  Although in the case of polymer solutions the existence of hydrodynamic
screening is considered as established, use of the same methods for suspensions
of hard spheres so far have failed to produce similar results. In this work we
reconsider this problem. Using superposition of topological, combinatorial and
London-style qualitative arguments, we prove the existence of screening in
suspensions. We show that the nature of hydrodynamic screening in suspensions
is analogous to that known for the Meissner effect in superconductors. The
extent of screening depends on volume fraction of hard spheres. The zero volume
fraction limit corresponds to the normal state. The case of finite volume
fractions-to the mixed state typical for superconductors of the second kind.
Such a state is becoming fully "superconducting" at some critical volume
fraction for which the (zero frequency) relative viscosity diverges. Our
analytical results describing this divergence are in accord with known scaling
results obtained by Brady and Bicerano et al which are well supported by
experimental data. We provide theoretical explanation of the divergence of
relative viscosity in terms of a topological-type transition which
mathematically can be made isomorphic to the more familiar Bose-Einstein
condensation transition. Because of this, the methods developed in this work
are not limited to suspensions only. In concluding section we mention other
applications of the developed formalism ranging from turbulence and
magnetohydrodynamics to high temperature superconductors, QCD, string models,
etc.
