The dynamics of flexible polymers in dilute solutions is studied taking into account the hydrodynamic memory, as a consequence of fluid inertia. As distinct from the Rouse-Zimm (RZ) theory, the Boussinesq friction force acts on the monomers (beads) instead of the Stokes force, and the motion of the solvent is governed by the nonstationary Navier-Stokes equations. The obtained generalized RZ equation is solved approximately using the preaveraging of the Oseen tensor. It is shown that the time correlation functions describing the polymer motion essentially differ from those in the RZ model. The mean-square displacement (MSD) of the polymer coil is at short times approximately t(2) (instead of approximately t). At long times the MSD contains additional (to the Einstein term) contributions, the leading of which is approximately t. The relaxation of the internal normal modes of the polymer differs from the traditional exponential decay. It is displayed in the long-time tails of their correlation functions, the longest lived being approximately t(-3/2) in the Rouse limit and t(-5/2) in the Zimm case, when the hydrodynamic interaction is strong. It is discussed that the found peculiarities, in particular, an effectively slower diffusion of the polymer coil, should be observable in dynamic scattering experiments.

The Rouse model of the dynamics of polymers in solution is generalized by taking into account the hydrodynamic memory during the motion of the polymer monomers in an incompressible liquid. This leads to new peculiarities in the behavior of the time correlation functions describing the polymer motion. It is demonstrated by the appearance of long-time tails of these functions. The mean square displacement of the polymer coil as a whole contains, in addition to the Einstein term ∼t, other contributions, the leading of which is ∼t1/2. The behavior of the correlation functions for internal modes differs from the traditional exponential relaxation: as t→∞, they consist of tails decaying like t−n/2, the longest-lived being ∼t−3/2.

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Abstract. The Rouse-Zimm equation for the position vectors of beads mapping the polymer is generalized by taking into account the viscous aftereffect and the hydrodynamic noise. For the noise, the random fluctuations of the hydrodynamic tensor of stresses are responsible. The preaveraging of the Oseen tensor for the nonstationary Navier-Stokes equation allowed us to relate the time correlation functions of the Fourier components of the bead position to the correlation functions of the hydrodynamic field created by the noise. The velocity autocorrelation function of the center of inertia of the polymer coil is considered in detail for both the short and long times when it behaves according to the t -3/2 law and does not depend on any polymer parameters. The diffusion coefficient of the polymer is close to that from the Zimm theory, with corrections depending on the ratio between the size of the bead and the size of the whole coil.

The surface vibration spectra of liquid droplets with flexible interfaces, like microemulsion droplets or vesicles, are studied. As distinct from the previous theories, we proceed with exact solutions of hydrodynamic equations for incompressible bulk fluids inside and outside the droplet. The dynamical equations for the interface are those obtained by Lebedev and Muratov ͓JETP 68, 1011 ͑1989͔͒ but with the improved continuity equation for the surface layer. Within the Helfrich's concept of the interfacial elasticity and taking into account the compressibility of the surface layer, the exact equation is obtained for the frequencies of the droplet vibrations. The equation describes uniformly a broad region of frequencies from the lowest, almost purely relaxation modes, up to the modes determined mainly by the change of the area per molecule of the layer. The dispersion laws for some of the modes are obtained analytically in the limits of large and small penetration depths of the corresponding waves. Our analysis corrects the previous results concerning the relaxation modes, the capillary wave frequency and the frequency of the mode connected with the fluctuations of molecules in the surface layer. An additional mode of this kind is obtained for almost incompressible layers. In the region corresponding to large penetration depths, a couple of modes exist with frequencies depending both on the surface elasticity and compressibility. In the limit of infinite compressibility of the layer, the lower of the two modes disappears. The conditions necessary for the existence of all the modes were specified. Some representative numerical solutions of the obtained equation are presented as depending on various values of the model parameters including those for realistic microemulsion systems.