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Séminaire Exceptionnel
"Matière et Systèmes Complexes"

                      

Jeudi 17 avril 2008 à 14h
Bâtiment Condorcet, 4ème étage, salle 454 A.

Jens Eggers
(
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.