We report on the linear and nonlinear rheology of surfactant solutions
of elongated wormlike micelles. The surfactant solutions placed under
scrutiny are made of cetylpyridinium chloride (CP+, Cl-) and sodium s
alicylate (Na+, Sal-) diluted in 0.5 M NaCl-brine. Both semidilute and
concentrated regimes of entangled micelles were investigated. Rheolog
ical experiments were performed at ambient temperature (T = 25-degrees
-C) for surfactant concentrations phi = 1 %-30 %. When submitted to a
steady shear high enough (for shear rate gamma typically higher than 1
-10 s-1) the solutions of wormlike micelles exhibit a first-order isot
ropic-to-nematic transition for all surfactant concentrations phi grea
ter-than-or-equal-to 6 %. The transition is characterized by a true pl
ateau in the shear rate dependence of the shear stress sigma (gamma).
For gamma above the transition rate gamma(I/N), sigma remains constant
at sigma(I/N). In the concentrated regime, the transition is clearly
first-order. However, the first-order character weakens upon increasin
g dilution, suggesting that at some critical concentration phi(c) it b
ecomes second-order. Below phi(c), the transition ceases to occur : th
e sigma(gamma)-behavior rather indicates a progressive and homogeneous
orientation of the micelles throughout the sample. Moreover, in the t
wo-phase domain (where both isotropic and nematic phases coexist) a ch
aracteristic transient behavior of the shear stress sigma(t) measured
at constant gamma > gamma(I/N) as a function of time has been observed
and investigated in detail. In agreement with the picture of the firs
t-order phase transition (in the domain of metastability), the transie
nt behavior could be interpreted quantitatively in terms of nucleation
and one-dimensional growth process. These results are finally compare
d to recent predictions by Spenley, Cates and MacLeish (Ref. [7]) who
described the nonlinear rheology of wormlike micelles in terms of mech
anical instability of shear-banding type.