Flow and mass transport processes through porous materials are ubiquitous in nature and industry. In order to study these phenomena, we developed a computational framework for massively parallel supercomputers based on lattice-Boltzmann and random-walk particle tracking methods. Using this framework, we simulated the flow and mass transport (advection-diffusion problem) in several types of ordered and disordered porous materials. The pore network of the materials was either generated

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... ally (using Jodrey-Tory method) or reconstructed using confocal laser scanning microscopy or scanning electron microscopy. The simulated flow velocity field and dynamics of the random-walk tracer ensemble were used to study the transient and asymptotic behavior of macroscopic transport parameters: permeability, effective diffusion, and hydrodynamic dispersion coefficients. This work has three distinct topics developed and analyzed in four chapters. Each chapter has been published as a separate study. The date of publication and corresponding journal name are denoted at the beginning of each chapter. The first part of this work (Chapter 1) is addressing a timely question of high-performance liquid chromatography on whether particle size distribution of the modern packing materials gives any advantage in terms of separation efficiency. The second part (Chapters 2 and 3) is focused on the effects of dimensionality and geometry of the channels on the transport inside different types of chromatographic supports (particulate packings, monoliths, and pillar arrays). In order to analyze these effects, we recorded transient values of the longitudinal and transverse hydrodynamic dispersion coefficients in unconfined, partially, and fully confined structures and analyzed the time and length scales of the transport phenomena within. In the last p [...]