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Flow of a liquid with an anisotropic viscosity tensor. (English) Zbl 0382.76002
Summary: This paper presents a simple model of an anisotropic incompressible viscous fluid, whose equations of state involve one anisotropic physical constant tensor (in the sense of J. G, Oldroyd [Proc. R. Soc. Lond., Ser. A 200, 523–541 (1950; Zbl 1157.76305)]). Attention is restricted to the case of a fluid that is everywhere transversely isotropic at some given instant, so that the model is essentially one of a liquid with initially just one privileged direction at each point. Transverse isotropy does not persist, however, in some flow situations.
Predictions are made for simple shearing flows and for channel and pipe flows with different initial directions of orientation. In some cases, the volume rate of flow under constant pressure-gradient decreases steadily and tends to zero after a long time.

MSC:
76A10 Viscoelastic fluids
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