Abstract
The problem of the squeeze film flow of a viscoelastic fluid between parallel, circular disks is analyzed. The upper disk is subject to small, axial oscillations. Lodge's “rubber-like liquid” is used as the viscoelastic fluid model, and fluid inertia forces are included. An exact solution to the equations of motion is obtained involving in-phase and out-of-phase components of velocity field and load, with respect to the plate velocity. Peculiar resonance phenomena in the load amplitude are exhibited at high Deborah number. At certain combinations of Reynolds number and Deborah number, the in-phase and/or out-of-phase velocity field components may attain an unusual circulating type of motion in which the flow reverses direction across the film. In the low Deborah number limit, and in the low Reynolds number limit, the results of this study reduce to those obtained by other workers.
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Abbreviations
- a, b :
-
parameters, defined by equations (29), (30)
- F :
-
load
- f, g :
-
arbitrary functions, equation (2)
- h :
-
film thickness
- K :
-
memory function
- m, n :
-
arbitrary functions, equation (9)
- p, q :
-
functions, equation (19); velocity field components, equation (23)
- r :
-
radial coordinate
- R :
-
disk radius
- Re :
-
Reynolds number
- S ij :
-
deviatoric stress tensor
- s :
-
past time = t−τ
- t :
-
present time
- v :
-
fluid velocity
- V :
-
upper disk velocity
- α, β :
-
auxiliary functions, equations (27), (28)
- γ ij, γij :
-
metric or strain tensor
- ε :
-
dimensionless oscillation amplitude
- θ, θ i :
-
relaxation time
- \(\bar \theta \) :
-
Deborah number
- μ, μ i :
-
viscosity
- ξ i :
-
convected coordinate
- ρ :
-
density
- τ :
-
time
- φ :
-
angular coordinate
- Φ :
-
phase angle
- ψ :
-
stream function
- ω :
-
oscillation frequency
- m:
-
mean value
- r, φ, z :
-
radial, angular, axial component
- s, c:
-
sine (in-phase) component; cosine (out-of-phase) component
- o:
-
convected coordinate
- *:
-
amplitude
- o:
-
derivative = d/djackie 0
- o:
-
dimensionless parameter, equations (14) and (22)
References
Stefan, J., “Versuche über die scheinbare Adhesion,” K. Akad. Wissenschaften, Math-Naturwissenschaftliche Klasse, Wien. Sitzungsberichte, v. 69, pp. 713, 1874.
Leider, P. J. and R. B. Bird, Ind. Eng. Chem. Fundam. 13, No. 4 (1974) 336.
Kuhn, K. C. and C. C. Yates, ASME Trans. 7 (1964) 299.
Terrill, R. M., Jour. Lub. Tech., Trans. ASME. Series F, 91 (1969) 126.
Kramer, J. M., Appl. Sci. Res. 30 (1974) 1.
Lodge, A. S., Elastic Liquids, Academic Press, London and New York, 1964.
Grimm, R. J., Appl. Sci. Res. 32 (1976) 149.
Appeldoorn, J. K., J. Lub. Tech., Trans. ASME, Ser. F 90, n. 3 (1968) 526.
Harnoy, A. and W. Philippoff, ASLE Trans. 19, n. 4 (1976) 301.
Leider, P. J., Ind. Eng. Chem. Fundam. 13, n. 4 (1974) 336.
Brindley, G., J. M. Davies and K. Walters, Jour. Non-Newtonian Fluid Mech. 1, n. 1 (1976).
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Tichy, J.A. The behavior of viscoelastic squeeze films subject to normal oscillations, including the effect of fluid inertia. Appl. Sci. Res. 33, 501–517 (1977). https://doi.org/10.1007/BF00411828
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DOI: https://doi.org/10.1007/BF00411828