We study theoretically the velocity cross-correlations of a viscous fluid confined in a slit between two viscoelastic media, and analyze the effect of these correlations on the motions of particles suspended in the fluid. The compliance of the confining boundaries gives rise to a long-ranged pair correlation, decaying only as  with the inter-particle distance . We show how this long-ranged effect may be used to extract the viscoelastic properties of the confining media without embedding tracer particles in them. We discuss the remarkable robustness of such a potential technique with respect to details of the confinement, and its  expected statistical advantages over standard two-point microrheology.

https://journals.aps.org/pre/abstract/10.1103/PhysRevE.96.022607