In this thesis, the lattice Boltzmann method (LBM) in conjunction with the Lagrangian particle tracking (LPT) algorithm are employed to numerically investigate: (i) the hydraulic responses to a linear array of finite-length nanoposts attached at the bottom wall of square microchannels under viscous flow conditions. Different configurations of the array are considered as these changes can directly contribute to flow pattern deformation. Simulation results indicate that the flow structure strongly depends on nanopost height and space between two adjacent nanoposts in the nanopost line, but not on the Reynolds number in the range examined. If nanoposts, however, are grown far apart from each other, a fully developed velocity profile can be recovered at sufficiently long distance downstream and an empirical correlation for calculating the recovery length is proposed; (ii) the applicability of a three-point gamma probability density function (PDF) found by Voronov et al. (Voronov R.S., VanGordon S.B., Sikavitsas, V.I., Papavassiliou, D.V., Appl. Phys. Let. 2010, 97:024101) for flow-induced stress distributions inside high porosity and randomly structured scaffolds to that in structured porous scaffolds. To do that, PDF of flow-induced stresses in different scaffold geometries are calculated via flow dynamics simulations. It is found that the direction of flow relative to the internal architecture of the scaffolds is important for stress distributions. The stress distributions follow a common distribution within statistically acceptable accuracy, when the flow direction does not coincide with the direction of internal structural elements of the scaffold; (iii) the bulk stress distributions in the pore space of columns packed with spheres. Three different ideally-packed and one randomly-packed configuration of the columns are considered under Darcy flow conditions. The stress distributions change when the packing type changes. In the Darcy regime, the normalized stress distribution for a particular packing type is independent of the pressure difference that drives the flow and presents a common pattern. The three parameter (3P) log-normal distribution is found to describe the stress distributions in the randomly packed beds within statistical accuracy. In addition, the 3P log-normal distribution is still valid when highly porous scaffold geometries rather than sphere beds are examined. It is also shown that the 3P log-normal distribution can describe the bulk stress distribution in consolidated reservoir rocks like Berea sandstone; (iv) the fate and transport of nanoparticles (NPs) as they propagate in porous columns that are packed with spherical particles. In this approach, physical phenomena that result in particle retention and remobilization are represented by a probability for attachment and detachment, respectively. The method is validated with experiments where polymer-stabilized purified multi-walled carbon nanotubes (PMWCNTs) propagate in a column packed with inert glass beads. Comparison of simulation results to the conventional filtration equation leads to the correlation of the simulation input parameters to macroscopically observed parameters, such as attachment and detachment rate constants. Together with the particle kinetics explored by the LBM/LPT simulations with simplicities, transport and kinetics of PMWCNTs in crushed Berea sandstone packed columns are experimentally investigated. The columns were saturated with brine solution, in which the salt concentration was varied from 0 to 10wt%. Experimental results show that the presence of polymer coating effectively eliminates the effects of salt on particle deposition when the salt concentration is less than or equal to 5wt%. At 10wt% salt, when the intensity of Van der Waals attraction strengthens, a drop in particle recovery compared to that of 5wt% is observed. A new filtration equation that accounts for the dynamic change of single collector efficiency as the deposition process advances is proposed.