Numerical study of the relative equilibrium of a droplet with a simply connected free surface on a rotating plane

Authors

  • Yauheni V. Audzeichyk Belarusian State University, 4 Niezaliežnasci Avenue, Minsk 220030, Belarus https://orcid.org/0000-0002-3854-5335
  • Pavel N. Konon Belarusian State University, 4 Niezaliežnasci Avenue, Minsk 220030, Belarus

Keywords:

relative equilibrium, rotating plane, rotational symmetry, Weber number, Bond number, Laplace formula, surface tension, contact angle
Supporting Agencies
The work was carried out with the financial support of the state program of scientific research «Energy and nuclear processes and technologies» (the subprogram «Energy processes and technologies», task 2.11 «Wave flows of capillary jets, layers, films in centrifugal, constant and variable temperature fields and their application in technological processes»).

Abstract

The paper investigates the shapes of relative rest of limited layers of liquid on a rotating horizontal plane in the field of gravity in the presence of surface tension. The layers under consideration have a simply connected free surface and rotational symmetry with respect to the line of action of the angular velocity. The mathematical formulation of this problem is reduced to a system of first-order ordinary differential equations with boundary and integral closing conditions. A new algorithm for the numerical solution of the resulting system is proposed, the influence of various dimensionless parameters on the characteristics of equilibrium droplet shapes is studied, and criteria for the existence of such shapes are determined. The paper is of theoretical interest, since the problem under consideration is one of the fundamental ones in the research of capillary phenomena. The developed numerical scheme can also be applied in a wider class of differential equations. The results of the article can be used in practical tasks related to coating, fiber and powder production by the centrifugal-disk method.

Author Biographies

  • Yauheni V. Audzeichyk, Belarusian State University, 4 Niezaliežnasci Avenue, Minsk 220030, Belarus

    postgraduate student at the department of theoretical and applied mechanics, faculty of mechanics and mathematics

  • Pavel N. Konon, Belarusian State University, 4 Niezaliežnasci Avenue, Minsk 220030, Belarus

    PhD (physics and mathematics), docent; associate professor at the department of theoretical and applied mechanics, faculty of mechanics and mathematics

References

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Published

2022-12-26

Issue

No. 3 (2022): Journal of the Belarusian State University. Mathematics and Informatics

Section

Theoretical and Applied Mechanics

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How to Cite

[1]
Audzeichyk, Y.V. and Konon, P.N. 2022. Numerical study of the relative equilibrium of a droplet with a simply connected free surface on a rotating plane. Journal of the Belarusian State University. Mathematics and Informatics. 3 (Dec. 2022), 79–90. DOI:https://doi.org/10.33581/2520-6508-2022-3-79-90.