Nonequilibrium interactions between multi-scale colloids regulate the suspension microstructure and rheology.

Understanding nonequilibrium interactions of multi-component colloidal suspensions is critical for many dynamical settings such as self-assembly and material processing. A key question is how the nonequilibrium distributions of individual components influence the effective interparticle interactions and flow behavior. In this work, we develop a first-principle framework to study a bidisperse suspension of colloids and depletants using a Smoluchowski equation and corroborated by Brownian dynamics (BD) simulations. Using nonlinear microrheology as a case study, we demonstrate that effective depletion interactions between driven colloids are sensitive to particle timescales out of equilibrium and cannot be predicted by equilibrium-based pair potentials like Asakura-Oosawa. Furthermore, we show that the interplay between Brownian relaxation timescales of different species plays a critical role in governing the viscosity of multi-component suspensions. Our model highlights the limitations of using equilibrium pair potentials to approximate interparticle interactions in nonequilibrium processes such as hydrodynamic flows and presents a useful framework for studying the transport of driven, interacting suspensions.