  Superfluid \4he atoms are injected (withdrawn) asymmetrically into (from) a
chamber filled with solid \4he. Two in situ capacitance pressure gauges are
located at the ends of the solid helium sample at different distances from
where the superfluid meets the solid \4he. The pressure change kinetics are
slower at the more distant gauge. This demonstrates the presence of a mass flux
bottleneck inside the solid helium sample. The temperature dependence of the
maximum flux reveals a crossover and this is discussed in the context of phase
slips on quasi-1-D pathways.
