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1. Master curves for FENE-P fluids in steady shear flow

   https://doi.org/10.1016/j.jnnfm.2022.104944  

   Yamani, Sami; McKinley, Gareth H. (March 2023, Journal of Non-Newtonian Fluid Mechanics)

   Poole, Robert J (Ed.)

   The FENE-P (Finitely-Extensible Nonlinear Elastic) dumbbell constitutive equation is widely used in simulations and stability analyses of free and wall-bounded viscoelastic shear flows due to its relative simplicity and accuracy in predicting macroscopic properties of dilute polymer solutions. The model contains three independent material parameters, which expressed in dimensionless form correspond to a Weissenberg number (Wi), i.e., the ratio of the dumbbell relaxation time scale to a characteristic flow time scale, a finite extensibility parameter (L), corresponding to the ratio of the fully extended dumbbell length to the root mean square end-to-end separation of the polymer chain under equilibrium conditions, and a solvent viscosity ratio. An exact solution for the rheological predictions of the FENE-P model in steady simple shear flow is available [Sureshkumar et al., Phys Fluids (1997)], but the resulting nonlinear and nested set of equations do not readily reveal the key shear-thinning physics that dominates at high Wi as a result of the finite extensibility of the polymer chain. In this note we review a simple way of evaluating the steady material functions characterizing the nonlinear evolution of the polymeric contributions to the shear stress and first normal stress difference as the shear rate increases, provide asymptotic expansions as a function of Wi , and show that it is in fact possible to construct universal master curves for these two material functions as well as the corresponding stress ratio. Steady shear flow experiments on three highly elastic dilute polymer solutions of different finite extensibilities also follow the identified master curves. The governing dimensionless parameter for these master curves is Wi/L and it is only in strong shear flows exceeding Wi/L > 1 that the effects of finite extensibility of the polymer chains dominate the evolution of polymeric stresses in the flow field. We suggest that reporting the magnitude of Wi/L when performing stability analyses or simulating shear-dominated flows with the FENE-P model will help clarify finite extensibility effects. 

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2. Role of micellar entanglements on kinetics of shear banding flow formation

   https://doi.org/10.1122/8.0000436  

   Rassolov, Peter; Mohammadigoushki, Hadi (January 2023, Journal of Rheology)

   We investigate the effects of micellar entanglement number on the kinetics of shear banding flow formation in a Taylor–Couette flow. Three sets of wormlike micellar solutions, each set with a similar fluid elasticity and zero-shear-rate viscosity, but with varying entanglement densities, are studied under the startup of steady shear. Our experiments indicate that in the set with low fluid elasticity, the transient shear banding flow is characterized by the formation of a transient flow reversal in a range of entanglement densities. Outside of this range, the transient flow reversal is not observed. For the sets of medium and high elasticities, the transient flow reversals exist for relatively small entanglement densities and disappear for large entanglement densities. Our analysis shows that wall slip and elastic instabilities do not affect the transient flow feature. We identify a correlation between micellar entanglement number, the width of the stress plateau, and the extent of the transient flow reversal. As the micellar entanglement number increases, the width of the stress plateau first increases; then, at a higher micellar entanglement number, the plateau width decreases. Therefore, we hypothesize that the transient flow reversal is connected to the micellar entanglement number through the width of the stress plateau. 

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3. Mesoscopic modeling of the effect of branching on the viscoelasticity of entangled wormlike micellar solutions

   https://doi.org/10.1103/PhysRevResearch.5.043024  

   Zou, Weizhong; Tan, Grace; Weaver, Mike; Koenig, Peter; Larson, Ronald G (October 2023, Physical Review Research)

   Liétor-Santos, J-J (Ed.)

   The effect of branches on the linear rheology of entangled wormlike micelle solutions is modeled by tracking the diffusion of micellar material through branch points. The model is equivalent to a Kirchhoff circuit model with the sliding of an entangled branch along an entanglement tube due to the constrained diffusion of micellar material analogous to the flux of current in the Kirchhoff circuit model. When combined with our previous mesoscopic pointer algorithm for linear micelles that can both break and fuse, the model adds a branch sprouting process and therefore enables simulation of the dynamics of structural change and stress relaxation in ensembles of micelle clusters of different topologies. Applying this new model to study the relationships between fluid rheology and microstructure of micelles, our results show that branches change the scaling law exponents for viscosity versus micelle strand length. This contrasts with the long-standing hypothesis that branches affect viscosity and relaxation in the same way that micelle ends do. The model also suggests a process for inferring branching density from salt-dependent linear rheology. This is exemplified by mixed surfactant solutions over a range of salt concentrations with flow properties measured using both mechanical rheometry and diffusing wave spectroscopy (DWS). By elucidating the connection between the branching characteristics, such as strand length and branching density, with the nonmonotonic variation of solution viscosity, the above model provides a powerful new tool to help extract branching information from rheology. 

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4. Slip-Spring and Kink Dynamics Models for Fast Extensional Flow of Entangled Polymeric Fluids

   https://doi.org/10.3390/polym11030465  

   Moghadam, Soroush; Saha Dalal, Indranil; Larson, Ronald (March 2019, Polymers)

   We combine a slip-spring model with an ‘entangled kink dynamics’ (EKD) model for strong uniaxial extensional flows (with Rouse Weissenberg number W i R ≫ 1 ) of long ( M w > 1   Mkg / mol for polystyrene) entangled polymers in solutions and melts. The slip-spring model captures the dynamics up to the formation of a ‘kinked’ or folded state, while the kink dynamics simulation tracks the dynamics from that point forward to complete extension. We show that a single-chain slip-spring model using affine motion of the slip-spring anchor points produces unrealistically high tension near the center of the chain once the Hencky strain exceeds around unity or so, exceeding the maximum tension that a chain entangled with a second chain is able to support. This unrealistic tension is alleviated by pairing the slip links on one chain with those on a second chain, and allowing some of the large tension on one of the two to be transferred to the second chain, producing non-affine motion of each. This explicit pairing of entanglements mimics the entanglement pairing also used in the EKD model, and allows the slip spring simulations to be carried out to strains high enough for the EKD model to become valid. We show that results nearly equivalent to those from paired chains are obtained in a single-chain slip-spring simulation by simply specifying that the tension in a slip spring cannot exceed the theoretical maximum value of ζ ′ ϵ ˙ L 2 / 8 where ζ ′ , ϵ ˙ and L are the friction per unit length, strain rate and contour length of the chain, respectively. The effects of constraint release (CR) and regeneration of entanglements is also studied and found to have little effect on the chain statistics up to the formation of the kinked state. The resulting hybrid model provides a fast, simple, simulation method to study the response of high molecular weight ( M w > 1   Mkg / mol ) polymers in fast flows ( W i R ≫ 1 ), where conventional simulation techniques are less applicable due to computational cost. 

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5. A deterministic–particle–based scheme for micro-macro viscoelastic flows

   https://doi.org/10.1016/j.jcp.2024.113589  

   Bao, Xuelian; Liu, Chun; Wang, Yiwei (November 2024, Journal of Computational Physics)

   In this article, we introduce a new method for discretizing micro-macro models of dilute polymeric fluids by integrating a finite element method (FEM) discretization for the macroscopic fluid dynamics equation with a deterministic variational particle scheme for the microscopic Fokker-Planck equation. To address challenges arising from micro-macro coupling, we employ a discrete energetic variational approach to derive a coarse-grained micro-macro model with a particle approximation first and then develop a particle-FEM discretization for the coarse-grained model. The accuracy of the proposed method is evaluated for a Hookean dumbbell model in a Couette flow by comparing the computed velocity field with existing analytical solutions. We also use our method to study nonlinear FENE dumbbell models in different scenarios, such as extensional flow, pure shear flow, and lid-driven cavity flow. Numerical examples demonstrate that the proposed deterministic particle approach can accurately capture the various key rheological phenomena in the original FENE model, including hysteresis and δ-function-like spike behavior in extensional flows, velocity overshoot phenomenon in pure shear flows, symmetries breaking, vortex center shifting, and vortices weakening in lid-driven cavity flows, with a small number of particles. 

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