Shear banding transition

Shear Banding Transition in Semidilute and Concentrated Giant Micelles. 

In the following, we review the phenomenology of shear banding flow in semldi-lute and concentrated wormlike micelles. This part is organized as follows. In Sect. 3.2, we describe the mechanical signature of the shear-banding transition. Section 3.3 is devoted to the characterization of the local flow field, while in Sect. 3.4, we focus on the structural properties of the banded state. 

During the past decade, many authors have paid close attention to the evolution of the shear stress as a function of time in systems exhibiting a stress plateau. The aim was to identify the mechanisms responsible for the shear-banding transition. In most cases, shear stress time series in response to steady shear rate consists of a slow transient (compared to the relaxation time of the system) before reaching steady state. Nonetheless, more complex fluctuating behaviors such as erratic oscillations suggestive of chaos or periodic sustained oscillations of large amplitude have been observed in peculiar systems. 

This scenario was originally interpreted as evidence of the shear-banding transition, the states of low and high shear rates being deduced from the molecular... 

Berret IF (2005) Rheology of wormUke micelles equilibrium properties and shear-banding transition. In Molecular gels, Elsevier, Dordrecht... 

Fuller G (1995) Rheology of wormbke micelles equilibrium properties and shear-banding transition In Optical rheometry of complex fluids, Oxford University Press, New York... 

Dhont JKG (1999) A constitutive relation describing the shear-banding transition. Phys Rev E 60(4) 4534-4544... 

Berret J-F (2004) Rheology of womdike micelles equdibrium properties and shear-banding transitions. In Weiss RG, Terech P (eds), Molecular gels. Materials with self-assembled fibrillar networks, pp. 667-720... 

One characteristic of shear banded flow is the presence of fluctuations in the flow field. Such fluctuations also occur in some glassy colloidal materials at colloid volume fractions close to the glass transition. One such system is the soft gel formed by crowded monodisperse multiarm (122) star 1,4-polybutadienes in decane. Using NMR velocimetry Holmes et al. [23] found evidence for fluctuations in the flow behavior across the gap of a wide gap concentric cylindrical Couette device, in association with a degree of apparent slip at the inner wall. The timescale of these fluctuations appeared to be rapid (with respect to the measurement time per shear rate in the flow curve), in the order of tens to hundreds of milliseconds. As a result, the velocity distributions, measured at different points across the cell, exhibited bimodal behavior, as apparent in Figure 2.8.13. These workers interpreted their data... 

M. M. Britton, R. W. Mair, R. K. Lambert, P.T. Callaghan 1999, (Transition to shear banding in pipe and Couette flow of wormlike micellar solutions), /. Rheol. 43, 897. 

Finally, when the testing temperature is near the glass transition temperature, a broad shear zone instead of discrete coarse shear bands develops at an angle of 45° to the direction of the external stress (Fig. 29 b). Inside this zone the spherulites are homogeneously deformed in direction to the main shear stress. It is expected that... 

The conditions under which a particular deformation mode (coarse shear banding or deformation in a diffuse shear zone) predominantes seem to depend mainly on the ambient temperature, T, as compared to the glass transition temperature, T, of the material. This hypothesis can be deduced from a diagram of shear modulus G vs. ratio T/T for the tested polymers (Fig. 32). The amorphous PS as well as the semi-crystalline polymers PP and PB-1 exhibit a tendency to formation of coarse shear bands when the ratio of T/T is distinctly smaller than 0.75. There exists a... 

Fig. 14. Optical micrograph of a thinned section showing the fracture subsurface. One half of the shear band pairs can be seen along the initial fracture subsurface (top left) and the transition to shear fracture at 45° to the craze plane can be seen (rigJjt)...

In PEI the DCG process, as in any polymer, is active. The epsilon CTPZ, however, was not observed. No plane strain shear bands have yet been observed. Some form of localized crack tip shear process can be activated, however, as evidenced by the inversion transition that occured at higher stresses (at the higher temperatures). The fracture surface did not show fracture to occur on a slanted 45 degree plane. The fracture plane was still normal to the leading direction. The fracture surface, however, was not smooth, as seen with craze fracture, but has a definite roughened texture which is associated with active localized shearing. This texture is often described as honeycomb or tufted. 

Several authors have given a basic theory for the prediction of the modulus of a composite (16-18). The line In Fig, 4 shows the theoretical curve for the reduction of the modulus (E/Eo) due to Incorporation of a soft rubber phase In a hard matrix at a temperature above the transition region of the soft phase and below the transition region of the hard phase (E > flexural modulus of the modified nylon and E0 flexural modulus of the unmodified nylon). The experimental points of systems 1 and 2 fit fairly well onto the theoretical curve. This proves that they are well-dispersed systems without Inclusions. The difference In Impact strength between system 1 and system 2 Is mainly due to the better lnterfaclal adhesion of system 2, by which crazes are stabilized and/or the formation of small shear bands Is Initiated. 

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