When a suspension is confined by completely rigid boundaries, the confinement makes the hydrodynamic interaction between the suspended particles qualitatively different. Because of momentum transport into the boundaries, the liquid no longer conserves momentum, and the amplitude of shear modes, developing in the liquid in response to particle motion, decays exponentially with distance. The correlations are now dominantly mediated by compression modes, and the perturbation due to particle motion can be represented at large distances as arising from an effective mass dipole. When the suspension is confined between two plates (quasi-two-dimensional suspension), the resulting flow field decays as 1/r^2 (as for a mass dipole in two dimensions).

In this study we relax the assumption of infinitely rigid boundaries and consider the case of confinement between two elastic plates. We find qualitative changes in the velocity pair correlation function. These include, in particular, a long-time regime where the velocity pair correlation has an unbounded range and a power-law decay with time.