| Understanding transport phenomena and their interplay with structural properties of liquids in inhomogeneous systems is of capital importance in many fields such as nanofluidics, science of materials, physiology and has several technological applications. In this talk, I will discuss how to relate the behavior of fluids in confining geometries to the underlying microscopic degrees of freedom. To this purpose we derive and solve in special cases an approximate kinetic equation for the one particle phase-space distribution function. Within the method, the interactions among the molecules are accounted for by a set of self consistent-fields or generalized forces, which locally depend on the density and velocity distributions of the particles. We discuss the nature of these forces and show their relation to thermodynamic properties and transport coefficients. The theory incorporates hydrodynamic flow, diffusion, surface tension, and the possibility for global and local viscosity variations determined, for instance, by the presence of interfaces and surfaces. Finally, we give explicitly a practical and efficient method to numerically solve the kinetic equation in confining geometries, utilizing concepts both from the Lattice Boltzmann method and density functional theory. Some numerical examples, such as the flow and the inter-species diffusion in a narrow slit-like channel are illustrated. |
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