  We model the behaviour of a single colloid embedded in a cross-linked polymer
gel, immersed in a viscous background fluid. External fields actuate the
particle into a periodic motion, which deforms the embedding matrix and creates
a local micro-cavity, containing the particle and any free volume created by
its motion. This cavity exists only as long as the particle is actuated and,
when present, reduces the local density of the material, leading to swelling.
We show that the model exhibits rich resonance features, but is overall
characterised by clear scaling laws at low and high driving frequencies, and a
pronounced resonance at intermediate frequencies. Our model predictions suggest
that both the magnitude and position of the resonance can be varied by varying
the material's elastic modulus or cross-linking density, whereas the local
viscosity primarily has a dampening effect. Our work implies appreciable
free-volume generation is possible by dispersing a collection of colloids in
the medium, even at the level of a simple superposition approximation.
