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Dissipative Structures of Marangoni Convection in a Thin Layer of liquid with Lattice of Localized and Continuously Distributed Heat Sources and Sinks

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Abstract

The three-dimensional solutions of nonlinear long-wavelength approximations for the problem of Marangoni convection in a thin horizontal layer of a viscous incompressible fluid with a free surface is being considered. The temperature distribution in the liquid corresponds to a uniform vertical gradient distorted by the imposition of a weakly inhomogeneous heat flux localized in the horizontal plane, caused by a lattice of either localized or continuously distributed heat sources and sinks. The lower boundary of the layer is solid and thermally insulated, while the upper one is free and deformable. The statement of the problem is motivated by the search for ways to control convection structures. The problem in long-wave approximation is described by a system of nonlinear transport equations for the amplitudes of temperature distribution and surface deformation. The numerical solution of the problem is based on the pseudospectral method. The dynamics of non-stationary dissipative structures is considered.

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Funding

This study was funded by the Russian Foundation for Basic Research within the framework of the joint Russian-German project 20–51-12010 NNIO_a.

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Authors and Affiliations

  1. Institute of Continuous Media Mechanics, Ural Branch of Russian Academy of Sciences, 1, Acad. Koroleva Street, 614013, Perm, Russia

    Igor I. Wertgeim

  2. Perm National Research Polytechnic University, 29, Komsomolskii Pr., 614990, Perm, Russia

    Vadim A. Sharifulin & Albert N. Sharifulin

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  1. Igor I. Wertgeim
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  2. Vadim A. Sharifulin
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Contributions

Albert N. Sharifulin. and Igor I. Wertgeim wrote the main manuscript text and Vadim A. Sharifulin prepared Figs. 1–5. All authors reviewed the manuscript.

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Correspondence to Vadim A. Sharifulin.

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Wertgeim, I.I., Sharifulin, V.A. & Sharifulin, A.N. Dissipative Structures of Marangoni Convection in a Thin Layer of liquid with Lattice of Localized and Continuously Distributed Heat Sources and Sinks. Microgravity Sci. Technol. 35, 36 (2023). https://doi.org/10.1007/s12217-023-10061-0

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