  We seek transport barriers and transport enhancers as material surfaces
across which the transport of diffusive tracers is minimal or maximal in a
general, unsteady flow. We find that such surfaces are extremizers of a
universal, non-dimensional transport functional whose leading-order term in the
diffusivity can be computed directly from the flow velocity. The most
observable (uniform) transport extremizers are explicitly computable as
null-surfaces of an objective transport tensor. Even in the limit of vanishing
diffusivity, these surfaces differ from all previously identified coherent
structures for purely advective fluid transport. Our results extend directly to
stochastic velocity fields and hence enable transport barrier and enhancer
detection under uncertainties.
