On bounded channel flows of viscoelastic fluids

Marshall J. Leitman; Epifanio G. Virga

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni (1988)

  • Volume: 82, Issue: 2, page 291-297
  • ISSN: 1120-6330

Abstract

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We show that the smooth bounded channel flows of a viscoelastic fluid exhibit the following qualitative feature: Whenever the channel is sufficiently wide, any bounded velocity field satisfying the homogeneous equation of motion is such that if the flow stops at some time, then the flow is never unidirectional throughout the channel. We first demonstrate the qualitative property of the bounded channel flows. Then we show explicitly how a piecewise linear approximation of a relaxation function can admit non-zero bounded channel flows, even if the original function does not.

How to cite

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Leitman, Marshall J., and Virga, Epifanio G.. "On bounded channel flows of viscoelastic fluids." Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni 82.2 (1988): 291-297. <http://eudml.org/doc/287462>.

@article{Leitman1988,
abstract = {We show that the smooth bounded channel flows of a viscoelastic fluid exhibit the following qualitative feature: Whenever the channel is sufficiently wide, any bounded velocity field satisfying the homogeneous equation of motion is such that if the flow stops at some time, then the flow is never unidirectional throughout the channel. We first demonstrate the qualitative property of the bounded channel flows. Then we show explicitly how a piecewise linear approximation of a relaxation function can admit non-zero bounded channel flows, even if the original function does not.},
author = {Leitman, Marshall J., Virga, Epifanio G.},
journal = {Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni},
keywords = {Viscoelastic fluids; Channel flow; Bounded flow; smooth bounded channel flows; viscoelastic fluid; piecewise linear approximation},
language = {eng},
month = {6},
number = {2},
pages = {291-297},
publisher = {Accademia Nazionale dei Lincei},
title = {On bounded channel flows of viscoelastic fluids},
url = {http://eudml.org/doc/287462},
volume = {82},
year = {1988},
}

TY - JOUR
AU - Leitman, Marshall J.
AU - Virga, Epifanio G.
TI - On bounded channel flows of viscoelastic fluids
JO - Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
DA - 1988/6//
PB - Accademia Nazionale dei Lincei
VL - 82
IS - 2
SP - 291
EP - 297
AB - We show that the smooth bounded channel flows of a viscoelastic fluid exhibit the following qualitative feature: Whenever the channel is sufficiently wide, any bounded velocity field satisfying the homogeneous equation of motion is such that if the flow stops at some time, then the flow is never unidirectional throughout the channel. We first demonstrate the qualitative property of the bounded channel flows. Then we show explicitly how a piecewise linear approximation of a relaxation function can admit non-zero bounded channel flows, even if the original function does not.
LA - eng
KW - Viscoelastic fluids; Channel flow; Bounded flow; smooth bounded channel flows; viscoelastic fluid; piecewise linear approximation
UR - http://eudml.org/doc/287462
ER -

References

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  1. HALE, J., Functional differential equations, Springer-Verlag, Berlin, 1971. Zbl0222.34003MR390425
  2. TRUESDELL, C. and NOLL, W., The non-linear field theories of mechanics, in "Encyclopedia of Physics", vol. III-3, Springer-Verlag, Berlin, 1965. Zbl0779.73004MR193816
  3. JOSEPH, D.D., RENARDY, M. and SAUT, J.C., Hyperbolicity and change of type in the flow of viscoelastic fluids, Archive Rational Mech. Anal., 87 (1984-85), 213-251. Zbl0572.76011MR768067DOI10.1007/BF00250725

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