Skip to main content
Log in

Abstract

The purpose of this work is to analyze the various kinds of capillary viscometers that have been used in the past, and to formulate the relation between the measured quantities and the viscosity of the fluid. Three kinds of capillary viscometers are discussed: the steady-state capillary, two capillaries in tandem and the Rankine viscometer. Improved working formulae are derived for every case. Throughout the work the fluid is assumed to be incompressible. However, a short discussion of the correction for compressibility is also provided.

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

Abbreviations

A(x) :

tank cross sectional area (see Fig. 15)

a :

radius of capillary

A, B, C :

constants (see (21))

G :

geometric coefficient (defined in (13))

g(x) :

function in (20b)

H :

driving head (see Fig. 15)

L :

length of capillary

L 0 :

distance from the inlet at which the velocity profile in the feeding tank is parabolic (see Fig. 6)

L′:

L+na (see (12))

M :

molecular weight of the gas

m :

mass flow rate

m :

constant due to inlet correction (see (7))

m 0 :

constant due to inlet correction (see (10))

n :

constant due to inlet correction (see (10))

p :

pressure

R :

radius of feeding tank; universal gas constant

Re :

Reynolds number

T :

temperature

ū :

average velocity in capillary

V :

volume

xxx0056; :

volumetric flow rate

x :

axial coordinate along the capillary

x 1, x 2 :

coordinates along the inlet and exit tanks, respectively (see Fig. 15)

α :

defined in (20a)

β :

defined in (20a)

Γ :

geometric factor (see (5))

Δp :

pressure drop

ζ :

defined in (13)

μ :

dynamic viscosity

ν :

kinematic viscosity

ρ :

density

τ :

efflux time

ψ(x):

function defined in (17)

*:

reference value

e:

exit of capillary

i:

inlet of capillary

l:

exit tank

u:

inlet tank

References

  1. Erk, S., Z. f. tech. Physik 10 (1929) 452.

    Google Scholar 

  2. Barr, G., A Monograph of Viscometry, Humphrey Milford, N.Y., 1931.

    Google Scholar 

  3. Gögüs, Y., Private communication. Details to be published.

  4. Korson, L., W. Drost-Hansen and F. J. Millero, J. Phys. Chem. 73 (1969) 371.

    Google Scholar 

  5. Korosi, A. and B. M. Fabuss, Anal. Chem. 40 (1968) 1.

    Google Scholar 

  6. Schlichting, H. (transl. J. Kestin), Boundary Layer Theory, 6th ed. McGraw-Hill, N.Y., 1968.

    Google Scholar 

  7. Penn, R. W. and E. A. Kearsley, An absolute determination of viscosity using channel flow, Report, Journ. of Res. of the N.B.S., 75A (1971) 553.

    Google Scholar 

  8. Boussinesq, J., Compt. Rend. 110 (1890) 1160, 1238, 1292.

    Google Scholar 

  9. Schiller, L., Z. Angew. Math. u. Phys. 2 (1922) 96.

    Google Scholar 

  10. Goldstein, S., Modern Developments in Fluid Dynamics, vol. I, Clarendon Press, Oxford, England, 1938.

    Google Scholar 

  11. Langhaar, H. L., J. Appl. Mech. 9 (1942) A55.

    Google Scholar 

  12. Sparrow, E. M., S. H. Lin and T. S. Lundgren, Phys. Fluids 7 (1964) 338.

    Google Scholar 

  13. Swindells, J. F., J. R. Coe, Jr. and T. B. Godfrey, J. Res. N.B.S. 42 (1952) 1.

    Google Scholar 

  14. Flynn, G. P., R. V. Hanks, N. A. Lemaire and J. Ross, J. Chem. Phys. 38 (1968) 1954.

    Google Scholar 

  15. Kao, J. T. F., W. Ruska and R. Kobayashi, Rev. Sci. Instr. 39 (1968) 824.

    Google Scholar 

  16. Schmidt, F. W. and B. Zeldin, A.I.Ch.E. 15 (1969) 612.

    Google Scholar 

  17. Prandtl, L. and O. J. Tietjens, Applied Hydro and Aerodynamics, McGraw-Hill, New York, 1939.

    Google Scholar 

  18. Reiman, W., J. Amer. Chem. Soc. 50 (1928) 40.

    Google Scholar 

  19. Dorsey, N. G., Phys. Rev. 28 (1926) 833.

    Article  Google Scholar 

  20. Christiansen, E. B. and H. E. Lemanen, A.I.Ch.E. J. 11 (1965) 995.

    Google Scholar 

  21. Hornbeck, R. E., Appl. Sci. Res., Sec. A. 13 (1964) 227.

    Google Scholar 

  22. Vrentas, J. S., J. L. Duda and K. G. Bargeron, A.I.Ch.E. J. 12 (1966) 937.

    Google Scholar 

  23. Friedman, M., J. Gillis and N. Liron, Appl. Sci. Res. 19 (1968) 426.

    Google Scholar 

  24. Abarbanel, S., S. Bennet, A. Brandt and J. Gillis, Trans. ASME 2 (1970) 2.

    Google Scholar 

  25. Couette, M. M., Ann. Chim. et Phys. (Serie 6) 21 (1890) 433.

    Google Scholar 

  26. Flynn, G. P., Ph.D. Thesis, Brown University (1962).

  27. Gibson, R. O., Ph.D. Thesis, University of Amsterdam (1933).

  28. Guevara, F. A., B. B. McInteer and W. E. Wageman, Phys. Fluids 12 (1969) 2499.

    Google Scholar 

  29. Cannon, M. R., R. E. Manning and J. D. Bell, Anal. Chem. 32 (1960) 3.

    Google Scholar 

  30. Guevara, F. A. and W. E. Wageman, Los Alamos Scientific Laboratory Report LA-3319, 1965.

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Kestin, J., Sokolov, M. & Wakeham, W. Theory of capillary viscometers. Appl. Sci. Res. 27, 241–264 (1973). https://doi.org/10.1007/BF00382489

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00382489

Keywords

Navigation