= Lubrication equation for a bubble with viscous exterior
{title2=$(a^2)_t=(8\lambda\mu)^{-1}[a^4(2\mu a_t/a+\gamma/a)_z]_z$}
Internal <Hagen-Poiseuille flow> of viscosity $\lambda\mu$ has axial volume flux $Q=-\pi a^4P_z/(8\lambda\mu)$ when the interfacial axial speed is negligible to leading order. <Conservation of mass> gives $(\pi a^2)_t+Q_z=0$. Combining with the exterior radial normal-stress balance gives the displayed implicit evolution equation. The radial viscous normal stress and capillary pressure both matter in its local pinch-off similarity.
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