Stochastic Interactions of Two Brownian Spheres in the Presence of Depletants

The pair interactions between hard spheres play an essential role in many processes such as macromolecular crowding, binding, self-assembly of particles, and many chemical and food processes. Here we focus on theoretical analysis of the long-time correlated stochastic motion of two hard spheres in a non-adsorbing polymer solution. The hard spheres are held by hypothetical optical traps. The pair mobility tenser is found using a two-layer approximation with pure solvent in the depletion zone surrounding the particle and uniform polymer solution elsewhere. The resulting mobility computed by the boundary integral analysis is used to define the level of thermal fluctuation. Results show how the mobility and the decay of displacement correlation functions modified by the polymer depletion effect. The attractive osmotic potential increases the auto-correlation of the pair particle motion, while reduces the cross-correlation of the particles. This work gives better understanding of the pair interactions in a suspension of non-adsorbing polymers as an essential step toward many-particle interactions.