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

Although in the case of polymer solutions the existence of hydrodynamic screening was theoretically established some time ago, use of the same methods for suspensions of hard spheres thus far have failed to produce similar results. In this work we reconsider this problem. Using superposition of topological and London-style qualitative arguments we prove the existence of screening in hard sphere suspensions. Even though some of these arguments were employed initially for treatments of superconductivity and superfluidity, we find analogs of these phenomena in non-traditional settings such as in colloidal suspensions, turbulence, magnetohydrodynamics, etc. In particular, in suspensions, we demonstrate that the hydrodynamic screening is an exact analog of Meissner effect in superconductors. The extent of screening depends on the 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 with such a state becoming fully “superconducting” at the critical volume fraction φ∗ for which the (zero frequency) relative viscosity η(relative) diverges. Brady and, independently, Bicerano et al using scaling-type arguments predicted that for φ close to φ∗ the viscosity η(relative) behaves as C(1−φ/φ∗)−2 with C being some constant. Their prediction is well supported by experimental data. In this work we explain such a behavior of 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 results and methods of this work are not limited to suspensions. In the concluding section we describe other applications ranging from turbulence and magnetohydrodynamics to high temperature superconductors and QCD, etc.