Recent technological advances enabled with use of nanoscale dimensions, opened a lot of room for various investigations, especially with mass transport through nanoporous media and nanochannels. One of the fields of research is reproducible fabrication of nanofluidic devices with characteristic size from several hundred down to few nanometers, where precise mass exchange and timing are essential. Accurate prediction of the diffusive transport is needed for rational control of physical phenomena. Another field, which is very important, is diffusion within biological system such as extracellular space, consisting of various fibers and particles, which all together affect diffusion process. Despite the increasing focus on nanofluidics in many of these applications, the laws governing molecular transport through nanoscale fluidic channels and porous media have not been fully understood. As the size of the channels and pores is reduced to the molecule size, classical continuum theories fail to predict even the basic characteristics of fluid transport. In chapter 2 we presented fundamentals of diffusion process and fields of application. As presented in this chapter, mass transport by diffusion is crucial process in biological systems. We have notified the basic nonlinear diffusion equations of mass balance, which are further used in finite element analysis. In chapter 3 we employed molecular dynamics simulations to study the effects of confinement and concentration on diffusive transport of glucose in silica nanochannels. It is found that glucose modifies the electrical properties of nanochannel walls and that, below 5 nm in channel height, glucose diffusion coefficient (diffusivity) is significantly reduced. With increasing concentration, the diffusivity is reduced linearly in the bulk, while it is reduced nonlinearly at the interface. The effective diffusivity reduction is related to the interface thickness, and has an unexpected reduction at low concentrations. Simulation results presented in chapter 3, consistent with the experimental observations, suggest that nanoconfinement is the essential cause of the observed altered fluid diffusive transport, not accounted for by classical theories, because of coupling of confinement and concentration effects. In chapter 4 we presented research of reproducible fabrication of nanofluidic devices with characteristic size from several hundred down to few nanometers, where emerging new material properties and transport phenomena made nanofluidic devices appealing for novel biomedical and industrial applications, including drug delivery, where precise mass exchange and timing are essential. Accurate prediction of the diffusive transport is needed for rational design of nanofluidic components. New transport mechanisms are observed whereby channel surface properties begin to dominate over volume properties. Numerical results are obtained using significantly upgraded PAK-T Finite Element Program, with the experimentally determined dependence of diffusion coefficient on concentration. The agreement between the experimental and numerical results allows using this software as a predictive tool for the rational design of nano-channeled devices for drug delivery, reducing the arduous tasks of production and characterization. As presented in Chapter 3, diffusion in nanospace does not strictly obey to Fick’s law, generally used in macro environment. Deviation from this law is due to surface effects, i.e. due to interaction between transported molecules and bounding surfaces. The continuum methods are not applicable at the nanoscale, therefore molecular dynamics approach remains to be used. Development of computational procedures to couple nanoscale, mesoscale and macroscale would be a desirable direction of research to elucidate mass transport occurring in the NDS devices and to aid the NDS design and optimization. A hierarchical modeling approach, which accounts for interface effects on the diffusion coefficient, is introduced in Chapter 5. The model employs molecular dynamics (MD) for calculation scaling functions to reduce the diffusion coefficient corresponding to “bulk” values. With this reduced diffusion coefficient, modeling is performed using the finite element method (FE) within an incremental iterative scheme. The scaling scheme was validated by predicting experimental glucose diffusion through a nanofluidic membrane with a correlation coefficient of 0.999. Comparison with experiments through a nanofluidic membrane showed interface effects to be crucial. In Chapter 6 we first present a new hierarchical multiscale microstructural model for diffusion within composite materials that incorporates both microstructural geometry and the interaction between diffusing particles and solid surfaces. This model, which couples Molecular Dynamics (MD) and the Finite Element (FE) method, is employed to construct a continuum diffusion model based on a novel numerical homogenization procedure. The procedure is general and robust, and evaluates constitutive material parameters of the continuum model. These parameters include the traditional equivalent bulk diffusion coefficients and the equivalent distances from the solid surface accounting for surface interaction effects. To demonstrate the model’s wide-range of applicability, we examined examples of diffusion of glucose within water through various geometrical/material configurations. The microstructural model, numerical homogenization and continuum model offer a new platform for modeling diffusion within complex composite and biological materials, capable of connecting the molecular and continuum scales. Najveći deo istraživanja u prošlosti iz oblasti difuzije je obavljen na nivou makro-skale gde fundamentalni zakoni, kao što su Fikov i Darsijev zakon, opisuju kretanje odgovarajuće supstance kroz proizvoljni medijum. Međutim, na kretanje supstance kroz pore složenih mikrostruktura utiču ne samo granične površine solida usled kojih se menjaju putanje supstance, već i hemijska interakcija između supstance i površina solida. Ova interakcija postaje veoma bitna i može znatno uticati na prosečnu brzinu difuzionog procesa u nano-ograničenom prostoru. Stoga, Fikov zakon ne može dovoljno precizno da opiše difuzioni proces pa se površinska interakcija, koja se javlja na molekulskom nivou, mora uzeti u obzir. Jedan od načina da se odrede karakteristike difuzije sa uticajem površina je molekularna dinamika (MD), pomoću koje je moguće odrediti interakciju između supstance i zida na atomskom i molekulskom nivou. Međutim, zbog velikog broja interakcija koje treba da budu uzete u obzir, MD postaje nepraktična čak i za veoma male domene (reda milimetra). Osim metoda molekularne dinamike, razvijen je veliki broj metoda mehanike kontinuma, kao što je metod konačnih elemenata, u cilju izučavanja poroznih sistema. Kod ovih kontinualnih metoda se uzimaju u obzir termodinamičke karakteristike, ali se ipak fizika uticaja površina ostavlja po strani.