Fluctuating viscoelasticity

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Abstract

The smaller the scales on which complex fluids are studied, the more fluctuations become relevant, e.g. in microrheology and nanofluidics. In this paper, a general approach is presented for including fluctuations in conformation-tensor based models for viscoelasticity, in accordance with the fluctuation-dissipation theorem. It is advocated to do this not for the conformation tensor itself, but rather for its so-called contravariant decomposition, in order to circumvent two major numerical complications. These are potential violation of the positive semi-definiteness of the conformation tensor, and numerical instabilities that occur even in the absence of fluctuations. Using the general procedure, fluctuating versions are derived for the upper-convected Maxwell model, the FENE-P model, and the Giesekus model. Finally, it is shown that the fluctuating viscoelasticity proposed here naturally reduces to the fluctuating Newtonian fluid dynamics of Landau and Lifshitz [L. D. Landau and E. M. Lifshitz, Fluid Mechanics, Vol. 6 of Course of Theoretical Physics, Pergamon Press, Oxford, 1959], in the limit of vanishingly small relaxation time.
Original languageEnglish
Pages (from-to)42-56
JournalJournal of Non-Newtonian Fluid Mechanics
Volume256
DOIs
Publication statusPublished - 2018

Fingerprint

Viscoelasticity
viscoelasticity
Conformation
Tensors
Conformations
Tensor
tensors
Fluctuations
Nanofluidics
theoretical physics
Complex Fluids
Fluctuation-dissipation Theorem
Numerical Instability
Newtonian fluids
fluid mechanics
Fluid Mechanics
Fluid mechanics
Newtonian Fluid
fluid dynamics
Fluid Dynamics

Keywords

  • Fluctuations
  • Viscoelasticity
  • Conformation tensor
  • Multiplicative decomposition
  • Complex fluids

Cite this

@article{efbf17c39947464f87565a584af7bbba,
title = "Fluctuating viscoelasticity",
abstract = "The smaller the scales on which complex fluids are studied, the more fluctuations become relevant, e.g. in microrheology and nanofluidics. In this paper, a general approach is presented for including fluctuations in conformation-tensor based models for viscoelasticity, in accordance with the fluctuation-dissipation theorem. It is advocated to do this not for the conformation tensor itself, but rather for its so-called contravariant decomposition, in order to circumvent two major numerical complications. These are potential violation of the positive semi-definiteness of the conformation tensor, and numerical instabilities that occur even in the absence of fluctuations. Using the general procedure, fluctuating versions are derived for the upper-convected Maxwell model, the FENE-P model, and the Giesekus model. Finally, it is shown that the fluctuating viscoelasticity proposed here naturally reduces to the fluctuating Newtonian fluid dynamics of Landau and Lifshitz [L. D. Landau and E. M. Lifshitz, Fluid Mechanics, Vol. 6 of Course of Theoretical Physics, Pergamon Press, Oxford, 1959], in the limit of vanishingly small relaxation time.",
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author = "M. H{\"u}tter and M.A. Hulsen and P.D. Anderson",
year = "2018",
doi = "10.1016/j.jnnfm.2018.02.012",
language = "English",
volume = "256",
pages = "42--56",
journal = "Journal of Non-Newtonian Fluid Mechanics",
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}

Fluctuating viscoelasticity. / Hütter, M.; Hulsen, M.A.; Anderson, P.D.

In: Journal of Non-Newtonian Fluid Mechanics, Vol. 256, 2018, p. 42-56.

Research output: Contribution to journalArticleAcademicpeer-review

TY - JOUR

T1 - Fluctuating viscoelasticity

AU - Hütter, M.

AU - Hulsen, M.A.

AU - Anderson, P.D.

PY - 2018

Y1 - 2018

N2 - The smaller the scales on which complex fluids are studied, the more fluctuations become relevant, e.g. in microrheology and nanofluidics. In this paper, a general approach is presented for including fluctuations in conformation-tensor based models for viscoelasticity, in accordance with the fluctuation-dissipation theorem. It is advocated to do this not for the conformation tensor itself, but rather for its so-called contravariant decomposition, in order to circumvent two major numerical complications. These are potential violation of the positive semi-definiteness of the conformation tensor, and numerical instabilities that occur even in the absence of fluctuations. Using the general procedure, fluctuating versions are derived for the upper-convected Maxwell model, the FENE-P model, and the Giesekus model. Finally, it is shown that the fluctuating viscoelasticity proposed here naturally reduces to the fluctuating Newtonian fluid dynamics of Landau and Lifshitz [L. D. Landau and E. M. Lifshitz, Fluid Mechanics, Vol. 6 of Course of Theoretical Physics, Pergamon Press, Oxford, 1959], in the limit of vanishingly small relaxation time.

AB - The smaller the scales on which complex fluids are studied, the more fluctuations become relevant, e.g. in microrheology and nanofluidics. In this paper, a general approach is presented for including fluctuations in conformation-tensor based models for viscoelasticity, in accordance with the fluctuation-dissipation theorem. It is advocated to do this not for the conformation tensor itself, but rather for its so-called contravariant decomposition, in order to circumvent two major numerical complications. These are potential violation of the positive semi-definiteness of the conformation tensor, and numerical instabilities that occur even in the absence of fluctuations. Using the general procedure, fluctuating versions are derived for the upper-convected Maxwell model, the FENE-P model, and the Giesekus model. Finally, it is shown that the fluctuating viscoelasticity proposed here naturally reduces to the fluctuating Newtonian fluid dynamics of Landau and Lifshitz [L. D. Landau and E. M. Lifshitz, Fluid Mechanics, Vol. 6 of Course of Theoretical Physics, Pergamon Press, Oxford, 1959], in the limit of vanishingly small relaxation time.

KW - Fluctuations

KW - Viscoelasticity

KW - Conformation tensor

KW - Multiplicative decomposition

KW - Complex fluids

U2 - 10.1016/j.jnnfm.2018.02.012

DO - 10.1016/j.jnnfm.2018.02.012

M3 - Article

VL - 256

SP - 42

EP - 56

JO - Journal of Non-Newtonian Fluid Mechanics

JF - Journal of Non-Newtonian Fluid Mechanics

SN - 0377-0257

ER -