Self-similar solution of the first Stokes problem for non-Newtonian fluids with power-law viscosity

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Abstract



The first Stokes problem is considered for flows of non-Newtonian fluids with effective viscosity varying in accordance with the power law. Self-similar solutions are constructed for the fluids, whose mechanical behavior is described by the Ostwald – de Waele and Herschel–Bulkley rheological models with the corresponding restrictions on the nonlinearity degree exponent n. It is shown that for the Ostwald – de Waele fluid self-similar solutions exist only for 0 < n < 1, which corresponds to the pseudoplastic behavior. At the same time, self-similar solutions for the Herschel–Bulkley fluid can be obtained only at n > 1, when this fluid exhibits the properties of dilatancy.

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About the authors

V. N. Kolodezhnov

Military Education and Science Center of the Air Forces "Prof. Zhukovski and Gagarin Air Force Academy"

Author for correspondence.
Email: kvn117@mail.ru
Russian Federation, Voronezh, 394064

References

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Supplementary files

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2. Fig. 1. Dependence of the integration constant C in the self–similar solution (2.11) on the exponent n in the rheological Ostwald-de Wael fluid model, which demonstrates pseudoplastic behavior.

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3. Fig. 2. Dependence of the np value of the self-similar variable, which determines the position of the interface between the shear flow zone and the stagnant zone for the Herschel–Bulkley liquid, on the exponent n.

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