Drips, Jets, Bugs: Singularities, Similarity Solutions, Scaling and Simulations

Leo P. Kadanoff            
The James Franck Institute
University of Chicago


This talk reports on work done by Andrea Bertozzi, Michael Brenner, Todd Dupont, Jens Eggers, Leo Kadanoff, Sid Nagel, X.D. Shi, Lene Oddershede, Itai Cohen, Shankar Venkataramani, and others.

We investigate the behavior of the interface between two fluids. We are interested in the singularities which develop when a mass of fluid breaks into two. Then there is a bridge connecting two pieces of fluid goes to zero thickness. Experiments, computer simulations, and theory are used to analyze several different physical situations: a dripping faucet, the pinch-off of a jet flow, two fluids being sucked up by a straw, and a liquid which comes to a sharp point.

In all cases, the analysis of the developing singularity is done in terms of similarity solutions, form-invariant local solutions which show simple scaling properties. The importance of these scaling solutions for computer simulations is stressed. A problem of aggregation of bacteria (or stars) is put forward as a particularly nice example of similarity behavior.