The confined Generalized Stokes-Einstein relation and its consequence on intracellular two-point microrheology

Two-point microrheology (TPM) is used to infer material properties of complex fluids from the correlated motion of hydrodynamically interacting probes embedded in the medium. The mechanistic connection between probe motion and material properties is propagation of disturbance flows, encoded in current TPM theory for unconfined materials. However, confined media e.g. biological cells and particle-laden droplets, require theory that encodes confinement into the flow propagator (Green's function). To test this idea, we use Confined Stokesian Dynamics simulations to explicitly represent many-body hydrodynamic couplings between colloids and with the enclosing cavity at arbitrary concentration and cavity size. We find that previous TPM theory breaks down in confinement, and we identify and replace the underlying key elements. We put forth a Confined Generalized Stokes-Einstein Relation and report the viscoelastic spectrum. We find that confinement alters particle dynamics and increases viscosity, owing to hydrodynamic and entropic coupling with the cavity. The new theory produces a master curve for all cavity sizes and concentrations and reveals that for colloids larger than 0.005 times the enclosure size, the new model is required.