SynopsisSpatially inhomogeneous shear flow occurs in entangled polymer solutions, both as steady state shear banding and transiently after a large step strain or during startup to a steady uniform shear rate. Theoretically, steady state shear banding is a hallmark of models with a nonmonotonic constitutive relation between total shear stress and applied shear rate, but transient banding is sometimes seen in fluids that do not shear band at steady state. We model this behavior using the diffusive Rolie-Poly model in a Newtonian solvent, whose steady state constitutive behavior can be monotonic or nonmonotonic depending on the degree of convective constraint release. We study monotonic steady state constitutive behavior. Linear stability analysis of the startup to a sufficiently high shear rate shows that spatial fluctuations are unstable at early times. There is a strong correlation between this instability and the negative slope of the (time dependent) constitutive curve. If the time integral of the most unstable eigenvalue is sufficiently large, then the system exhibits transient shear bands that later vanish in steady state. We show how perturbations, due to fluctuations or the inhomogeneous stresses, can trigger this instability. This transient behavior is similar to recent observations in entangled polymer solutions. V C 2011 The Society of Rheology.

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We present a fully nonlinear model of the elasticity smectic-A elastomers, and compare our results with a wide range of experimental observations: extreme Poisson ratios, the in-plane modulus, the modulus before and after threshold to layer rotation in response to stretches along the layer normal, the threshold strain, the characteristic, and singular rotation of layers after the threshold. We calculate the x-ray scattering from rotating layers and compare with available data. The model is derived in two ways: from geometrical constraints imposed by layers on a nematic elastomer, and from application of statistical mechanics to a microscopic model of the effect of crosslink points confined in a corrugated potential.

Adams and Olmsted Reply: Wang [1] makes the following points about our Letter [2]: (1) He infers that, ''contrary to its title, shear banding [in [2]] emerged from monotonic curves only if there was a stress gradient,'' and he points out that nonquiescent relaxation was found (experimentally) after step strain in geometries without a stress gradient [3]. (2) He disagrees with the values of the parameters we used. (3) In some recent experiments the flow was homogeneous after cessation of step strain, and only subsequently developed nonquiescent macroscopic motion [3]. We only showed step strains that developed an inhomogeneity before cessation of flow, as in [4].(1) As our title stated [2], we showed that a fluid with a monotonic constitutive curve based on Doi-Edwards (DE) theory can have signatures similar to shear banding. These signatures arise from a stress gradient (e.g., the bowed steady state velocity profile obtained in the stress gradient of a cone and plate rheometer [5] or transient bandinglike profiles during startup). Flat geometries can have transient bandinglike signatures: e.g., two clearly defined bands of shear rates during large amplitude oscillatory shear (LAOS) [2,6], or inhomogeneous bandinglike transients during startup flows in the presence of inhomogeneous spatial fluctuations (noise) (Fig. 1) [2].(2) Our parameters were matched to experiment, for a nonlinear model in which the parameters d and R roughly correspond to their rigorously defined counterparts in linear rheology. Because we use (the best available) crude nonlinear theory, the parameters do not correspond precisely. We used ¼ =ðG d Þ ' 10 À5 based on a plateau modulus G ' 3 kPa, reptation time d ' 20 s, and solvent viscosity ' 1 Pa s [7]. Although d = R $ 10 3 implies too many entanglements, it fits the nonlinear constitutive behavior of the experiments well [5]. This inconsistency is an unsatisfactory feature of current theory.(3) The step strain results in [2] should be compared with [4] (Fig. 5), where the velocity profile became inhomogeneous before cessation. Figure 2 shows a calculation in which inhomogeneities develop only after cessation of flow, during a strong recoil. This is for startup in a flat geometry with noisy initial conditions, and resembles [4] (Fig. 3) if there were no experimental wall slip.Wang's newest experiments show dramatic rupture and internal fracture, despite a homogeneous velocity before cessation [3] (similar fracture planes could be interpreted in [8], Fig. 3(f), but in a cone-and-plate geometry; moreover, those data are also consistent with wall slip and simple recoil). Our calculations (Fig. 2) go some way towards modeling this phenomenon, but do not capture the rupture, and have not yet been adequately modified to incorporate slip. It remains a strong challenge to distinguish which experimental features are captured by tube models, and which (e.g., rupture) require new physical insight. One suggestion is the ''elastic yielding'' in [1] which may be similar to modifying the DE model to incor...

We investigate the soft elastic modes of smectic elastomers, that is shape change without energy cost. We use a microscopic model for their nonlinear elasticity, similar to those used for nematic elastomers. We consider two different phases of smectic elastomer; the biaxial smectic A for a simple illustration, and smectic C phases which are of great practical significance. We show that only one nontrivial trajectory of the director gives soft deformations. We give a geometrical interpretation of this soft elastic mode and give an explicit example.