Mesoscopic modeling of flow and dispersion phenomena in fractured solids

AbstractThe problem of hydrodynamic dispersion in porous media is considered and numerical predictions of the mixing degree in a single intersection are provided. The flow field in the intersection and adjacent pores or fractures is calculated using a lattice Boltzmann model for single phase flow. A particle-tracking scheme is used, subsequently, that monitors the migration of solute particles in the area of the intersection taking into account the local flow field and a Brownian field. Mixing is quantified in terms of the probability of solute transfer across the junction into the opposite fracture. To circumvent the problem of large computational times for cases of fast flow compared to diffusion, a lattice Boltzmann advection–diffusion model is used, that offers significant savings on computational time without sacrificing accuracy. It is shown that the solute dispersion in a fracture network is a strong function of the Reynolds number, even if the Peclet number remains constant, due to the extensive recirculation areas that may develop in regions close to the junction

Transport and reaction phenomena in multilayer membranes functioning as bioartificial kidney devices

Classic hemodialysis only provides a limited removal of protein bound uremic toxins (PBUT) in patients with chronic kidney disease. A bioartificial kidney device, BAK, composed of a living cell monolayer of conditionally immortalized proximal tubule epithelial kidney cells (ciPTEC) cultured of hollow fiber polymeric membrane can remove protein bound uremic toxins from the blood in combination with classic hemodialysis. The development and clinical implementation of the BAK requires lots of optimization. This investigation is expensive and time consuming therefore modeling studies could help to optimize experiments and improve its design. In this work, a 3D mathematical model of the BAK is developed. The transport and reaction mechanisms associated with the removal of PBUT indoxyl sulfate are considered and various conditions are simulated. The model describes a single hollow fiber membrane and considers different domains for the blood flow, the membrane, the cell monolayer, and the dialysate region. A mathematical description of the relevant transport and/or reaction mechanisms is provided in each domain, and the corresponding differential equations are solved numerically. Since not all the modeling constants are experimentally available, a parametric study is performed for their quantification, including the active transport kinetics of the toxins through the cell monolayer, in comparison to the passive transport rates by diffusion. The parametric study also provides a background for the extraction of usually unknown quantities, including notably the Organic Anion Transporter (OAT) concentrations, with the support of experimental data. Satisfactory reproduction of experimental findings is achieved, and the role of systemic variables that affect significantly the uremic toxin removal is identified

Critical Evaluation of Macroscopic Theories for Multi-Component Diffusion in Ideal Langmuir Sorbents

Materials research involves many areas for which a proper understanding of multi-component mass transport is essential. Examples include sintering and transport-limited reaction in syntheses. In addition, materials may be principally designed for direct manipulation of mass transport, as in membrane materials. Macroscopic descriptions for mass transport are available, but physical interpretation of related transport parameters is generally not straightforward and often relies on microscopic considerations. We will show that, even for diffusion in a simple ideal Langmuir type lattice, macroscopic theories should be used with caution. Differences in mobilities of dissimilar species can set off percolation behavior, causing the flux of the more mobile species to vanish. Such behavior is, for instance, observed for zeolite membranes and cannot be predicted by commonly accepted macroscopic transport theories. Correlations between successive movements of molecules cause a decrease in the self-diffusion coefficient, DS. For non-equilibrium transport it can be shown that correlation effects in most cases disappear in which case non-equilibrium transport becomes related to the component diffusion coefficient D, instead of the smaller DS