Pressure-driven flow of solid helium
  The recent torsional oscillator results of Kim and Chan suggest a supersolid phase transition in solid 4He. 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 1.2x10-14 m/s, corresponding to a supersolid velocity at least 7 orders of magnitude smaller than the critical velocities inferred from the torsional oscillator measurements. 
James Day and John Beamish