OurBigBook.comSite Source code

Small oscillation of a planar gas bubble in an annular liquid

For

a = a_{0} (1 + ϵ)

, equilibrium outer radius

b_{0}

, and a bubble gas obeying

p_{0} π a^{2} = constant

, the linearization is

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} )} .

 Ancestors (7)

 Incoming links (1)

Solution