Séminaire PMMH - Jens Eggers, U. of Bristol, UK

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15 avril 11:00 » 12:00 — Salle réunion PMMH 1

Theory of bubble tips in strong viscous flows

A free surface, placed in a strong viscous flow (such that viscous forces overwhelm surface tension), often develops ends with very sharp tips. For example, observe a bubble in a shampoo bottle, turned upside down. We shown that the axisymmetric shape of the ends, non-dimensionalized by the tip curvature,is governed by a universal similarity solution. The shape of the similarity solution is close to a cone, but whose slope varies with the square root of the logarithmic distance from the tip.

Pursuing the calculation of the tip similarity solution to next order, we demonstrate matching to previous slender-body analyses, which fail near the tip. This allows us to resolve the long-standing problem, first raised by G.I. Taylor, of finding the global solution of a bubble in a strong hyperbolic flow. Our results are shown to agree in detail with experiments (performed by S. Courrech du Pont, Paris Diderot), as well as full numerical simulations of the Stokes equation.





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