Gradient and vorticity banding

Abstract

"Banded structures" of macroscopic dimensions can be induced by simple shear flow in many different types of soft matter systems. Depending on whether these bands extend along the gradient or vorticity direction, the banding transition is referred to as "gradient banding" or "vorticity banding," respectively. The main features of gradient banding can be understood on the basis of a relatively simple constitutive equation. This minimal model for gradient banding will be discussed in some detail, and its predictions are shown to explain many of the experimentally observed features. The minimal model assumes a decrease of the shear stress of the homogeneously sheared system with increasing shear rate within a certain shear-rate interval. The possible microscopic origin of the severe shear-thinning behaviour that is necessary for the resulting nonmonotonic flow curves is discussed for a few particular systems. Deviations between experimental observations and predictions by the minimal model are due to obvious simplifications within the scope of the minimal model. The most serious simplifications are the neglect of concentration dependence of the shear stress (or on other degrees of freedom) and of the elastic contributions to the stress, normal stresses, and the possibility of shear-induced phase transitions. The consequences of coupling of stress and concentration will be analyzed in some detail. In contrast to predictions of the minimal model, when coupling to concentration is important, a flow instability can occur that does not require strong shear thinning. Gradient banding is sometimes also observed in glassy-and gel-like systems, as well as in shear-thickening systems. Possible mechanisms that could be at the origin of gradient-band formation in such systems are discussed. Gradient banding can also occur in strongly entangled polymeric systems. Banding in these systems is discussed on the basis of computer simulations. Vorticity banding is less well understood and less extensively investigated experimentally as compared to gradient banding. Possible scenarios that are at the origin of vorticity banding will be discussed. Among other systems, the observed vorticity-banding transition in rod-like col-loids is discussed in some detail. It is argued, on the basis of experimental observations for these colloidal systems, that the vorticity-banding instability for such colloidal suspensions is probably related to an elastic instability, reminiscent of the Weissenberg effect in polymeric systems. This mechanism might explain vorticity banding in discon-tinuously shear-thickening systems and could be at work in other vorticity-banding systems as well. This overview does not include time-dependent phenomena like oscillations and chaotic behaviour.

Interplay between elastic instabilities and shear-banding: three categories of Taylor–Couette flows and beyond

“…6). This fact calls for a re-evaluation of experimental situations where the so-called 'vorticity banding' was observed [88][89][90][91][92][93]. Note moreover that the 'non-monotonic shear-thickening flow curve' underlying vorticity banding could be simply due to the emergence of secondary flows responsible for the increased resistance to flow.…”

Constitutive equations for the flow behavior of entangled polymeric systems: Application to star polymers

“…It appears that the entanglements of polymeric chains are at the origin of the strong shear thinning behavior, which is necessary for gradient banding. 1 On the other hand, in recent experimental work with entangled synthetic polymers shear banding was not observed, but instead interfacial slip was suggested as the origin of strain loss. 10,11 Gradient banding has also been found in glassy starlike polymers.…”

“…This is due to advances in theoretical understanding as well as experimental instrumentation. [1][2][3][4] In particular, a number of experimental studies of polymeric systems have revealed the occurrence of shear banding along the gradient direction in such systems. For example, experiments on entangled DNA solutions 5,6 and solutions of synthetic polymers [7][8][9] show pronounced gradientbanding velocity profiles.…”

Helicopter rotation and smectic-isotropic coexistence of strongly attractive rods

“…As a consequence, this helicopter rotation might be expected as well for colloidal rods systems in the proximity of a wall. It can also be speculated that for confined dense systems, clusters of rods undergoing helicopter oscillations close to a wall would separate from each other in regions perpendicular to the wall, which could be related to the still unclear phenomena of vorticity-band formation [23].…”