Search

We report on shear startup data for two wormlike micellar solutions, differing only in concentration and type of two binding aromatic sodium salts. The surfactant molecule is cetylpiridinium chloride at a fixed concentration (100 mM). Sodium salicylate (NaSal) and diclofenac sodium (Diclo) are used as binding salts at concentrations 68 mM NaSal and 52 mM Diclo such that both systems are fully entangled and their linear viscoelastic response is essentially identical. Both systems show the linear response typical of a wormlike micellar solution, with terminal behavior at low frequencies, a well-defined moduli crossover, and a plateau modulus. In the nonlinear regime, however, the behavior of the two systems is totally different, suggesting that the molecular structure difference of the salts and their binding activity to the surfactant molecule are both crucial to determine the fast flow behavior. The NaSal solution shows a very complex rheological response, with strain hardening and very sharp stress peaks, whereas the solution containing Diclo behaves much like ordinary linear polymers, exhibiting pronounced overshoots as well as moderate undershoots in the transient shear viscosity, before approaching the steady state. This polymerlike behavior has also been proved by successfully comparing data with predictions of a constitutive equation recently adopted for both entangled polymers and linear wormlike micelles. As far as NaSal is concerned, a phenomenological model based on rubber network theory is developed, which describes the flow singularities. A physical interpretation of the different behavior in the nonlinear regime is also suggested.

We here extend to integral constitutive equations of the Doi–Edwards type the analysis of shear banding instabilities during shear startup recently performed by Moorcroft and Fielding [J. Rheol. 58, 103–147 (2014)]. Shear banding is the instability encountered in simple shear flows, whereby different shear rates coexist along the sample thickness, so that the velocity profile departs from the usually assumed linear profile. Results of both linear and nonlinear stability analysis mostly confirm those obtained by Moorcroft and Fielding [J. Rheol. 58, 103–147 (2014)] with the Rolie–Poly equation [Likhtman, A. E., and R. S. Graham, J. Non-Newtonian Fluid Mechan. 114, 1–12 (2003)] (which is an approximate differential counterpart of the Doi–Edwards integral one “[The Theory of Polymer Dynamics (Clarendon, Oxford, 1986)]”), but some significant differences are also found. Features that coincide with those predicted by the Rolie–Poly equation include: (i) For the nonmonotonic flow curve of the original Doi–Edwar...

In the classical theory of Doi and Edwards for entangled polymers the strain measure Q arises from the assumption of affine deformation of the tube segments. On the other hand, we have recently argued [G. Marrucci, F. Greco, and G. Ianniruberto, “Possible role of force balance on entanglements,” Macromol. Symp. (in press)] that force balance on the nodes of the entangled network generates departures from affinity. An ad hoc “lattice” model of the network was then proposed to fulfill force balance automatically, at least for single-step deformations. The corresponding strain measure is linked to the square root of the Finger tensor, and is therefore easy to use. Predictions obtained with the new strain measure are here compared with a variety of step strain data.

The two‐dimensional model previously considered is here used to obtain predictions in the complex situation of the tumbling regime which prevails at low shear rates. Although each domain is permanently in a time‐dependent, periodic regime, the macroscopic response can be stationary in time because of the well‐known polydomain structure. First, the average steady rheological response for this situation is calculated by taking a polydomain structure which neglects interdomain interactions. Although the steady state predictions thus obtained favorably compare with the experimental results throughout the range of shear rates, the transient start‐up responses do not, because of the crucial role played by the interactions in such a case. These interactions, due to Frank elasticity, are then introduced in the model in the simplest possible way, i.e., by use of a mean field potential. Under this assumption, also the predictions of transient behavior in the tumbling regime show the correct qualitative features.

The two‐dimensional model introduced in a previous paper to describe the nematic phase of rodlike polymers is used to obtain predictions of transient rheological response at high shear rates. First, the transient behavior of a single domain is considered. It is found that, between the tumbling and nontumbling regimes, an intermediate range of shear rates exists where the director continuously oscillates between two orientations close to the shear direction, a result independently obtained in a recent work by Larson, who has considered the full three‐dimensional case. Polydomain structure, typical of polymeric liquid crystals, is then considered. In this paper, results for this case are given for the nontumbling regime only, whereas the tumbling and oscillating regimes are considered in the next paper.

The molecular model used by Doi and Edwards in developing their rheological theory admits a simple form for the free energy of deformation, at least when the independent alignment approximation is used. A general expression is derived, as well as the specific form which applies to an instantaneous shear deformation. The latter is used to analyze the possibility that instabilities, or “deformational phase separations,” arise in the course of stress relaxation experiments. The results of the analysis are compared with recent experimental results by Osaki and Kurata and by Vrentas and Graessley which show an anomalous relaxation behavior.