Asymptotic Formula for the Spectrum of the Linear Problem Describing Periodic Polymer Flows in an Infinite Channel

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Asymptotic Formula for the Spectrum of the Linear Problem Describing Periodic Polymer Flows in an Infinite Channel. / Blokhin, A. M.; Tkachev, D. L.; Yegitov, A. V.

In: Journal of Applied Mechanics and Technical Physics, Vol. 59, No. 6, 01.11.2018, p. 992-1003.

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

BibTeX

@article{365b4d457ba140f880ddd56f995c9755,

title = "Asymptotic Formula for the Spectrum of the Linear Problem Describing Periodic Polymer Flows in an Infinite Channel",

abstract = "In this paper, we study a new rheological model (a modification of the well-known Pokrovskii–Vinogradov model) which is shown by computational experiments to take into account the nonlinear effects occurring during melt flows and polymer solutions in regions with complex boundary geometry. For the case where the main solution is an analogue of the Poiseuille flow in an infinite flat channel (viscoelastic polymer fluid considered), an asymptotic formula is obtained for the distribution of points of the spectrum of the linear problem. It is shown that small perturbations have the additional property of periodicity in the variable that runs along the axis of the channel.",

keywords = "Lyapunov stability, Poiseuille type flow, polymer medium, rheological model",

author = "Blokhin, {A. M.} and Tkachev, {D. L.} and Yegitov, {A. V.}",

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

year = "2018",

month = nov,

day = "1",

doi = "10.1134/S0021894418060044",

language = "English",

volume = "59",

pages = "992--1003",

journal = "Journal of Applied Mechanics and Technical Physics",

issn = "0021-8944",

publisher = "Maik Nauka-Interperiodica Publishing",

number = "6",

}

RIS

TY - JOUR

T1 - Asymptotic Formula for the Spectrum of the Linear Problem Describing Periodic Polymer Flows in an Infinite Channel

AU - Blokhin, A. M.

AU - Tkachev, D. L.

AU - Yegitov, A. V.

PY - 2018/11/1

Y1 - 2018/11/1

N2 - In this paper, we study a new rheological model (a modification of the well-known Pokrovskii–Vinogradov model) which is shown by computational experiments to take into account the nonlinear effects occurring during melt flows and polymer solutions in regions with complex boundary geometry. For the case where the main solution is an analogue of the Poiseuille flow in an infinite flat channel (viscoelastic polymer fluid considered), an asymptotic formula is obtained for the distribution of points of the spectrum of the linear problem. It is shown that small perturbations have the additional property of periodicity in the variable that runs along the axis of the channel.

AB - In this paper, we study a new rheological model (a modification of the well-known Pokrovskii–Vinogradov model) which is shown by computational experiments to take into account the nonlinear effects occurring during melt flows and polymer solutions in regions with complex boundary geometry. For the case where the main solution is an analogue of the Poiseuille flow in an infinite flat channel (viscoelastic polymer fluid considered), an asymptotic formula is obtained for the distribution of points of the spectrum of the linear problem. It is shown that small perturbations have the additional property of periodicity in the variable that runs along the axis of the channel.

KW - Lyapunov stability

KW - Poiseuille type flow

KW - polymer medium

KW - rheological model

UR - http://www.scopus.com/inward/record.url?scp=85059646130&partnerID=8YFLogxK

U2 - 10.1134/S0021894418060044

DO - 10.1134/S0021894418060044

M3 - Article

AN - SCOPUS:85059646130

VL - 59

SP - 992

EP - 1003

JO - Journal of Applied Mechanics and Technical Physics

JF - Journal of Applied Mechanics and Technical Physics

SN - 0021-8944

IS - 6

ER -

ID: 18073713