Abstract
| Original language | English |
|---|---|
| Pages (from-to) | 42-56 |
| Journal | Journal of Non-Newtonian Fluid Mechanics |
| Volume | 256 |
| DOIs | |
| Publication status | Published - 2018 |
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Keywords
- Fluctuations
- Viscoelasticity
- Conformation tensor
- Multiplicative decomposition
- Complex fluids
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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 journal › Article › Academic › peer-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 -