  Selectively heating a microscopic colloidal particle embedded in a soft
elastic matrix is a situation of high practical relevance. For instance, during
hyperthermic cancer treatment, cell tissue surrounding heated magnetic
colloidal particles is destroyed. Experiments on soft elastic polymeric
matrices suggest a very long-ranged, non-decaying radial component of the
thermophoretically induced displacement fields around the microscopic heat
centers. We theoretically confirm this conjecture using a macroscopic
hydrodynamic two-fluid description. Both, thermophoretic and elastic effects
are included in this theory. Indeed, we find that the elasticity of the
environment can cause the experimentally observed large-scale radial
displacements in the embedding matrix. Additional experiments confirm the
central role of elasticity. Finally, a linearly decaying radial component of
the displacement field in the experiments is attributed to the finite size of
the experimental sample. Similar results are obtained from our theoretical
analysis under modified boundary conditions.
