Inhomogeneous shear flows of wormlike micelles:mA master dynamic phase diagram

Abstract

We report on the nonlinear mechanical response of surfactant wormlike micelles subjected to steady shear flow. The system placed under scrutiny is made of cetylpyridinium chloride, sodium salicylate, and salted water at 0.5M NaCl (abbreviated as CPCl-Sal). We have investigated solutions in the intermediate concentration ranges, at \ensuremath{\varphi}=6%, 8% and \ensuremath{\varphi}=12% for temperatures ranging between 20 \ifmmode^\circ\else\textdegree\fi{}C and 50 \ifmmode^\circ\else\textdegree\fi{}C. In these T and \ensuremath{\varphi} ranges, we first confirm that the present system is a true Maxwell fluid. As a consequence, the nonlinear rheology can be formulated in terms of the normalized quantities, \ensuremath{\sigma}=\ensuremath{\sigma}/${\mathrm{G}}_{0}$ and \ensuremath{\gamma}-dot=\ensuremath{\gamma}-dot${\mathrm{\ensuremath{\tau}}}_{\mathrm{R}}$ , where ${\mathrm{G}}_{0}$ is the elastic plateau modulus and ${\mathrm{\ensuremath{\tau}}}_{\mathrm{R}}$ the terminal relaxation time of the Maxwell fluid. Second, we demonstrate that the flow curves of the CPCl-Sal wormlike micelles \ensuremath{\sigma} (\ensuremath{\gamma}-dot) are invariant with respect to relative changes in temperature and concentration. This enables us to define superimposition procedures between flow curves obtained at different temperatures and concentrations and to derive the so-called 'master dynamic phase diagram' of the CPCl-Sal wormlike micelles. One crucial feature of this master phase diagram is the existence of a critical behavior at T=${\mathrm{T}}_{\mathrm{c}}$ . Here, the stress \ensuremath{\sigma} levels off progressively up to a plateau that is reduced to a single flat point of coordinates (\ensuremath{\sigma}=0.9, \ensuremath{\gamma}-dot=3). The low-temperature regime (T${\mathrm{T}}_{\mathrm{c}}$ ) is again identified by a shear stress plateau beginning by a true discontinuity of slope in the \ensuremath{\sigma} (\ensuremath{\gamma}-dot) behavior. At high T (>${\mathrm{T}}_{\mathrm{c}}$ ), \ensuremath{\sigma} increases monotonously at all shear rates. In order to examine the state of shearing at the stress plateau, flow birefringence experiments were undertaken with a rheo-optical device working with polarized light propagating parallel to the vorticity axis of the Couette. In the plateau regime, the flow is clearly inhomogeneous. Within the gap of a cell, two phases of very different birefringence are observed in the steady state of shearing, as well as after cessation of the shearing.