A contaminated air bubble of radius rises through still water ( , , )

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

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

Problem

A contaminated air bubble of radius R=25 μmR = 25\,\mathrm{\mu m} rises through still water (ρ=1000 kg m−3\rho = 1000\,\mathrm{kg\,m^{-3}}, η=1.0×10−3 Pa s\eta = 1.0\times10^{-3}\,\mathrm{Pa\,s}, g=9.8 m s−2g = 9.8\,\mathrm{m\,s^{-2}}). The surfactant film on its surface makes it behave as a rigid sphere. ((a)) Find its terminal rise speed UU by balancing buoyancy against Stokes drag on a rigid sphere, treating the air's weight as negligible. ((b)) Find the Reynolds number based on the bubble's diameter and confirm that the Stokes regime applies.

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