The FENE-L and FENE-LS Closure Approximations for the Kinetic Theory of Finitely Extensible Dumbbells

Lielens, Grégory; Keunings, Roland; Legat, Vincent

doi:10.1007/978-3-642-51062-5_41

Cited by 18 publications

(46 citation statements)

References 2 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…For constitutive equations inspired by molecular models, one option is to describe the polymer population by the conformation tensor, A, defined as the ensemble average of the tensorial product of the individual end-to-end vectors, R , (often written A = 〈R R 〉) (Rallison & Hinch 1988). Higher order moments can be employed in more sophisticated representations (Lielens et al 1999;Ilg et al 2010). Figure 2: Bead-rod model for a polymer chain.…”

Section: General Approachmentioning

confidence: 99%

A multiscale model for the rupture of linear polymers in strong flows

et al. 2018

View full text Add to dashboard Cite

Polymer-containing solutions used across research and industry are commonly exposed to mechanically harsh fluid processes, for example shear and extensional forces during flow through porous media or rapid microdispensing of biopharmaceutical molecules. These forces are strong enough to break the covalent bonds in the polymer backbone. As this scission phenomenon can change the functional and fluid-flow properties as well as introduce reactive radicals into the solution, it must be understood and controlled. Experiments and models to date have only provided partial or qualitative insights into this behaviour. Here we build a link between the molecular-scale degradation models and the macroscale laminar flow of dilute solutions in any given geometry. A free-draining bead–rod model is used to investigate rupture events at the molecular scale. It is shown by uniaxial extension simulations of an ensemble of chains that scission can be conveniently described at the macroscopic scale as a first-order reaction whose rate is a function of the conformation tensor of the macromolecules and the velocity gradient of the flow. This approach is implemented in the finite volume code OpenFOAM by elaborating an appropriate constitutive equation for the conformation tensor. The macroscopic model is run and analysed for ultra-dilute solutions of poly(methyl methacrylate) in ethyl acetate and polyethylene oxide in water, using the geometry of an abrupt contraction flow and neglecting any viscoelastic effect. This multiscale approach bridges the gap between phenomenological observations of mechanically induced chemical degradation in large-scale applications and the rich field of molecular-scale models of macromolecules under flow.

show abstract

Section: General Approachmentioning

confidence: 99%

A multiscale model for the rupture of linear polymers in strong flows

et al. 2018

View full text Add to dashboard Cite

show abstract

“…Simulation of complex viscoelastic flows using bead-rod chain or bead-spring chain models with so many internal degrees of freedom is still not computationally feasible, and much recent work has been directed at developing simpler, closedform models that accurately capture or "coarse-grain" the macroscopic stressconformation hysteresis arising from molecular individualism on the microscale. The first models treated the additional stress arising from the strong local rate of deformation as explicitly viscous-like (see for example Rallison 1997, Verhoef et al 1998, whereas more recent models have attempted to capture the progressive changes in the average internal structure of the molecules during stretching and relaxation using additional scalar evolution equations (Lielens et al 1998, Lhuillier 2001. It remains to be seen which approach best describes kinematically complex "mixed" flows of polymer solutions containing regions of both strong elongation and shearing.…”

Section: Figure 14mentioning

confidence: 99%

FILAMENT-STRETCHINGRHEOMETRY OFCOMPLEXFLUIDS

McKinley

Sridhar

2002

Annu. Rev. Fluid Mech.

456

341

View full text Add to dashboard Cite

Key Words transient extensional viscosity, polymer solution rheology, elongational flows Abstract Filament-stretching rheometers are devices for measuring the extensional viscosity of moderately viscous non-Newtonian fluids such as polymer solutions. In these devices, a cylindrical liquid bridge is initially formed between two circular end-plates. The plates are then moved apart in a prescribed manner such that the fluid sample is subjected to a strong extensional deformation. Asymptotic analysis and numerical computation show that the resulting kinematics closely approximate those of an ideal homogeneous uniaxial elongation. The evolution in the tensile stress (measured mechanically) and the molecular conformation (measured optically) can be followed as functions of the rate of stretching and the total strain imposed. The resulting rheological measurements are a sensitive discriminant of molecularly based constitutive equations proposed for complex fluids. The dynamical response of the elongating filament is also coupled to the extensional rheology of the polymeric test fluid, and this can lead to complex viscoelastic-flow instabilities such as filament necking and rupture or elastic peeling from the rigid end-plates.

show abstract

“…Due to the very high computational cost of micro-macro simulations, another route which has been followed (see e.g. [14,16,22,32,33,35]) is to look for an approximate closure at the macroscopic level, namely a model of the form: 14) which is close to the microscopic model (1.7)-(1.8). Here M denotes an ensemble of macroscopic state variables that depend on time and space.…”

Section: Introductionmentioning

confidence: 99%

A numerical closure approach for kinetic models of polymeric fluids: Exploring closure relations for FENE dumbbells

Samaey¹,

Lelièvre²,

Legat³

2011

Computers & Fluids

View full text Add to dashboard Cite

International audienceWe propose a numerical procedure to study closure approximations for FENE dumbbells in terms of chosen macroscopic state variables, enabling to test straightforwardly which macroscopic state variables should be included to build good closures. The method involves the reconstruction of a polymer distribution related to the conditional equilibrium of a microscopic Monte Carlo simulation, conditioned upon the desired macroscopic state. We describe the procedure in detail, give numerical results for several strategies to define the set of macroscopic state variables, and show that the resulting closures are related to those obtained by a so-called quasi-equilibrium approximation

show abstract

The FENE-L and FENE-LS Closure Approximations for the Kinetic Theory of Finitely Extensible Dumbbells

Cited by 18 publications

References 2 publications

A multiscale model for the rupture of linear polymers in strong flows

A multiscale model for the rupture of linear polymers in strong flows

FILAMENT-STRETCHINGRHEOMETRY OFCOMPLEXFLUIDS

A numerical closure approach for kinetic models of polymeric fluids: Exploring closure relations for FENE dumbbells

Contact Info

Product

Resources

About