Material barriers to diffusive and stochastic transport

Area of Science:

• Fluid dynamics
• Transport phenomena
• Surface science

Background:

• Understanding diffusive tracer transport in unsteady flows is crucial for various scientific and engineering applications.
• Identifying surfaces that control transport (barriers and enhancers) is a key challenge.

Purpose of the Study:

• To identify and characterize material surfaces that act as transport barriers or enhancers in general, unsteady fluid flow.
• To develop a universal framework for detecting these transport-controlling surfaces.

Main Methods:

• Formulated a universal, nondimensional transport functional to identify extremizing surfaces.
• Computed the leading-order term of the functional from flow velocity.
• Defined objective transport tensors to explicitly compute uniform transport extremizers as null surfaces.

Main Results:

• Identified surfaces that minimize (barriers) or maximize (enhancers) diffusive tracer transport.
• Demonstrated that these surfaces are extremizers of a universal transport functional.
• Showed that these surfaces differ from previously known coherent structures, even in the vanishing diffusivity limit.
• Extended the methodology to stochastic velocity fields, enabling detection under uncertainty.

Conclusions:

• The study provides a robust method for identifying transport barriers and enhancers in complex fluid flows.
• The findings are applicable to both deterministic and stochastic velocity fields, enhancing their practical utility.
• This work offers new insights into controlling transport phenomena at material surfaces.