  It is well known that the similar universal behavior of infinite-size (bulk)
systems of different nature requires the same basic conditions: space
dimensionality; number components of order parameter; the type (short- or
long-range) of the intermolecular interaction; symmetry of the fluctuation part
of thermodynamical potential. Basic conditions of similar universal behavior of
confined systems needs the same supplementary conditions such as the number of
monolayers for a system confinement; low crossover dimensionality, i.e.,
geometric form of restricted volume; boundary conditions on limiting surfaces;
physical properties under consideration. This review paper is aimed at studying
all these conditions of similar universal behavior for diffusion processes in
confined liquid systems. Special attention was paid to the effects of spatial
dispersion and low crossover dimensionality. This allowed us to receive
receiving correct nonzero expressions for the diffusion coefficient at the
critical point and to take into account the specific geometric form of the
confined liquid volume. The problem of 3D \Leftrightarrow 2D dimensional
crossover was analyzed. To receive a smooth crossover for critical exponents,
the Kawasaki-like approach from the theory of mode coupling in critical
dynamics was proposed. This ensured a good agreement between data of computer
experiment and theoretical calculations of the size dependence of the critical
temperature T_{c}(H) of water in slitlike pores. The width of the quasi-elastic
scattering peak of slow neutrons near the structural phase transition in the
aquatic suspensions of plasmatic membranes (mesostructures with the typical
thickness up to 10 nm) was studied.
