Fluid pinch-off in superfluid and normalHe4

Abstract

We present frames from high-speed videos of the pinch-off of liquid ${}^4\mathrm{He}$ droplets. The temperature of the fluid droplets ranged from $1.33\mathrm{K}\text{to}4.8\mathrm{K}$, and the size of the drops was proportional to the temperature-dependent capillary length. We observed no qualitative difference between pinch-off in the normal and superfluid states. In both cases, the shape of the fluid in the final stages of pinch-off resembles a cone piercing a sphere, which is typical of other low-viscosity fluids. The evolution of the minimum neck radius $r_{\mathit{min}}$ can be characterized by power laws $r_{\mathit{min}}\propto {\tau }^n$, where $\tau$ is the time remaining until pinch-off occurs. In the regime near pinch-off, the data from image analysis are consistent with $n=2∕3$. The data at the beginning of the pinch process when the neck is of the order of the capillary length are also described by $n=2∕3$, but with a different proportionality factor. There is an intermediate crossover regime characterized by $n=2∕5$.