A study of shear banding in polymer solutions

Abstract

In a recent letter [M. Cromer, M. C. Villet, G. H. Fredrickson, and L. G. Leal, “Shear banding in polymer solutions,” Phys. Fluids 25, 051703 (2013)], we showed the existence of a steady shear-banded velocity profile for a model polymer solution with an underlying monotonic constitutive curve. The driving mechanism is the coupling of the polymer stress to an inhomogeneous concentration profile. To further understand this phenomenon, in this paper we investigate the underlying linear instability as well as probe the model parameters and their effect on transient and steady state solutions. The linear stability analysis of the steady, base homogeneous model shows that, in opposition to diffusion, the polymer concentration moves up stress gradients in a shear flow creating a critical balance such that, for a range of parameters, an instability occurs that drives the system away from homogeneity. The simulation of the full nonlinear equations in planar one-dimensional shear reveals a window within which the linear instability manifests itself as a shear-banded flow. Unlike the case for a nonmonotonic constitutive curve for which two bands are predicted, there is no apparent selection process for a monotonic curve that sets the number of bands in planar shear. Thus, we find the possibility of greater than two bands, the number of which is determined by the ratio of the polymer correlation length to the channel width. In addition to steady shear banding, transient phenomena are also probed revealing a complicated band transition (i.e., number of bands changing in time) as well as elastic recoil in a Taylor-Couette cell, each of which have been observed in experiment. Finally, as we showed in our letter, a nonlinear subcritical instability exists resulting in multiple steady states depending upon the wall ramp speed. Here, we show that this phenomenon can occur for realistic parameter values, in particular those obtained for a particular polymer solution that has shown this multiple steady state behavior experimentally.

Triggers and signatures of shear banding in steady and time-dependent flows

“…This was first explored in the context of polymeric fluids [53][54][55]. It has recently been studied again in polymers [56,57], and also applied to yield stress colloidal fluids [58,59]. The signature of concentration coupling in the steady state composite flow curve is an upward slope in the "plateau" of the banding regime.…”

Viscoelasticity and nonlinear simple shear flow behavior of an entangled asymmetric exact comb polymer solution

“…(i) Polymers are known to be problematic in strong, nonlinear flows in the sense that they have the tendency to display instabilities, i.e., not deform homogeneously [5]. Instabilities in flowing polymers are receiving more and more attention in recent years [6][7][8][9][10]. Controversies between the experimental findings of different groups have in fact been reported [7,10].…”

“…It has been shown that the effects of slight differences between the flow fields due to, e.g., alignment issues of the flow geometries play a key role for the occurrence of instabilities [7] and this could potentially explain the discrepancies between different studies. The issue remains however open and the current lack of understanding of the experimental conditions for homogeneous flow or shear banding [6][7][8][9][10] leave the issue of experimental and theoretical analysis of polymeric response in strong nonlinear flows wide open [8,9,11]. (ii) The syntheses of model polymers are mainly performed by anionic polymerization high-vacuum techniques resulting in well-defined molecular structures, which however come in very small quantities (typically <1 g) [12][13][14].…”

Yield stress and onset of nonlinear time-dependent rheological behaviour of gellan fluid gels

“…From the aforementioned results we can deduce that the rheological response at nominal 2.25 Pa was consistent with a practical yield stress since some results supported that the fluid gel studied was hardly able to flow, while others showed a marked shear rate. This unstable response may be associated with the onset of very shear thinning behaviour when fluid gels are under yield stress and is also indicative of the occurrence of shear banding (also termed shear localization) (Möller et al, 2006), which is favoured by the lack of concentration homogeneity (Cromer et al, 2014). This is relevant for gellan fluid gels on account of their heterogeneous microstructure.…”