A large air bubble rising through a still pond has flattened into a spherical cap and…

PHYSICS · Multi-part · Fermi University Physics · Fluids & Continuum Physics · Solid continuum mechanics and complex fluids · Solid continuum mechanics and complex fluids

Bending, Ringing, Breaking and Flowing, Ch Bubbles, drops and cavitation

Problem

A large air bubble rising through a still pond has flattened into a spherical cap and is filmed rising at

U = 0.35\,\mathrm{m\,s^{-1}}

. Take

g = 9.8\,\mathrm{m\,s^{-2}}

, and treat the bubble as large enough that surface tension and viscosity do not set its rise speed. ((a)) Using the Davies-Taylor result

U=\tfrac23\sqrt{gR_{\rm n}}

, estimate the radius of curvature

R_{\rm n}

of the cap at its nose. ((b)) A second cap in the same pond is filmed rising at

0.70\,\mathrm{m\,s^{-1}}

, twice as fast. A colleague concludes that its nose radius must be twice as large. Find its actual nose radius, and say what the colleague has assumed.

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