  We study the interaction of two parallel rigid cylinders on the surface of a
thin elastic film supported on a pool of liquid. The excess energy of the
surface due to the curvature of the stretched film induces attraction of the
cylinders that can be quantified by the variation of their gravitational
potential energies as they descend into the liquid while still floating on the
film. Although the experimental results follow the trend predicted from the
balance of the gravitational and elastic energies of the system, they are
somewhat underestimated. The origin of this discrepancy is the hysteresis of
adhesion between the cylinder and the elastic film that does not allow the
conversion of the total available energy into gravitational potential energy as
some part of it is recovered in stretching the film behind the cylinders while
they approach each other. A modification of the model accounting for the
effects of adhesion hysteresis improves the agreement between theoretical and
experimental results. The contribution of the adhesion hysteresis can be
reduced considerably by introducing a thin hydrogel layer atop the elastic film
that enhances the range of attraction of the cylinders (as well as rigid
spheres) in a dramatic way. Morphological instabilities in the gel project
corrugated paths to the motion of small spheres, thus leading to a large
numbers of particles to aggregate along their defects. These observations
suggest that a thin hydrogel layer supported on a deformable elastic film
affords an effective model system to study elasticity and defects mediated
interaction of particles on its surface.
