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Research Papers

Slow Steady Viscous Flow of Newtonian Fluids in Parallel-Disk Viscometer With Wall Slip

[+] Author and Article Information
Y. Leong Yeow1

Department of Chemical and Biomolecular Engineering, The University of Melbourne, Victoria, Australia 3010yly@unimelb.edu.au

Yee-Kwong Leong

School of Mechanical Engineering, The University of Western Australia, Crawley, Western Australia, Australia 6009

Ash Khan

Department of Civil and Chemical Engineering, RMIT University, Victoria, Australia 3000

1

Corresponding author.

J. Appl. Mech 75(4), 041001 (May 09, 2008) (7 pages) doi:10.1115/1.2910901 History: Received April 03, 2006; Revised March 03, 2008; Published May 09, 2008

The parallel-disk viscometer is a widely used instrument for measuring the rheological properties of Newtonian and non-Newtonian fluids. The torque-rotational speed data from the viscometer are converted into viscosity and other rheological properties of the fluid under test. The classical no-slip boundary condition is usually assumed at the disk-fluid interface. This leads to a simple azimuthal flow in the disk gap with the azimuthal velocity linearly varying in the radial and normal directions of the disk surfaces. For some complex fluids, the no-slip boundary condition may not be valid. The present investigation considers the flow field when the fluid under test exhibits wall slip. The equation for slow steady azimuthal flow of Newtonian fluids in parallel-disk viscometer in the presence of wall slip is solved by the method of separation of variables. Both linear and nonlinear slip functions are considered. The solution takes the form of a Bessel series. It shows that, in general, as a result of wall slip the azimuthal velocity no longer linearly varies in the radial direction. However, under conditions pertinent to parallel-disk viscometry, it approximately remains linear in the normal direction. The implications of these observations on the processing of parallel-disk viscometry data are discussed. They indicate that the method of Yoshimura and Prud’homme (1988, “Wall Slip Corrections for Couette and Parallel-Disk Viscometers  ,” J. Rheol., 32(1), pp. 53–67) for the determination of the wall slip function remains valid but the simple and popular procedure for converting the measured torque into rim shear stress is likely to incur significant error as a result of the nonlinearity in the radial direction.

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Copyright © 2008 by American Society of Mechanical Engineers
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Figures

Grahic Jump Location
Figure 2

Radial variation of shear stress for no slip (ns), linear slip (ln), square dependence (sq), square-root dependence (rt), and linear slip with critical wall shear stress (cr). The darker curves are for the stress at the disk surfaces and the lighter curves are for the stress at the midplane.

Grahic Jump Location
Figure 3

Square dependence wall slip. (a) Variation of azimuthal velocity with radius at the upper disk (U), mid plane (M), and lower disk (L). (b) Variation of azimuthal velocity with axial coordinate at different radial positions. (c) Variation of shear rate with axial coordinate at different radial positions.

Grahic Jump Location
Figure 4

Square-root dependence wall slip. (a) Variation of azimuthal velocity with radius at the upper disk (U), midplane (M), and lower disk (L). (b) Variation of azimuthal velocity with axial coordinate at different radial positions. (c) Variation of shear rate with axial coordinate at different radial positions.

Grahic Jump Location
Figure 5

Linear slip with critical wall shear stress. (a) Variation of azimuthal velocity with radius at the upper disk (U), midplane (M), and lower disk (L). (b) Variation of azimuthal velocity with axial coordinate at different radial positions. (c) Variation of shear rate with axial coordinate at different radial positions.

Grahic Jump Location
Figure 1

Linear slip law. (a) Variation of azimuthal velocity with radius at the upper disk (U), midplane (M), and lower disk (L). (b) Variation of azimuthal velocity with axial coordinate at different radial positions.

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