Fluid Dynamics of Beetle Juice: A Mathematical Scavenger Hunt
The Florida tortoise beetle (Hemisphaerota cyanea) is a small, purplish-blue beetle which feeds on palm trees and is common to the Southeastern United States. It would be rather unremarkable, were it not for its ingenious defense mechanism against predatory ants: When attacked, the beetle clings to the ground with more persistence than the ants muster in their assault. The beetle achieves this strong adhesion by excreting an oily liquid (“beetle juice”) through thousands of openings at its leg endings, thus forming liquid bridges with the substrate. In this way the beetle can withstand pulling forces up to 60 times and more of its body mass.
Motivated by this defense mechanism, I present a dynamical system modeling surface tension- induced flows of liquids in networks of interconnected channels. These channel flows are driven by “volume scavenging” where fluid droplets of varying sizes leech off one another to increase in volume. Volume exchange arises by pressure differences that drive liquid from one droplet to another along the network of channels. The analysis of the nonlinear dynamics will be accompanied by animations, highlighting the similarities of microfluidic behavior (volume scavenging) and socioeconomic competition (“winner-takes-all markets”). The presentation is based on joint work with Paul Steen, the late Maxwell M. Upson Chair in Engineering at Cornell University.
Thomas Hagen is a Professor of Mathematics at the University of Memphis. Before joining the UofM in 2003, he had academic appointments at the University of Wales, UK and the Technical University Munich, Germany. He was born and grew up in West Germany, began his academic career in Munich, with a major in mathematics and a minor in computer science, received a Master of Science degree in applied mathematics from the University of Texas at Dallas in 1995 and graduated with a doctorate in mathematics from Virginia Tech in 1998.
Thomas’ research interests lie in applied analysis, especially partial differential equations, dynamical systems, and fluid mechanics. He was a Fulbright scholar and the recipient of both research and teaching awards. He is married and has a daughter in elementary school.