Short-ranged pair distribution function for concentrated suspensions of soft particles

Many rheological properties of concentrated suspensions of soft particles jammed together beyond the random close packing limit for hard-spheres are determined by the contacts between the particles and are computable from the short range value of the pair distribution function. It is a challenge to compute the structure of these amorphous suspensions because they are athermal, non-equilibrium materials. Here we develop a microscopic theory to predict the short ranged pair distribution function with a transport or conservation of mass equation for the stationary state that includes a concentration dependent mean force that captures the effect of the bulk suspension on the pair interaction. The resulting distribution function is singular as the concentration approaches random close packing as expected from the theory for hard spheres. The pair distribution function and elastic properties that can be calculated from it are validated by computer simulations and experiments with concentrated suspensions of particles with varying soft potentials.