Self-Similar Capillary Pinchoff of an Inviscid Fluid

We study how an axisymmetric drop of inviscid fluid breaks under the action of surface tension. The evolution of various initial shapes is calculated numerically using a boundary-element method, and finite-time breakage is observed in detail. The pinchoff region is shown to have lengths scaling as ${\tau }^{2/3}$, where $\tau$ is the time remaining until pinchoff, and is found to adopt a unique shape with two cones of angles $18.1°$ and $112.8°$, independent of the initial conditions. The velocity potential in the intermediate region between the small pinchoff region and the large bulk of the drops is shown to take the form ${\mathrm{Ar}}^{1/2}{P}_{1/2}\left(\cos \theta \right)+B\tau /r+\dots$ .