This research is concerned with the nonlinear dynamics of free-surface flows, and in particular their rich variety of singularities. An example, showing the formation of a drop, is seen above. This singularity corresponds to a self-similar solution of the Navier-Stokes equation (Eggers (1997)), leading to pinch-off in finite time. Most recently, we included thermal fluctuations into the dynamics, to describe some of the features of the break-up of a jet only a few nanometers in diameter (Eggers (2002)).
Other singularities form spontaneously on free surfaces if the fluid is driven sufficiently strongly. We have investigated the stability of such singularities, to show that they serve as channels through which air can be entrained into the fluid (Eggers (2001)). Self-similarity is the common feature of singular flows, allowing for a unifying description of a wide class of phenomena. Very often one is thus able to capture the crucial events in the evolution of a flow. Further examples include the coalescence of drops, drops in shear flows, Taylor cones, and moving contact lines.