  Under conditions of sufficiently slow flow, foams, colloids, granular matter,
and various pastes have been observed to exhibit shear localization, i.e.
regions of flow coexisting with regions of solid-like behavior. The details of
such shear localization can vary depending on the system being studied. A
number of the systems of interest are confined so as to be quasi-two
dimensional, and an important issue in these systems is the role of the
confining boundaries. For foams, three basic systems have been studied with
very different boundary conditions: Hele-Shaw cells (bubbles confined between
two solid plates); bubble rafts (a single layer of bubbles freely floating on a
surface of water); and confined bubble rafts (bubbles confined between the
surface of water below and a glass plate on top). Often, it is assumed that the
impact of the boundaries is not significant in the ``quasi-static limit'', i.e.
when externally imposed rates of strain are sufficiently smaller than internal
kinematic relaxation times. In this paper, we directly test this assumption for
rates of strain ranging from $10^{-3}$ to $10^{-2} {\rm s^{-1}}$. This
corresponds to the quoted quasi-static limit in a number of previous
experiments. It is found that the top plate dramatically alters both the
velocity profile and the distribution of nonlinear rearrangements, even at
these slow rates of strain.
