Dynamical phenomena in dilute lyotropic solutions are investigated. We consider the case when lyotropic molecules form a system of membranes determining the main peculiarities of these systems. We are interested in the effect of fluctuations of the membranes on dynamical characteristics of the systems. A membrane possesses two soft degrees of freedom associated with its bending deformations and with variations of the surface density ${\mathit{n}}_{\mathit{s}}$ of molecules constituting the membrane, which we term elastic deformations. Bending fluctuations are governed by the Helfrich module κ whereas the elastic fluctuations (variations of ${\mathit{n}}_{\mathit{s}}$) are governed by the ‘‘internal’’ compressibility of the membrane which we characterize by an elastic module B. Correspondingly, there are two characteristic surface modes where the motion of the solvent is localized near the membrane. In the linear approximation these modes prove to be overdamped. Due to the softness of these modes, dynamic fluctuation effects related to nonlinear interaction of the modes should be taken into account. To investigate these effects the Wyld-diagram technique is used. It is constructed on the basis of nonlinear equations describing the dynamics of a membrane immersed into a liquid. We have shown that bending fluctuations are most important. Our investigation is performed in the framework of the perturbation theory in g≃T/κ which is believed to be a small dimensionless parameter, describing the ‘‘strength’’ of the bending fluctuations.

These fluctuations produce only small logarithmic corrections to the characteristics of the bending mode whereas they essentially modify the dynamical behavior of the elastic degree of freedom. Namely, these fluctuations drastically change the frequency dependence of the susceptibility describing the relaxation of ${\mathit{n}}_{\mathit{s}}$ to the equilibrium. We consider also the influence of dynamical fluctuations of membranes on the macroscopic characteristics of the system such as viscosity coefficients. To find the fluctuation contribution ${\mathit{n}}_{\mathrm{fl}}$ to the viscosity coefficients we calculate a response of the system of membranes to a macroscopic (long-wavelength) motion of the liquid, with fluctuations of the membranes taken into account. The main part of ${\mathit{n}}_{\mathrm{fl}}$ is associated with the elastic part of the membrane stress tensor but is strongly renormalized by the bending fluctuations. The quantity ${\mathit{n}}_{\mathrm{fl}}$ possesses a complicated frequency dispersion. In the high-frequency region it behaves as ${\mathrm{\omega }}^{\mathrm{-}5/3}$, in the intermediate frequency region it behaves as ${\mathrm{\omega }}^{\mathrm{-}1/3}$, and for small ω it remains constant. The ratio of this constant to the viscosity of the solvent is of the order of ${\mathit{g}}^{\mathrm{-}1}$, i.e., ${\mathit{n}}_{\mathrm{fl}}$ exceeds the viscosity of a pure solvent.

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