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The new exact weak solution of the equations for the ideal incompressiblefluid dynamics in the finite layer inside two plates with solid boundaries isobtained. The solution meets a devised non-linear finite dimension Hamiltoniandynamic system for the coordinates and the Lamb impulses of N point vortexdipoles (PVD), i.e. extremely small solid spherical particles, moving withrespect to the fluid. For N=2 the necessary condition for the collapse (or theconverging in one point during the finite time) of two PVD is stated. On thebase of the proposed theory, the new hydrodynamic mechanism of converging fortwo small spherical particles (of the same radius) is introduced and used forinterpreting the observed paradoxical effects of attraction for micro particleswith the same sign of electrical charge in the colloid and dusty plasmasystems. The correspondence of the condition for collapse of two PVD with theexperimentally observed data where convergence of two like-chargedmicro-spheres moving in the fluid layer is observed only when definitenecessary restrictions on the fluid layer depth are imposed from above andbelow (J. C. Crocker, D. G. Grier, 1996) is stated. We also state thepossibility of correspondence between the obtained condition of collapse fortwo PVD in the limit of unbounded fluid and known numerical results on thethreshold of the impact parameter for the realization of resonance bond state(and corresponding stochastic dynamic regime) for two finite size vortexdipoles during their scattering in unbounded fluid (S. V. Manakov, L. N.Shchur, 1983; L. Tophoj, H. Aref, 2008). Here we show that in the latterprocess the size of dipoles is not so important as it was thought before.

Collapse of Point Vortex Dipoles in a Bounded Fluid Layer and the  Hydrodynamic Mechanism of Mutual Attraction of Like-Charged Micro-Particles  in the Colloid or Dusty Plasma Systems