"Matière et Systèmes Complexes"
17 avril 2008 à 14h
Bâtiment Condorcet, 4ème
étage, salle 454 A.
(School of Mathematics, University of Bristol)
Breaking drops, collapsing cavities, and dripping crystals
When a drop
falls from a faucet, the size of the fluid neck separating the drop
from the nozzle goes to zero, producing very small length scales. The
fluid motion close to breakup is self-similar and universal: it does
not depend on initial conditions. This is easily confirmed
experimentally, since convergence onto the similarity solution is
exponential, thus non-universal behavior quickly falls away. In other
examples of pinch-off, however, the linearization around the asymptotic
solution (the fixed point) has zero eigenvalues, so convergence is
slow. For the dripping of a $^3$He crystal, the expansion around the
fixed point has a quadratic non-linearity. In the case of a gas bubble
breaking up in water, the non-linearity is of third order. For the
latter case in particular, the asymptotic behavior is virtually
unobservable; instead, the scaling appears to be characterized by
anomalous scaling exponents, as reported in recent experiments.