  An exact method is developed for computing the height of an elastic medium
subjected to centrifugal compression, for arbitrary constitutive relation
between stress and strain. Example solutions are obtained for power-law media
and for cases where the stress diverges at a critical strain -- for example as
required by packings composed of deformable but incompressible particles.
Experimental data are presented for the centrifugal compression of
thermo-responsive N-isopropylacrylamide (NIPA) microgel beads in water. For
small radial acceleration, the results are consistent with Hertzian elasticity,
and are analyzed in terms of the Young elastic modulus of the bead material.
For large radial acceleration, the sample compression asymptotes to a value
corresponding to a space-filling particle volume fraction of unity. Therefore
we conclude that the gel beads are incompressible, and deform without
deswelling. In addition, we find that the Young elastic modulus of the
particulate gel material scales with cross-link density raised to the power
3.3+-0.8, somewhat larger than the Flory expectation.
