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It is well known that the similar universal behavior of infinite-size (bulk)systems of different nature requires the same basic conditions: spacedimensionality; number components of order parameter; the type (short- orlong-range) of the intermolecular interaction; symmetry of the fluctuation partof thermodynamical potential. Basic conditions of similar universal behavior ofconfined systems needs the same supplementary conditions such as the number ofmonolayers 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 studyingall these conditions of similar universal behavior for diffusion processes inconfined liquid systems. Special attention was paid to the effects of spatialdispersion and low crossover dimensionality. This allowed us to receivereceiving correct nonzero expressions for the diffusion coefficient at thecritical point and to take into account the specific geometric form of theconfined liquid volume. The problem of 3D \Leftrightarrow 2D dimensionalcrossover was analyzed. To receive a smooth crossover for critical exponents,the Kawasaki-like approach from the theory of mode coupling in criticaldynamics was proposed. This ensured a good agreement between data of computerexperiment and theoretical calculations of the size dependence of the criticaltemperature T_{c}(H) of water in slitlike pores. The width of the quasi-elasticscattering peak of slow neutrons near the structural phase transition in theaquatic suspensions of plasmatic membranes (mesostructures with the typicalthickness up to 10 nm) was studied.

Universality classes and critical phenomena in confined liquid systems