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Nonlinear Waves in Film Viscous Liquid Flows at Arbitrary Kapitsa Numbers

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Abstract—

The methods and results of the mathematical simulation of nonlinear waves generated by hydrodynamic instability in traveling capillary films of a viscous liquid are discussed. Two model systems of differential equations for the local values of the layer thickness h and the fluid flow rate q are considered. The single-parameter (h–q) Kapitsa–Shkadov model that ensures the effective simulation of low-viscosity liquid film flows has received wide acceptance in world literature devoted to film hydrodynamics. The two-parameter (h–q)1 model extends the possibilities for direct calculation of nonlinear waves in the higher viscosity liquid films. A succession of the systems of model equations is given, the scenarios of instability and bifurcation are discussed, and the results of calculations of wave structures in comparison with the experimental data are given.

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Funding

The work was carried out with financial support from the Russian Foundation for Basic Research (projects nos. 18-01-00762 and 19-11-50105).

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Authors and Affiliations

  1. Moscow State University, Moscow, Russia

    A. N. Beloglazkin & V. Ya. Shkadov

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  1. A. N. Beloglazkin
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  2. V. Ya. Shkadov
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Correspondence to A. N. Beloglazkin or V. Ya. Shkadov.

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Translated by E.A. Pushkar

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Beloglazkin, A.N., Shkadov, V.Y. Nonlinear Waves in Film Viscous Liquid Flows at Arbitrary Kapitsa Numbers. Fluid Dyn 56, 539–551 (2021). https://doi.org/10.1134/S0015462821040029

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  • DOI: https://doi.org/10.1134/S0015462821040029

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