Nonequilibrium osmotic pressure in sticky-probe active microrheology

We present a theoretical study of the influence of interparticle attractions and hydrodynamic interactions on nonequilibrium osmotic pressure in a colloidal suspension via active microrheology, where a Brownian probe driven by external forces through the suspension is tracked to infer rheology. To model this system, we solve a Smoluchowski equation to obtain structure and compute osmotic pressure through statistical mechanics. Attractions decrease equilibrium osmotic pressure and phase-separate a suspension at higher volume fractions when the second virial coefficient is sufficiently negative, B₂ ≈ –1/2. Under external forcing, nonequilibrium osmotic pressure evolves nonmonotonically with both attraction and flow strength. We demonstrate that strong hydrodynamic interactions dramatically lower the nonequilibrium osmotic pressure in attractive systems and can even induce negative osmotic pressure in flowing systems, driving flow-induced particle aggregation and potential nonequilibrium phase separation. Our results suggest that detailed knowledge of both attractive and repulsive forces, and of hydrodynamic interactions, enables tuning of tracer particle motion inside sticky environments such as biological fluids and control over aggregation kinetics in self-assembly processes.