aminar flow systems are at the center of numerous advances in medical, biological, chemical, and material processing applications that are important for improving human health, advancing scientific discovery, and maintaining national security. Fluid mixing plays a crucial role in many of these applications. Analysis of vortex motion in laminar flow provides insight into the dynamics of vorticity-dominated fluid systems.

Financial support for my research has come from:

My research activities are focused on the analysis of transport and mixing in laminar flows.

*Click on the thumbnails below to view full size images.*

*Background image shows separating streamlines for a stationary point vortex lattice.*

Stirring a viscous fluid with three rods perpendicular to the plane of view.

**(left)**Initial condition, with three lines of dye connected to the rods.

**(center)**Stirring with a finite order motion, which primarily twists the fluid around the three rods.

**(right)**Stirring with a pseudoAnosov motion, which 'braids' the fluid around the rods and produces topological chaos. The Thurston-Nielsen theory provides a quantitative lower bound in the stretch rate in this case.

Separating streamlines in a point vortex model of an 'exotic wake' with three vortices generated per shedding cycle. The vortices are labeled according to their strengths and continue periodically to both the left and the right. This configuration is steady in a frame of reference moving with the vortices. Stirring experiments in a pulsed source-sink device. The mixing chamber measures 71mm x 21mm x 50μm. Fluid is inserted into and removed from the chamber through the holes in opposing corners (dark circles). Dye distributions are shown for (a) α≈10%, n=19; (b) α≈17%, n=19; (c) α≈26%, n=5; and (d) α≈26%, n=19; where α is the fraction of the domain volume that is replaced during each pulse and n is the number of pulses. Choosing α≈17% produces the best mixing out of those cases shown.

Poincaré sections showing chaotic transport in a pulsed source-sink system with flow alternating between two source-sink pairs. The percentages indicate the fraction of the domain volume that is pulsed before switching source-sink pairs.