  Materials such as foams, concentrated emulsions, dense suspensions or
colloidal gels, are yield stress fluids. Their steady flow behavior,
characterized by standard rheometric techniques, is usually modeled by a
Herschel-Bulkley law. The emergence of techniques that allow the measurement of
their local flow properties (velocity and volume fraction fields) has led to
observe new complex behaviors. It was shown that many of these materials
exhibit shear banding in a homogeneous shear stress field, which cannot be
accounted for by the standard steady-state constitutive laws of simple yield
stress fluids. In some cases, it was also observed that the velocity fields
under various conditions cannot be modeled with a single constitutive law and
that nonlocal models are needed to describe the flows. Doubt may then be cast
on any macroscopic characterization of such systems, and one may wonder if any
material behaves in some conditions as a Herschel-Bulkley material. In this
paper, we address the question of the existence of a simple yield stress fluid
behavior. We first review experimental results from the literature and we point
out the main factors (physical properties, experimental procedure) at the
origin of flow inhomogeneities and nonlocal effects. It leads us to propose a
well-defined procedure to ensure that steady-state bulk properties of the
materials are studied. We use this procedure to investigate yield stress fluid
flows with MRI techniques. We focus on nonthixotropic dense suspensions of soft
particles (foams, concentrated emulsions, Carbopol gels). We show that, as long
as they are studied in a wide (as compared to the size of the material
mesoscopic elements) gap geometry, these materials behave as 'simple yield
stress fluids': they are homogeneous, they do not exhibit steady-state shear
banding, and their steady flow behavior in simple shear can be modeled by a
local continuous monotonic constitutive equation which accounts for flows in
various conditions and matches the macroscopic response.
