  The screening of hydrodynamic interactions (HI) essentially affects
macroscopic properties of polymeric solutions. This screening depends not only
on the polymer concentration but has a dynamic nature. In the present work, a
bead-spring theory is developed, in which this phenomenon is described for
solutions of nonentangled polymer coils. The equation of motion for the beads
of a test polymer is solved together with the Brinkman's equation for the
solvent velocity that takes into account the presence of other coils in
solution. The time correlation functions for the polymer normal modes are
found. A tendency to the screening of HI is demonstrated on the coil diffusion
as well as on the relaxation of its internal modes. With the growing
concentration of the coils they both show a transition to the exact Rouse
behavior. The viscosity of the solution and some other observable quantities
are calculated. As the time increaes, the time-dependent quantities change
their behavior from the Rouse regime through the Zimm one again to the Rouse
dynamics at long times.
