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We report some experimental observations regarding a new type of long-range interaction between rigid particles that prevails when they are suspended in an ultrasoft elastic gel. A denser particle submerges itself to a considerable depth inside the gel and becomes elasto-buoyant by balancing its weight against the elastic force exerted by the surrounding medium. By virtue of a large elasto-capillary length, the surface of the gel wraps around the particle and closes to create a line singularity connecting the particle to the free surface of the gel. A substantial amount of tensile strain is thus developed in the gel network parallel to the free surface that penetrates to a significant depth inside the gel. The field of this tensile strain is rather long-range because of a large gravito-elastic correlation length and sufficiently strong to pull two submerged particles into contact. The particles move toward each other with an effective force following an inverse linear distance law. When more monomers or dimers of the particles are released inside the gel, they orient rather freely inside the capsules where they are located and attract each other to form closely packed clusters. Eventually, these clusters themselves interact and coalesce. This is an emergent phenomenon in which gravity, capillarity, and elasticity work in tandem to create a long-range interaction. We also present the results of a related experiment, in which a particle suspended inside a thickness-graded gel moves accompanied by the continuous folding and the relaxation of the gel's surface.

Surface Folding-Induced Attraction and Motion of Particles in a Soft Elastic Gel: Cooperative Effects of Surface Tension, Elasticity, and Gravity