On the Voitkunskii Amfilokhiev Pavlovskii Model of Motion of Aqueous Polymer Solutions

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On the Voitkunskii Amfilokhiev Pavlovskii Model of Motion of Aqueous Polymer Solutions. / Pukhnachev, V. V.; Frolovskaya, O. A.

In: Proceedings of the Steklov Institute of Mathematics, Vol. 300, No. 1, 01.01.2018, p. 168-181.

Research output: Contribution to journal › Article › peer-review

BibTeX

@article{0750c1e4f4064233974c54d42c5eda7a,

title = "On the Voitkunskii Amfilokhiev Pavlovskii Model of Motion of Aqueous Polymer Solutions",

abstract = "We study the mathematical properties of the model of motion of aqueous polymer solutions (Voitkunskii, Amfilokhiev, Pavlovskii, 1970) and its modifications in the limiting case of small relaxation times (Pavlovskii, 1971). In both cases, we examine plane unsteady laminar flows. In the first case, the properties of the flows are similar to those of the flow of an ordinary viscous fluid. In the second case, there may exist weak discontinuities that are preserved during the motion. We also address the steady flow problem for a dilute aqueous polymer solution moving in a cylindrical tube under a longitudinal pressure gradient. In this case, a flow with rectilinear trajectories (an analog of the classical Poiseuille flow) is possible. However, in contrast to the latter, the pressure in this flow depends on all three spatial variables.",

author = "Pukhnachev, {V. V.} and Frolovskaya, {O. A.}",

note = "Publisher Copyright: {\textcopyright} 2018, Pleiades Publishing, Ltd.",

year = "2018",

month = jan,

day = "1",

doi = "10.1134/S0081543818010145",

language = "English",

volume = "300",

pages = "168--181",

journal = "Proceedings of the Steklov Institute of Mathematics",

issn = "0081-5438",

publisher = "Maik Nauka Publishing / Springer SBM",

number = "1",

}

RIS

TY - JOUR

T1 - On the Voitkunskii Amfilokhiev Pavlovskii Model of Motion of Aqueous Polymer Solutions

AU - Pukhnachev, V. V.

AU - Frolovskaya, O. A.

PY - 2018/1/1

Y1 - 2018/1/1

N2 - We study the mathematical properties of the model of motion of aqueous polymer solutions (Voitkunskii, Amfilokhiev, Pavlovskii, 1970) and its modifications in the limiting case of small relaxation times (Pavlovskii, 1971). In both cases, we examine plane unsteady laminar flows. In the first case, the properties of the flows are similar to those of the flow of an ordinary viscous fluid. In the second case, there may exist weak discontinuities that are preserved during the motion. We also address the steady flow problem for a dilute aqueous polymer solution moving in a cylindrical tube under a longitudinal pressure gradient. In this case, a flow with rectilinear trajectories (an analog of the classical Poiseuille flow) is possible. However, in contrast to the latter, the pressure in this flow depends on all three spatial variables.

AB - We study the mathematical properties of the model of motion of aqueous polymer solutions (Voitkunskii, Amfilokhiev, Pavlovskii, 1970) and its modifications in the limiting case of small relaxation times (Pavlovskii, 1971). In both cases, we examine plane unsteady laminar flows. In the first case, the properties of the flows are similar to those of the flow of an ordinary viscous fluid. In the second case, there may exist weak discontinuities that are preserved during the motion. We also address the steady flow problem for a dilute aqueous polymer solution moving in a cylindrical tube under a longitudinal pressure gradient. In this case, a flow with rectilinear trajectories (an analog of the classical Poiseuille flow) is possible. However, in contrast to the latter, the pressure in this flow depends on all three spatial variables.

UR - http://www.scopus.com/inward/record.url?scp=85047566757&partnerID=8YFLogxK

U2 - 10.1134/S0081543818010145

DO - 10.1134/S0081543818010145

M3 - Article

AN - SCOPUS:85047566757

VL - 300

SP - 168

EP - 181

JO - Proceedings of the Steklov Institute of Mathematics

JF - Proceedings of the Steklov Institute of Mathematics

SN - 0081-5438

IS - 1

ER -

ID: 13632480