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Flow stability of viscous liquid layer with moment stresses on an inclined plane

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Abstract

The flow stability of a liquid layer on an inclined plane with account for molecular spin [1, 2] has been considered in [3] in the absence of moment stresses within the liquid. It was shown in [3] that molecular spin has a destabilizing effect on the flow. In the following we study the combined effect of molecular spin and internal moment stresses on the behavior of three-dimensional disturbances. The validity of Squire's theorem is established. The flow stability of a layer of relatively long-wave disturbances is studied by the method of sequential approximations [4, 5] under the assumption that the rotational viscosity coefficient ηr is significantly smaller than the Newtonian viscosity coefficient η.

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References

  1. H. Grad, “Statistical mechanics, thermodynamics, and fluid dynamics of systems with arbitrary number of integrals,” Comm. Pure Appl. Math., vol. 5, no. 4, 1952.

  2. E. L. Aero, A. N. Bulygin, and E. V. Kuvshinskiy, “Asymmetric Hydrodynamics,” PMM, vol. 29, no. 2, 1965.

  3. A. T. Listrov, “The Flow stability of a Grad model liquid layer along an inclined plane,” Izv. AN SSSR, MZhG [Fluid Dynamics], no. 6, 1966.

  4. Yu. P. Ivanilov, “The stability of plane-parallel viscous liquid flow over an inclined bottom,” PMM, vol. 14, no. 2, 1960.

  5. Yih Chia-Shun, “Stability of liquid flow down an inclined plane,” Phys. Fluids, vol. 6, no. 3, 1963.

  6. C. C. Lin, Hydrodynamic Stability [Russian translation], Izd. inostr. lit., 1958.

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  1. Voronezh

    Nguen Van Diep & A. T. Listrov

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  1. Nguen Van Diep
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  2. A. T. Listrov
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Van Diep, N., Listrov, A.T. Flow stability of viscous liquid layer with moment stresses on an inclined plane. Fluid Dyn 3, 16–20 (1968). https://doi.org/10.1007/BF01013544

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  • DOI: https://doi.org/10.1007/BF01013544

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