  We perform micro-rheological experiments with a colloidal bead driven through
a viscoelastic worm-like micellar fluid and observe two distinctive shear
thinning regimes, each of them displaying a Newtonian-like plateau. The shear
thinning behavior at larger velocities is in qualitative agreement with
macroscopic rheological experiments. The second process, observed at
Weissenberg numbers as small as a few percent, appears to have no analog in
macro rheological findings. A simple model introduced earlier captures the
observed behavior, and implies that the two shear thinning processes correspond
to two different length scales in the fluid. This model also reproduces
oscillations which have been observed in this system previously. While the
system under macro-shear seems to be near equilibrium for shear rates in the
regime of the intermediate Newtonian-like plateau, the one under micro-shear is
thus still far from it. The analysis suggests the existence of a length scale
of a few micrometres, the nature of which remains elusive.
