= Rayleigh equation for an inviscid spherical bubble
{c}
{title2=$R\ddot R+3\dot R^2/2=(p_g-p_\infty)/\rho$}
In radial <potential flow> outside a spherical bubble, <incompressibility> and the moving-boundary condition give $u_r=R^2\dot R/r^2$ and $\phi=-R^2\dot R/r$. The <Unsteady Bernoulli equation>, with its gauge fixed at infinity, yields the displayed radius equation when surface tension and viscosity are neglected. Pressure continuity at the interface identifies the liquid pressure with the gas pressure $p_g$. The vacuum special case is <Rayleigh collapse of a spherical cavity>.
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