Singularities
and Topological Phase Transitions in Fluids: Breaking Away, Selective Withdrawal
and Islets
in the Stream
The exhilarating spray
from waves crashing into the shore, the distressing sound of a faucet leaking
in the night, and the indispensable role of bubbles dissolving gas into the
oceans are but a few examples of the ubiquitous presence and profound
importance of drop formation and splashing in our lives. During fission, a fluid forms a neck that
becomes vanishingly thin at the point of breakup. This topological transition is accompanied by
a dynamic singularity in which physical properties such as pressure
diverge. Singularities of this sort
often organize the overall dynamical evolution of nonlinear systems. I will first discuss the role of
singularities in the breakup of droplets. I will then present a second
experiment, selective withdrawal, in which we study the steady-state shape of a
liquid as it is withdrawn by a nozzle through a surrounding fluid. Here, a
change in topology may again be accompanied by a singularity. Applications of
this geometry that rely on singular dynamical behavior are relevant for the
coating of biological particles that may be of particular use in medical
transplantation technologies.