  We study the interaction of small hydrophobic particles on the surface of an
ultra-soft elastic gel, in which a small amount of elasticity of the medium
balances the weights of the particles. The excess energy of the surface of the
deformed gel causes them to attract as is the case with the generic capillary
interactions of particles on a liquid surface. The variation of the
gravitational potential energies of the particles resulting from their descents
in the gel coupled with the superposition principle of Nicolson allow a fair
estimation of the distance dependent attractive energy of the particles. This
energy follows a modified Bessel function of the second kind with a
characteristic elastocapillary decay length that decreases with the elasticity
of the medium. An interesting finding of this study is that the particles on
the gel move towards each other as if the system possesses a negative
diffusivity that is inversely proportional to friction. This study illustrates
how the capillary interaction of particles is modified by the elasticity of the
medium, which is expected to have important implications in the surface force
driven self-assembly of particles. In particular, this study points out that
the range and the strength of the capillary interaction can be tuned in by
appropriate choices of the elasticity of the support and the interfacial
tension of the surrounding medium. Manipulation of the particle interactions is
exemplified in such fascinating mimicry of the biological processes as the
tubulation, phagocytic engulfment and in the assembly of particles that can be
used to study nucleation and clustering phenomena in well controlled settings.
