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Microsecond relaxation processes in shear and extensional flows of weakly elastic polymer solutions
PDE analysis of a class of thermodynamically compatible viscoelastic rate-type fluids with stress-diffusion
We establish the long-time existence of large-data weak solutions to a system
of nonlinear partial differential equations. The system of interest governs the
motion of non-Newtonian fluids described by a simplified viscoelastic rate-type
model with a stress-diffusion term. The simplified model shares many
qualitative features with more complex viscoelastic rate-type models that are
frequently used in the modeling of fluids with complicated microstructure. As
such, the simplified model provides important preliminary insight into the
mathematical properties of these more complex and practically relevant models
of non-Newtonian fluids. The simplified model that is analyzed from the
mathematical perspective is shown to be thermodynamically consistent, and we
extensively comment on the interplay between the thermodynamical background of
the model and the mathematical analysis of the corresponding
initial-boundary-value problem
Orientation dependent elastic stress concentration at tips of slender objects translating in viscoelastic fluids
Elastic stress concentration at tips of long slender objects moving in
viscoelastic fluids has been observed in numerical simulations, but despite the
prevalence of flagellated motion in complex fluids in many biological
functions, the physics of stress accumulation near tips has not been analyzed.
Here we theoretically investigate elastic stress development at tips of slender
objects by computing the leading order viscoelastic correction to the
equilibrium viscous flow around long cylinders, using the weak-coupling limit.
In this limit nonlinearities in the fluid are retained allowing us to study the
biologically relevant parameter regime of high Weissenberg number. We calculate
a stretch rate from the viscous flow around cylinders to predict when large
elastic stress develops at tips, find thresholds for large stress development
depending on orientation, and calculate greater stress accumulation near tips
of cylinders oriented parallel to motion over perpendicular.Comment: Supplementary information include
Effect of polymer-stress diffusion in the numerical simulation of elastic turbulence
Elastic turbulence is a chaotic regime that emerges in polymer solutions at
low Reynolds numbers. A common way to ensure stability in numerical simulations
of polymer solutions is to add artificially large polymer-stress diffusion. In
order to assess the accuracy of this approach in the elastic-turbulence regime,
we compare numerical simulations of the two-dimensional Oldroyd-B and FENE-P
models sustained by a cellular force with and without artificial diffusion. We
find that artificial diffusion can have a dramatic effect even on the
large-scale properties of the flow and we show some of the spurious phenomena
that may arise when artificial diffusion is used.Comment: 17 page
Particle-laden two-dimensional elastic turbulence
The aggregation properties of heavy inertial particles in the elastic
turbulence regime of an Oldroyd-B fluid with periodic Kolmogorov mean flow are
investigated by means of extensive numerical simulations in two dimensions.
Both the small and large scale features of the resulting inhomogeneous particle
distribution are examined, focusing on their connection with the properties of
the advecting viscoelastic flow. We find that particles preferentially
accumulate on thin highly elastic propagating waves and that this effect is
largest for intermediate values of particle inertia. We provide a quantitative
characterization of this phenomenon that allows to relate it to the
accumulation of particles in filamentary highly strained flow regions producing
clusters of correlation dimension close to 1. At larger scales, particles are
found to undergo turbophoretic-like segregation. Indeed, our results indicate a
close relationship between the profiles of particle density and fluid velocity
fluctuations. The large-scale inhomogeneity of the particle distribution is
interpreted in the framework of a model derived in the limit of small, but
finite, particle inertia. The qualitative characteristics of different
observables are, to a good extent, independent of the flow elasticity. When
increased, the latter is found, however, to slightly reduce the globally
averaged degree of turbophoretic unmixing.Comment: 12 pages, 9 figures. Submitted to EPJ
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