Adams and Olmsted Reply:

Abstract

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...

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

“…At these high shear rates the number of entanglements is essentially zero, and the only remaining interaction forces are due to the "effective potential" W given in Eq. (24). This potential consists of two contributions: the potential V due to core-core interactions and a contribution that is related to the number of entanglements in equilibrium.…”

“…Note that tubemodel theories can account for the fast flow-induced disentanglement leading to shear thinning (the so-called convected constraint release) 23 and associated shear banding. 24 In fact, a rather refined analysis of the shear-rate dependence of the release of entanglement constraints is now available based on these ideas, 25,26 although this issue is currently much under debate.…”

Criteria for Shear Banding in Time-Dependent Flows of Complex Fluids

“…However most practical flows involve a strong time-dependence, whether perpetually or during a startup process in which a steady flow is established from an initial rest-state. Data in polymers [8][9][10][11][12][13][14][15], surfactants [16][17][18], soft glasses [19][20][21][22], and simulations [23][24][25][26][27][28][29][30] reveals that shear bands often also arise during these time-dependent flows, and can be sufficiently long lived to represent the ultimate flow response of the material for practical purposes, even if the constitutive curve is monotonic, dΣ/dγ > 0.In view of these widespread observations, crucially lacking is any known criterion for the onset of banding in time-dependent flows. This Letter provides such criteria, with the same fluid-universal status as the criterion given above in steady state: independent of the internal constitutive properties of the particular fluid in question, and depending only on the shape of the experimentally measured rheological response function.…”

Charge separation measurements in Pb–Pb collisions at LHC energies

“…In addition, the inclusion of the measured elliptic flow, does not alter either the strength or the sign of the correlations. Figure. 2 presents the comparison of the centrality dependence of the integrated 3-(left plot) and 2-particle (right plot) correlators measured by ALICE in Pb-Pb collisions at √ s NN = 2.76 TeV (red circles) and by STAR in Au-Au collisions at √ s NN = 0.2 TeV (green stars) [9].…”