Dripping is usually associated with fluid motion, but here we describe the analogous phenomenon of a He3 crystal growing and melting under the influence of surface tension and gravity. The pinch-off of the crystal is described by a purely geometric equation of motion, viscous dissipation or inertia being negligible. In analogy to fluid pinch-off, the minimum neck radius Rn goes to zero like a power law, but with a new scaling exponent of 1 2. However, for a significant part of the neck's macroscopic evolution the scaling exponent is found to be much closer to 1 3. This observation may be consistent with simulations and theoretical results showing a very slow approach to the asymptotic pinch solution, making the "critical region" very small, both in time and space. After pinch-off, we observe a similar 1 3 -scaling for the recoil of a crystal tip, both in simulation and experiment. For very early times our experiments are consistent with an approximate theory predicting an asymptotic regime with exponent 1 2. Future experiments must show whether the transient 1 3 scaling is a universal feature of crystal melting, or perhaps an artifact of our experimental setup.
|Journal||Physical Review E: Statistical, Nonlinear, and Soft Matter Physics|
|Publication status||Published - 27 Apr 2007|