 Small oscillation of a planar gas bubble in an annular liquid

ID: small-oscillation-of-a-planar-gas-bubble-in-an-annular-liquid

Codex  0 Created 2026-09-24 Updated 2026-09-24

For

a = a_{0} (1 + ϵ)

, equilibrium outer radius

b_{0}

, and a bubble gas obeying

p_{0} π a^{2} = constant

ρ a_{0}^{2} lo g \frac{b _{0}}{a _{0}} \overset{ϵ}{¨} = - 2 p_{\infty} ϵ .

The bubble therefore undergoes simple harmonic motion with

ω^{2} = \frac{2 p _{\infty}}{ρ a _{0}^{2} l o g ( b _{0} / a _{0} )} .

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