Freezing and Pressure-Driven Flow of Solid Helium in Vycor

The recent torsional oscillator results of Kim and Chan suggest a supersolid phase transition in solid ${}^4\mathrm{He}$ confined in Vycor. We have used a capacitive technique to directly monitor density changes for helium confined in Vycor at low temperature and have used a piezoelectrically driven diaphragm to study the pressure-induced flow of solid helium into the Vycor pores. Our measurements showed no indication of a mass redistribution in the Vycor that could mimic supersolid decoupling and put an upper limit of about $0.003\mu \mathrm{m}/\mathrm{s}$ on any pressure-induced supersolid flow in the pores of Vycor.