Modeling the inhomogeneous response and formation of shear bands in steady and transient flows of entangled liquids

Abstract

We simulate the spatial and temporal evolution of inhomogeneous flow fields in viscometric devices such as cylindrical Couette cells. The computations focus on a class of two species elastic network models which are prototypes for a model which can capture, in a self-consistent manner, the creation and destruction of elastically-active network segments as well as diffusive coupling between the microstructural conformations and the local state of stress in regions with large spatial gradients of local deformation. For each of these models, the 'flow curve' of stress and apparent shear rate resulting from an assumption of homogeneous deformation is non-monotonic and linear stability analysis shows that the region of non-monotonic response is unstable. Steady-state calculations of the full inhomogeneous flow field lead to localized shear bands that grow linearly in extent across the gap as the apparent shear rate is incremented. Time-dependent calculations in step strain experiments and in start up of steady shear flow show that the velocity profile in the gap and the total stress measured at the bounding surfaces are coupled and evolve in a complex non-monotonic manner as the shear bands develop. These spatio-temporal dynamics are consistent with time-resolved particle imaging velocimetry measurements in both concentrated solutions of monodisperse entangled polymers and in wormlike micellar solutions. The computational results have a number of implications for experimental observations of 'apparent' or 'gap-averaged' quantities in nearly-viscometric devices, and lead to plateaus or 'yield-like' transitions in the steady flow curve and deviations from the Lodge-Meissner relation in non-ideal step shearing deformations.

Probing shear-banding transitions of the VCM model for entangled wormlike micellar solutions using large amplitude oscillatory shear (LAOS) deformations

“…When the wall stops moving and changes direction, during this short period of relaxation there is a stored elastic stress in the fluid which leads to a brief local flow reversal of the shear band. A similar viscoelastic recoil in the local fluid velocity is observed in both experiments and simulations of the start-up of steady shear flow [19]. Both models exhibit a range of times over which the kink velocity is out of phase with the wall forcing, but the range is more confined, and the effect is sharper and more pronounced in the VCM model than in the PEC model.…”

“…These models are self-consistently derived from kinetic network theory and accurately capture the coupling between the local microstructural conformation and the resulting macroscopic stress response [16,19]. This family of models, referred to as VCM for brevity, captures individual contributions to the total viscoelastic stress arising from long entangled chains (species 'A') and from a shorter, unentangled 'B' species.…”

“…Some candidate EoS, the Johnson-Segalman model for example, exhibit nonphysical responses in rapidly-varying deformations [18]; other models do not exhibit proper linear viscoelastic behavior in the limit of small deformations. The VCM class of models [16] do predict appropriate behavior in shear, step strain and also in extensional flows [19] [20].…”

Shear banding in large amplitude oscillatory shear (LAOStrain and LAOStress) of polymers and wormlike micelles

“…An early exception can be found in [71,72], which studied a model of wormlike micellar surfactants with a nonmonotonic constitutive curve in LAOStrain. Another exception is in the paper of Adams and Olmsted [73], which recognized that shear banding can arise even in the absence of any nonmonotonicity in the underlying constitutive curve.…”

Spatially resolved quantitative rheo-optics of complex fluids in a microfluidic device

“…This phenomenon is known as shear-banding and has formed the basis of many macroscopic rheological studies, as well as theoretical and modeling work by [Fielding (2007); Lu et al (2000); Vasquez et al (2007); Zhou et al (2008)]. …”