= Plug-flow criterion for a column in a low-viscosity annulus
{title2=$\lambda\ll h^2/a^2$}
A column of <viscosity> $\mu$ in an annulus of <viscosity> $\lambda\mu$ and gap $h\ll a$ drives return flow of speed $O(a|w|/h)$ in a closed container. Annular shear scales as $\lambda\mu a|w|/h^2$, inducing relative core-velocity variation $O(\lambda a^2/h^2)$. Thus the <extensional equations for a slender Newtonian column> admit a leading plug-like axial <velocity> when $\lambda\ll h^2/a^2$. The small <viscosity> ratio alone is insufficient when the gap is very narrow.
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