Energy constrained transport maximization across a fluid interface.

With enhancing mixing in micro- or nanofluidic applications in mind, the problem of maximizing fluid transport across a fluid interface subject to an available energy budget is examined. The optimum cross-interface perturbing velocity is obtained explicitly in the time-periodic instance using an Euler-Lagrange constrained optimization approach. Numerical investigations which calculate transferred lobe areas and cross-interface flux are used to verify that the predicted strategy achieves optimum transport.

Topology of chaotic mixing patterns.

A stirring device consisting of a periodic motion of rods induces a mapping of the fluid domain to itself, which can be regarded as a homeomorphism of a punctured surface. Having the rods undergo a topologically complex motion guarantees at least a minimal amount of stretching of material lines, which is important for chaotic mixing. We use topological considerations to describe the nature of the injection of unmixed material into a central mixing region, which takes place at injection cusps.

Topology, braids and mixing in fluids.

Stirring of fluid with moving rods is necessary in many practical applications to achieve homogeneity. These rods are topological obstacles that force stretching of fluid elements. The resulting stretching and folding is commonly observed as filaments and striations, and is a precursor to mixing.

Topological mixing with ghost rods.

Topological chaos relies on the periodic motion of obstacles in a two-dimensional flow in order to form nontrivial braids. This motion generates exponential stretching of material lines, and hence efficient mixing. Boyland, Aref, and Stremler [J.