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Nelin. Dinam., 2005, Volume 1, Number 1, Pages 69–109 (Mi nd191)  

This article is cited in 6 scientific papers (total in 6 papers)

Mixing of viscous fluids

V. V. Meleshkoa, T. S. Krasnopol'skayab

a National Taras Shevchenko University of Kyiv
b Institute of Hydromechanics of NAS of Ukraine

Abstract: The paper presents a new methodology for investigating and evaluating the basic properties of distributive laminar mixing in creeping flows. Our analysis is based upon conservation of some topological properties (e.g. connectedness and orientation) of the Lagrangian interface line under continuous transformations induced by an Eulerian velocity field. The principal advantage of our approach for line tracking is that despite complicated stretching and folding, the area of the blob, enclosed by the contour, is preserved. This gives possibility to develop three criteria for estimating the quality of mixing. The objective of this article is to expound the methodology of investigation of distributive laminar mixing of highly viscous materials by considering a typical example of two-dimensional Stokes flow in an annular wedge cavity. Our methodology is based on the following steps: (1) determination of an analytical solution for the velocity field in the cavity; (2) observations on the deformation of the interface contour line of the stirring blob; (3) finding and classification of periodic points; (4) construction of statistical quantity measures for estimation of the quality of mixing at any given moment of time.

Keywords: mixing, stirring, coarse grained density.

Full text: PDF file (803 kB)
UDC: 536.25

Citation: V. V. Meleshko, T. S. Krasnopol'skaya, “Mixing of viscous fluids”, Nelin. Dinam., 1:1 (2005), 69–109

Citation in format AMSBIB
\Bibitem{MelKra05}
\by V.~V.~Meleshko, T.~S.~Krasnopol'skaya
\paper Mixing of viscous fluids
\jour Nelin. Dinam.
\yr 2005
\vol 1
\issue 1
\pages 69--109
\mathnet{http://mi.mathnet.ru/nd191}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Vinnikov V.V., Ganiev K.O., Reviznikov D.L., Cheredov V.V., “Kompleks programm dlya modelirovaniya protsessov volnovogo peremeshivaniya”, Trudy MAI, 2008, no. 32, 6  elib
    2. Vinnikov V.V., Ganiev K.O., Reviznikov D.L., Ukrainskii L.E., “Dipolnyi metod dlya modelirovaniya protsessov peremeshivaniya”, Vestn. Mosk. aviatsionnogo in-ta, 16:2 (2009), 15  mathscinet  elib
    3. Guloyan Yu.A., “Fiziko-khimicheskie i tekhnologicheskie faktory okrashivaniya steklomassy”, Steklo i keramika, 2013, no. 1, 7–14  elib
    4. Karaeva J.V., Khalitova G.R., “Evaluation of Mixing Quality in Anaerobic Digester”, J. Renew. Sustain. Energy, 7:5 (2015), 053111  crossref  isi  elib  scopus
    5. Ganiev R.F. Revisnikov D.L. Sukharev T.Yu. Ukrainskii L.E., “Wave Mixing in Oscillatory-Type Power Plants”, J. Mach. Manuf. Reliab., 46:3 (2017), 219–224  crossref  isi  scopus
    6. Ganiev R.F. Reviznikov D.L. Sukharev T.Yu. Ukrainskii L.E., “Optimization of the Spatial Arrangement of Working Elements in Oscillatory-Type Plants”, J. Mach. Manuf. Reliab., 47:1 (2018), 1–5  crossref  mathscinet  isi  scopus
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