Jet formation in bubbles bursting at a free surface
Résumé
We study numerically bubbles bursting at a free surface and the
subsequent jet formation. The Navier-Stokes equations with a free
surface and surface tension are solved using a marker-chain approach.
Differentiation and boundary conditions near the free surface are satisfied using least-squares methods. Initial
conditions involve a bubble connected to the outside atmosphere by a preexisting opening in a
thin liquid layer. The evolution of the bubble is studied as a function
of bubble radius. A jet forms with or without the formation of a tiny
air bubble at the base of the jet. The radius of the droplet formed at
the tip of the jet is found to be about one tenth of the initial bubble
radius. A series of critical radiuses exist, for which a transition from
a dynamics with or without bubbles exist. For some parameter values, the jet formation is
close to a singular flow, with a conical cavity
shape and a large curvature or
cusp at the bottom. This is
compared
to similar singularities investigated in other
contexts such as Faraday
waves.
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