Nonlinear Differential Equation of the Surface Section of Gas-Liquid

  • L. A. ProkudinaEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11386)


Study of flow of thin layers of viscous liquids (liquid films) is of great theoretical and practical importance. For liquid films is the basis of technological processes in many industries: petrochemical, thermal power, food and other. The development of nonlinear mathematical models that adequately reflect the real flow of a liquid film, the contact and interaction between fluids (gas-liquid), the calculation characteristics of the film flow is an important task.

Presents the nonlinear mathematical model of the state of free surface liquid film, accounting for the interaction with the gas flow is a nonlinear differential equation of fourth order for deflection of the free liquid surface from the unperturbed state \(\psi (x,t)\), where x – the spatial variable, t – time.

The transition to the finite-difference equation is completed. Computational algorithms for the calculation of wave characteristics and deviation of free surface liquid film in contact with the gas stream are developed. The results of computational experiments for the vertical film of water at moderate Reynolds numbers are presented.


Liquid film Instability Finite-difference equation Reynolds number Shear stress 



Supported by Ministry of Education and Science of the Russian Federation within the framework of the basic part of the State task “Development, research and implementation of data processing algorithms for dynamic measurements of spatially distributed objects”, Terms of Reference 8.9692.2017/8.9 from 17.02.2017.


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Authors and Affiliations

  1. 1.South Ural State UniversityChelyabinskRussia

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