  Mixing between two different miscible fluids with a mutual interface must be
initiated by fluid transporting across this fluid interface, caused for example
by applying an unsteady velocity agitation. In general, there is no necessity
for this physical flow barrier between the fluids to be associated with
extremal or exponential attraction as might be revealed by applying Lagrangian
coherent structures, finite-time Lyapunov exponents or other methods on the
fluid velocity. It is shown that streaklines are key to understanding the
breaking of the interface under velocity agitations, and a theory for locating
the relevant streaklines is presented. Simulations of streaklines in a
cross-channel mixer and a perturbed Kirchhoff's elliptic vortex are
quantitatively compared to the theoretical results. A methodology for
quantifying the unsteady advective transport between the two fluids using
streaklines is presented.
