A small air bubble of radius rises through a clean silicone oil of density and viscosity

PHYSICS · Multi-part · Fermi University Physics · Fluids & Continuum Physics · Viscous flow and dynamical similarity · Viscous flow and dynamical similarity

Fluid Dynamics, Ch Stokes flow, lubrication and viscous wetting

Problem

A small air bubble of radius a=0.30 mma=0.30\,\mathrm{mm} rises through a clean silicone oil of density ρ=800 kg m−3\rho=800\,\mathrm{kg\,m^{-3}} and viscosity μ=0.020 Pa s\mu=0.020\,\mathrm{Pa\,s}. Air has viscosity μ′=1.81×10−5 Pa s\mu'=1.81\times10^{-5}\,\mathrm{Pa\,s} and density 1.20 kg m−31.20\,\mathrm{kg\,m^{-3}}; the bubble surface is free of surfactant. ((a)) Using the Hadamard-Rybczynski drag, find the bubble's terminal rise speed. ((b)) Find what the rise speed would be if the bubble instead behaved as a rigid sphere, and give the ratio of the two speeds.

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