  Amorphous glassy materials of diverse nature -- concentrated emulsions,
granular materials, pastes, molecular glasses -- display complex flow
properties, intermediate between solid and liquid, which are at the root of
their use in many applications. A classical feature, well documented yet not
really understood, is the very non-linear nature of the flow rule relating
stresses and strain rates. Using a microfluidic velocimetry technique, we
characterize the flow of thin layers of concentrated emulsions, confined in
gaps of different thicknesses by surfaces of different roughness. Beyond the
classical non-linearities of the rheological behaviour, we evidence finite size
effects in the flow behaviour and the absence of an intrinsic local flow rule.
In contrast, a rather simple non-local flow rule is shown to account for all
the velocity profiles. This non-locality of the dynamics is quantified by a
length, characteristic of the cooperativity of the flow at these scales, that
is unobservable in the liquid state (lower concentrations) and that increases
with concentration in the jammed state. Beyond its practical importance for
applications involving thin layers, e.g. coatings, our assessment of
non-locality and cooperativity echoes observations on other glassy, jammed and
granular systems, suggesting a possible fundamental universality.
