Theory of bubble tips in strong viscous flows

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• Jens Eggers, U. Bristol
• Friday 27 January 2023, 16:00-17:00
• MR2, Centre for Mathematical Sciences, Wilberforce Road, Cambridge.

If you have a question about this talk, please contact Prof. Jerome Neufeld.

A free surface, placed in a strong viscous flow (such that viscous forces overwhelm surface tension), often develops ends with very sharp tips. We show 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 the 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 the experiment as well as full numerical simulations of the Stokes equation.

This talk is part of the Fluid Mechanics (DAMTP) series.

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