  Main characteristics of colloidal systems that develop fluid phases with
different mechanical properties, namely shear-banding fluids, are briefly
reviewed both from experimental and theoretical (modelling) point of view. A
non-monotonic shear stress vs. shear rate constitutive relation is presented.
This relation derives from a phenomenological model of a shear ratedependent
viscosity describing structural changes and involves the possibility of
multivalued shear rates under a given shear stress. In the case of a
stress-dependent viscosity, the same model allows one to predict vorticity
banding. Predictions of this model under controlled stress are discussed,
namely occurrence of a kind of top- and bottom-jumping of the shear rate in
response to stress increasing-decreasing. Applying this model to evaluation of
the flow curve of such colloidal systems is performed. Particular emphasis is
placed on the adequate computation of the shear rate function in cylindrical
Couette cells in order to handle the corresponding flow curve which exhibits
the well-known shear stress plateau. Indeed, as different fluid phases coexist
in the flow domain, measured (torque vs. angular velocity) data cannot be
directly converted into rheometric (shear stress vs. shear rate) functions. As
the lacking non-local terms in the model prevents the direct determination of
the stress-plateau, this value is included as an adjustable parameter. Thus
model predictions satisfactorily match up experimental data of wormlike
micellar solutions from the literature.
