The Spectrum of the Lagrange Velocity Autocorrelation Function in Confined Anisotropic Liquids

Abstract: The results of our further analysis of the thermal hydrodynamic fluctuations in an anisotropic liquid under heterogeneous conditions are represented. The heterogeneity is modeled in the form of a plane-parallel layer, the liquid is considered is taken to be incompressible, and the rapid processes of the angular momentum relaxation to equilibrium are ignored. The extended system of hydrodynamics equations is linearized for small deviations from the equilibrium values. For the case of spontaneous fluctuation fields being present in the system of equations for the velocity and inertia tensor components, the boundary problem solution is found in the form of an expansion in the harmonic functions. The spectral densities of the fluctuation correlation functions are obtained by using the fluctuation dissipation theorem (FDT). A special attention is paid to the correlation functions (CFs) for the velocity field in the anisotropic liquid. The spectrum of the Lagrange velocity autocorrelation function (LVACF) and the collective part of the self–diffusion coefficient of the molecules are determined as functions of the coordinate normal to the confining planes