Pressure-Driven Flow of Solid Helium

The recent torsional oscillator results of Kim and Chan show an anomalous mass decoupling, interpreted by the authors as a supersolid phase transition, in solid ${}^4\mathrm{He}$. We have used a piezoelectrically driven diaphragm to study the flow of solid helium through an array of capillaries. Our measurements showed no indication of low temperature flow, placing stringent restrictions on supersolid flow in response to a pressure difference. The average flow speed at low temperatures was less than $1.2\times {10}^{-14}\mathrm{m}/\mathrm{s}$, corresponding to a supersolid velocity at least 7 orders of magnitude smaller than the critical velocities inferred from the torsional oscillator measurements.