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EXACT POISEUIL-TYPE SOLUTIONS FOR VISCOELASTIC POLYMER FLUID FLOWS THROUGH A CIRCULAR PIPE

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Abstract

Resolving equations describing stationary flows of an incompressible viscoelastic polymer fluid through a circular pipe are derived on the basis of the rheological mesoscopic Pokrovskii–Vinogradov model. Exact solutions of the equations are obtained, and constraints on the values of rheological parameters that ensure their existence are formulated. These results enable one to constructively describe the breakdown of Poiseuille-type laminar flow. The size and orientation of polymer fluid macromolecules play a key role in the mechanics of this process. The mathematical description of the process uses singular points of the solutions.

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Authors and Affiliations

  1. Sobolev Institute of Mathematics, Siberian Branch, Russian Academy of Sciences, Novosibirsk, Russia

    B. V. Semisalov

  2. Novosibirsk National Research State University, Novosibirsk, Russia

    B. V. Semisalov

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  1. B. V. Semisalov
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Correspondence to B. V. Semisalov.

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Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, 2023, Vol. 64, No. 4, pp. 139-151. https://doi.org/10.15372/PMTF20230413.

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Semisalov, B.V. EXACT POISEUIL-TYPE SOLUTIONS FOR VISCOELASTIC POLYMER FLUID FLOWS THROUGH A CIRCULAR PIPE. J Appl Mech Tech Phy 64, 675–685 (2023). https://doi.org/10.1134/S0021894423040132

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  • DOI: https://doi.org/10.1134/S0021894423040132

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