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

Topological character of hydrodynamic screening in suspensions of hard spheres: an example of universal phenomenon