Hostname: page-component-7c8c6479df-24hb2 Total loading time: 0 Render date: 2024-03-28T15:52:58.477Z Has data issue: false hasContentIssue false

An experimental investigation of the flow of non-Newtonian fluids between rotating disks

Published online by Cambridge University Press:  21 April 2006

A. Sirivat
Affiliation:
Department of Mechanical Engineering, University of Pittsburgh, Pittsburgh, PA 15261, USA
K. R. Rajagopal
Affiliation:
Department of Mechanical Engineering, University of Pittsburgh, Pittsburgh, PA 15261, USA
A. Z. Szeri
Affiliation:
Department of Mechanical Engineering, University of Pittsburgh, Pittsburgh, PA 15261, USA

Abstract

The results of an experimental investigation on the flow of a non-Newtonian fluid between rotating, parallel disks are described in this paper. These results are qualitatively different from those exhibited by linearly viscous fluids in that a narrow layer of exceedingly high velocity gradients appears in the non-Newtonian fluid.

Type
Research Article
Copyright
© 1988 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Adams, M. L. & Szeri, A. Z. 1982 Incompressible flow between finite disks. Trans. ASME E: J. Appl. Mech. 49, 114.Google Scholar
Batchelor, G. K. 1951 Note on a class of solutions of the Navier-Stokes equations representing steady rotationally-symmetric flow. Q. J. Mech. Appl. Maths 4, 2941.Google Scholar
Berker, R. 1979 A new solution of the Navier-Stokes equation for the motion of a fluid contained between two parallel planes rotating about the same axis. Archiwum Mechaniki Stosowanej 31, 265280.Google Scholar
Bernstein, B., Kearsley, E. A. & Zapas, L. J. 1963 A study of stress relaxation with finite strain. Trans. Soc. Rheol. 7, 391410.Google Scholar
Connelly, R. W. & Greener, J. 1985 High-shear viscometry with a rotational parallel-disk-device. J. Rheol. 29, 209226.Google Scholar
Dijkstra, D. & Van Heust, G. J. F. 1983 The flow between finite rotating disks enclosed by a cylinder. J. Fluid Mech. 128, 123154.Google Scholar
Faller, A. J. 1963 An experimental study of the instability of the laminar Ekman boundary layer. J. Fluid Mech. 15, 560576.Google Scholar
Greenspan, D. 1972 Numerical studies of flow between rotating co-axial disks. J. Inst. Maths. Applics 9, 370377.Google Scholar
Gregory, N., Stuart, J. T. & Walker, W. S. 1955 On the stability of three dimensional boundary layers with application to the flow due to a rotating disk. Phil. Trans. R. Soc. Lond. A 248, 155199.Google Scholar
Holodniok, M., Kubicek, M. & Hlavacek, V. 1978 Computation of flow between two rotating co-axial disks. J. Fluid Mech. 81, 579596.Google Scholar
Holodniok, M., Kubicek, M. & Hlavacek, V. 1981 Computation of flow between two rotating co-axial disks: multiplicity of steady state solutions. J. Fluid Mech. 108, 227240.Google Scholar
Huilgol, R. R. & Keller, J. B. 1985 Flow of viscoelastic fluids between rotating disks: Part 1. J. Non-Newtonian Fluid Mech. 18, 101110.Google Scholar
Huilgol, R. R. & Rajagopal, K. R. 1987 Non-axisymmetric flow of a viscoelastic fluid between rotating disks. J. Non-Newtonian Fluid Mech. 23, 423434.Google Scholar
Von Kármán, T. 1921 Über laminare und turbulente Reibung. Z. Angew. Math. Mech. 1, 232252.Google Scholar
Kaye, A. 1962 Note 134. College of Aeronautics, Cranfield Institute of Technology.
Lai, C.-Y., Rajagopal, K. R. & Szeri, A. Z. 1984 Asymmetric flow between parallel rotating disks. J. Fluid Mech. 146, 203225.Google Scholar
Lance, G. N. & Rogers, M. H. 1961 The axially symmetric flow of a viscous fluid between two infinite rotating disks. Proc. R. Soc. Lond. A 266, 109121.Google Scholar
Mellor, G. L., Chapple, P. J. & Stokes, V. 1968 On the flow between a rotating and a stationary disk. J. Fluid Mech. 31, 95112.Google Scholar
Nguyen, N. D., Ribault, J. P. & Florent, P. 1975 Multiple solutions for the flow between coaxial disks. J. Fluid Mech. 68, 369388.Google Scholar
Oldroyd, J. G. 1950 On the formation of rheological equations of state. Proc. R. Soc. Lond. A 200, 523541.Google Scholar
Parter, S. V. 1982 On the swirling flow between rotating co-axial disks: A survey. In Theory and Applications of Singular Perturbations, Proc. of a Conf. Oberwolfach, 1981 (ed. W. Ecklhaus & E. M. DeJager). Lecture Notes in Mathematics, vol. 942, pp. 258280. Springer.
Parter, S. V. & Rajagopal, K. R. 1984 Swirling flow between rotating plates. Arch. Rat. Mech. Anal. 86, 305315.Google Scholar
Pearson, C. E. 1965 Numerical solutions for time-dependent viscous flow between two rotating coaxial disks. J. Fluid Mech. 21, 623633.Google Scholar
Pesch, H. J. & Rentrop, P. 1965 Numerical solutions of the flow between two counter-rotating co-axial disks. J. Fluid Mech. 21, 623633.Google Scholar
Rajagopal, K. R. 1987 Recent developments in the swirling flow of Newtonian and non-Newtonian fluids between rotating plates. Mechanics Today (to appear).Google Scholar
Roberts, S. M. & Shipman, J. S. 1976 Computation of the flow between a rotating and stationary disk. J. Fluid Mech. 68, 369388.Google Scholar
Schultz, D. & Greenspan, D. 1974 Simplification and improvement of a numerical method for Navier-Stokes problems. In Proc. Colloquium on Differential Equations, Keszthely, Hungary, pp. 201222.
Stewartson, K. 1953 On the flow between two rotating co-axial disks. Proc. Camb. Phil. Soc. 49, 333341.Google Scholar
Szeri, A. Z., Schneider, S. J., Labbe, F. & Kaufmann, H. N. 1983 Flow between rotating disks. Part 1. Basic flow. J. Fluid Mech. 134, 103131.Google Scholar
Truesdell, C. & Noll, W. 1965 The non-linear field theories of mechanics. In Handbuch der Physik (ed. S. Flugge), III/3. Springer.
Wagner, M. H. 1976 Analysis of time dependent non-linear stress growth data for shear and elongational flow of a low-density branched polyethylene line melt. Rheol. Acta 15, 133.CrossRefGoogle Scholar
Wilson, L. O. & Schryer, N. L. 1978 Flow between a stationary and rotating disk with suction. J. Fluid Mech. 85, 579596.Google Scholar