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We show that non-Brownian suspensions of repulsive spheres below jammingdisplay a slow relaxational dynamics with a characteristic time scale thatdiverges at jamming. This slow time scale is fully encoded in the structure ofthe unjammed packing and can be readily measured via the vibrational density ofstates. We show that the corresponding dynamic critical exponent is the samefor randomly generated and sheared packings. Our results show that a widevariety of physical situations, from suspension rheology to algorithmic studiesof the jamming transition are controlled by a unique diverging timescale, witha universal critical exponent.

Universal relaxation dynamics of sphere packings below jamming