  The role of surface tension gradients in the apparent viscosity of liquid
foams remains largely unexplained. In this article, we develop a toy-model
based on a periodic array of 2D hexagonal bubbles, each bubble being separated
from its neighbors by a liquid film of uniform thickness. The two interfaces of
this thin liquid film are allowed to slide relatively to each other, thus
shearing the liquid phase in between. We solve the dynamics under external
shear of this minimal system and we show that the continuity of the surface
tension around the whole bubble is the relevant condition to determine the
bubble rotation rate and the energy dissipation. This result is expected to be
robust in more complex situations and illustrates that thin film dynamics
should be solve at the scale of the whole bubble interface when interface
rheology matters.
