Plane surface suddenly set in motion in a non-Newtonian fluid. (English) Zbl 0846.76006

Summary: The flow field of a fluid being called “the third order fluid” or the “fluid of grade three” is considered in the vicinity of a plane wall, suddenly set in motion. The velocity field of the flow is described by a fourth order nonlinear partial differential equation. The solution of this differential equation shows that for short time a strong non-Newtonian effect is present in the velocity field. However, for long time the velocity field becomes a Newtonian one.


76A05 Non-Newtonian fluids
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[1] Bird, R. B.: Useful non-Newtonian models. Ann. Rev. Fluid Mech.8, 13–34 (1976). · Zbl 0407.76004
[2] Teipel, I.: The impulsive motion of a flat plate in a visco-elastic fluid. Acta Mech.39, 277–279 (1981).
[3] Batchelor, G. K.: An introduction to fluid dynamics. Cambridge: Cambridge University Press 1967. · Zbl 0152.44402
[4] Beavers, G. S., Joseph, D. D.: The rotating rod viscometer. J. Fluid Mech.69, 475–511 (1975). · Zbl 0315.76004
[5] Joseph, D. D., Beavers, G. S., Fosdick, R. I.: The free surface on a liquid between cylinders rotating at different speeds. Arch. Rat. Mech. Anal.49, 321–401 (1973). · Zbl 0265.76114
[6] Rajagopal, K. R., Na, T. Y.: On Stokes’ problem for a non-Newtonian fluid. Acta Mech.48, 233–239 (1983). · Zbl 0528.76003
[7] Tanner, R. I.: Note on the Rayleigh problem for a visco-elastic fluid. ZAMP13, 573–580 (1962). · Zbl 0127.40402
[8] Truesdell, C., Noll, W.: The non-linear field theories of mechanics. In: Handbuch der Physik III/3, Berlin-Heidelberg-New York: Springer 1965. · Zbl 0779.73004
[9] Abramowitz, M., Stegun, I. A.: Handbook of mathematical functions. New York: Dover 1965. · Zbl 0171.38503
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