  We report on the decay of a passive scalar in chaotic mixing protocols where
the wall of the vessel is rotated, or a net drift of fluid elements near the
wall is induced at each period. As a result the fluid domain is divided into a
central isolated chaotic region and a peripheral regular region. Scalar
patterns obtained in experiments and simulations converge to a strange
eigenmode and follow an exponential decay. This contrasts with previous
experiments [Gouillart et al., Phys. Rev. Lett. 99, 114501 (2007)] with a
chaotic region spanning the whole domain, where fixed walls constrained mixing
to follow a slower algebraic decay. Using a linear analysis of the flow close
to the wall, as well as numerical simulations of Lagrangian trajectories, we
study the influence of the rotation velocity of the wall on the size of the
chaotic region, the approach to its bounding separatrix, and the decay rate of
the scalar.
