • Papanastasiou TC (1987) Flows of materials with yield. J Rheol 31:385–404

    Article  CAS  Google Scholar 

  • Quested P, Redgrove J (2003) Issues concerning measurement of the viscosity of liquid metals. Presented at IUPAC Meeting

  • Roscoe R (1958) Viscosity determination by the oscillating vessel method. Proc Phys Soc 72:576–584

    Article  CAS  Google Scholar 

  • Shvidkovskiy YeG (1962) Certain problems related to the viscosity of fused metals. NASA-TT-F-88 [In Russian: (1955) Moscow, GITTL]

  • Torklep K, Oye HA (1979) An absolute oscillating cylinder (or cup) viscometer. J Phys E: Sci Instrum 12:875–885

    Article  Google Scholar 

  • Vignau IM, Azou P, Bastien P (1966) Theorie d’un viscosimetre absolu a deux couches liquides utilisant des oscillations de torsion. C R Acad Sci 262B:862–865

    Google Scholar 

  • Wang D, Overfelt RA (2002) Oscillating cup viscosity measurements of aluminum alloys: A201, A319 and A356. Int J Thermophys 23:1063–1076

    Article  CAS  Google Scholar 

  • Wilhelm M, Maring D, Spiess H-W (1998) Fourier-transform rheology. Rheol Acta 37:399–405

    Article  CAS  Google Scholar 

  • Yelyukhina IV (2006) The observation and measurement of the non-Newtonian properties of high-temperature fluids using the torsional-oscillation method. High Temp 44:406–413

    Article  CAS  Google Scholar 

Download references

Acknowledgements

The work was supported by the RFBR (No 10-01-96042_ural).

Author information

Authors and Affiliations

  1. Department of Theoretical Mechanics, South Ural State University, Lenin ave. 76, 454080, Chelyabinsk, Russia

    Inna Elyukhina

Authors
  1. Inna Elyukhina
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Inna Elyukhina.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Elyukhina, I. Nonlinear oscillating-cup viscometry. Rheol Acta 50, 327–334 (2011). https://doi.org/10.1007/s00397-010-0517-y

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00397-010-0517-y

Keywords

Search

Navigation