= Capillary instability of an annular liquid lining
{title2=$\beta=\frac{\sigma h_0^3}{3\mu}k^2(a^{-2}-k^2)$}
A thin liquid lining inside a rigid cylindrical tube has <pressure> perturbation $p_1=-\sigma(a^{-2}h_1+h_{1,xx})$ at leading order in $h_0/a$. <Lubrication theory> gives flux $q=-h_0^3p_x/(3\mu)$, so <mass conservation> gives the displayed growth rate. Long waves with $0<k^2a^2<1$ grow, while short waves are stabilized by <curvature>. The maximum occurs at $k^2a^2=1/2$.
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