Computational investigation of diffusion, flow, and multi-scale mass transport in disordered and ordered materials using high-performance computing

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 algorithmically (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 part of this work (Chapter 4) we investigated the influence of the shell thickness and diffusivity on separation efficiency of the core--shell packings. Based on the simulation results, we extended the Giddings theory of coupled eddy dispersion and confirmed the validity of the Kaczmarski-Guiochon model of interparticle mass-transfer. Overall, this study extends the understanding of the connection of geometry and morphology of the porous materials with their macroscopic transport parameters

On the two-domain equations for gas chromatography.

We present an analysis of gas chromatographic columns where the stationary phase is not assumed to be a thin uniform coating along the walls of the cross section. We also give an asymptotic analysis assuming that the parameter {beta} = KD{sup II}{rho}{sup II}/D{sup I}{rho}{sup I} is small. Here K is the partition coefficient, and D{sup i} and {rho}{sup i}, i = I, II are the diffusivity and density in the mobile (i = I) and stationary (i = II) regions

High-Performance Computing of Flow, Diffusion, and Hydrodynamic Dispersion in Random Sphere Packings

This thesis is dedicated to the study of mass transport processes (flow, diffusion, and hydrodynamic dispersion) in computer-generated random sphere packings. Periodic and confined packings of hard impermeable spheres were generated using Jodrey–Tory and Monte Carlo procedure-based algorithms, mass transport in the packing void space was simulated using the lattice Boltzmann and random walk particle tracking methods. Simulation codes written in C programming language using MPI library allowed an efficient use of the high-performance computing systems (supercomputers). The first part of this thesis investigates the influence of the cross-sectional geometry of the confined random sphere packings on the hydrodynamic dispersion. Packings with different values of porosity (interstitial void space fraction) generated in containers of circular, quadratic, rectangular, trapezoidal, and irregular (reconstructed) geometries were studied, and resulting pre-asymptotic and close-to-asymptotic hydrodynamic dispersion coefficients were analyzed. It was demonstrated i) a significant impact of the cross-sectional geometry and porosity on the hydrodynamic dispersion coefficients, and ii) reduction of the symmetry of the cross section results in longer times to reach close-to-asymptotic values and larger absolute values of the hydrodynamic dispersion coefficients. In case of reconstructed geometry, good agreement with experimental data was found. In the second part of this thesis i) length scales of heterogeneity persistent in unconfined and confined sphere packings were analyzed and correlated with a time behavior of the hydrodynamic dispersion coefficients; close-to-asymptotic values of the dispersion coefficients (expressed in terms of plate height) were successfully fitted to the generalized Giddings equation; ii) influence of the packing microstructural disorder on the effective diffusion and hydrodynamic dispersion coefficients was investigated and clear qualitative corellation with geometrical descriptors (which are based on Delaunay and Voronoi spatial tessellations) was demonstrated

Microchip HPLC: Experimental investigation of separation efficiency, column characteristics, and coupling with mass spectrometry

This work deals with separation efficiency and column characteristics of particle-packed HPLC microchips. The impact of conduit geometry on the chromatographic performance of typical particulate microchip packings is investigated. For this purpose, HPLC/UV-microchips with separation channels of quadratic, trapezoidal, or Gaussian cross-section were fabricated by direct laser ablation and lamination of multiple polyimide layers and then slurry-packed with either 3 or 5 µm spherical porous C8-silica particles under optimized packing conditions. Experimentally determined plate height curves for the empty microchannels are compared with dispersion coefficients from theoretical calculations. Packing densities and plate height curves for the various microchip packings are presented and conclusively explained. 3 µm packings display a high packing density irrespective of their conduit geometries and their performance reflects the dispersion behaviour of the empty channels. Dispersion in 5 µm packings correlates with the achieved packing densities, which are limited by the number and accessibility of corners in a given conduit shape. Interparticle void volumes and porosities of packed capillaries and of commercially available, analytical, reversed-phase HPLC columns have been determined using intraparticle Donnan exclusion of a small, unretained, co-ionic tracer (nitrate ions). The operational domain of this approach has been characterized for bare silica, reversed-phase, and strong cation-exchange materials with different particle sizes, intraparticle pore sizes, and construction (fully porous or core-shell) in dependence of the mobile phase ionic strength. At low buffer concentrations nitrate ions are completely electrostatically excluded from the intraparticle mesopore space, which is reflected by a plateau region in the elution curves. The elution volume in the plateau region equals the interparticle void volume. Clearly defined plateau regions were observed for all columns, even those densely packed with core-shell and sub-2 µm particles, enabling the accurate determination of interparticle porosities to three decimal places in a fast and convenient way. Interparticle porosities agree well with those analyzed by inverse size-exclusion chromatography (ISEC). Limitations to the use of Donnan exclusion (electrostatic exclusion) and ISEC (mechanical exclusion) arise as either type of exclusion becomes noticeable also in the cusp regions between particles, or as the intraparticle pores are so large that complete electrostatic and size exclusion are difficult to realize. Dynamic changes in mobile phase composition during high performance liquid chromatography (HPLC) gradient elution coupled to mass spectrometry (MS) sensitively affect electrospray modes. The impact of the eluent composition on spray stability and MS response by infusion and injection experiments with a small tetrapeptide in water-acetonitrile mixtures was investigated. The employed HPLC/ESI-MS configuration uses a microchip equipped with enrichment column, separation column, and make-up flow (MUF) channel. One nano pump is connected to the separation column, while a second one delivers solvent of exactly inverted composition to the MUF channel. Both solvent streams are united behind the separation column, before the ESI tip, such that the resulting electrosprayed solution always has identical composition during a gradient elution. Analyte peak parameters without and with MUF compensation are determined and discussed with respect to the electrospray mode and eluent composition. The post-column MUF significantly improves spray and signal stability over the entire solvent gradient, without compromising the performance of the HPLC separation column. It can also be conveniently implemented on microchip platforms

Advection-diffusion in inertial flow through periodically converging-diverging tubes

A direct numerical simulation of advection-diffusion in a sinusoidal tube was carried out using the commercial finite-volume code STAR-CD. The Reynolds numbers varied from Re = 0.1 to Re = 14.5. At the larger Reynolds numbers, steady-state eddies formed in the diverging sections and significantly influenced the macroscale dispersion. Long tailing was observed in the breakthrough curves. The results were compared to a 1-dimensional source-sink model using the semi-analytical solute transport code STAMMT-L. It was found that the results were generally described by both a single-rate model and a lognormal multi-rate model. It was observed that the velocity distribution within the inertial regime had significant influence on dispersion, even at weak inertial flowrates which did not experience flow separation

Microfluidic Pumping With Surface Tension Force and Magnetohydrodynamic Drive

Micropumping is difficult to design and control as compared to their macro-scale counterparts due to the size limitation. The first part of this dissertation focuses on micropumping with surface tension forces. A simple, single-action, capillary pump/valve consisting of a bi-phase slug confined in a non-uniform conduit is described. At low temperatures, the slug is solid and seals the conduit. Once heated above its melting temperature, the liquid slug moves spontaneously along a predetermined path due to surface tension forces imbalance. This technique can be easily combined with other propulsion mechanisms such as pressure and magnetohydrodynamics (MHD). The second part of this dissertation focuses on MHD micropumping, which provides a convenient, programmable means for propelling liquids and controlling fluid flow without a need for mechanical pumps and valves. Firstly, we examined the response of a model one dimensional electrochemical thin film to time-independent and time-dependent applied polarizations, using the Nernst-Planck (NP) model with electroneutrality and the Poisson-Nernst-Planck (PNP) model without electro -neutrality, respectively. The NP model with well designed boundary conditions was v developed, proved capable of describing the bulk behavior as accurate as the full PNP model. Secondly, we studied the MHD propelled liquid motion in a uniform conduit patterned with cylinders. We proved equivalence in MHD and pressure driven flow patterns under certain conditions. We examined the effect of interior obstacles on the electric current flow in the conduit and showed the existence of particular pillar geometry that maximizes the current. Thirdly, we looked at MHD flow of a binary electrolyte between concentric cylinders. The base flow was similar to the pressure driven flow in the same setup. The first order perturbation fields, however, behave differently as the traditional Dean’s flow. We carried out one-dimensional linear stability analysis for the unbounded small gap situation and solved it as an eigenvalue problem. Two-dimensional nonlinear simulation was performed for finite gap size or bounded situations. We observed strong directionality of the applied electric field for the onset of stability. Results in this study could help enhance the stability of the system or introduce secondary motion depending on the nature of the applications

A reduced order model for the study of asymmetries in linear gas chromatography for homogeneous tubular columns.

In gas chromatography, a chemical sample separates into its constituent components as it travels along a long thin column. As the component chemicals exit the column they are detected and identified, allowing the chemical makeup of the sample to be determined. For correct identification of the component chemicals, the distribution of the concentration of each chemical along the length of the column must be nearly symmetric. The prediction and control of asymmetries in gas chromatography has been an active research area since the advent of the technique. In this paper, we develop from first principles a general model for isothermal linear chromatography. We use this model to develop closed-form expressions for terms related to the first, second, and third moments of the distribution of the concentration, which determines the velocity, diffusion rate, and asymmetry of the distribution. We show that for all practical experimental situations, only fronting peaks are predicted by this model, suggesting that a nonlinear chromatography model is required to predict tailing peaks. For situations where asymmetries arise, we analyze the rate at which the concentration distribution returns to a normal distribution. Numerical examples are also provided

Adipic Acid Sonocrystallization in Continuous Flow Microchannels

Crystallization is widely employed in the manufacture of pharmaceuticals during the intermediate and final stages of purification and separation. The process defines drug chemical purity and physical properties: crystal morphology, size distribution, habit and degree of perfection. Particulate pharmaceuticals are typically manufactured in conventional batch stirred tank crystallizers that are still inadequate with regard to process controllability and reproducibility of the final crystalline product. Variations in crystal characteristics are responsible for a wide range of pharmaceutical formulation problems, related for instance to bioavailability and the chemical and physical stability of drugs in their final dosage forms. This thesis explores the design of a novel crystallization approach which combines in an integrated unit continuous flow, microreactor technology, and ultrasound engineering. By exploiting the various benefits deriving from each technology, the thesis focuses on the experimental characterization of two different nucleation systems: a droplet-based system and a single-phase system. In the former, channel fouling is avoided using a carrier fluid to segment the crystallizing solution in droplets, thus avoiding the contact with the walls. In the latter channel blockage is prevented using larger channel geometries and employing higher flow rates. The flexibility of the developed setup also allows performing stochastic nucleation studies to estimate the nucleation kinetics under silent and sonicated conditions. The experiments reveal that very high nucleation rates, small crystal sizes, narrow size distributions and high crystal yields can be obtained with both setups when the crystallizing solution is exposed to high pressure field as compared to silent condition. It is concluded that transient cavitation of bubbles and its consequences are a significant mechanism for enhancing nucleation of crystals among several proposed in the literature. A preliminary study towards the development and design of a growth stage is finally performed. Flow pulsation is identified as a potential method to enhance radial mixing and narrow residence time distribution therefore achieving optimal conditions for uniform crystal growth. The results suggest that increasing values of Strouhal number as well as amplitude ratio improve axial dispersion. Helically coiled tubes are identified as potential structures to further improve fluid dynamic dispersion

Hydrodynamic and mass transfer study of micro-packed beds in sigle-and two-phase flow

Les micros-lit fixes sont des milieux poreux miniaturisés ralliant les avantages à la fois des microréacteurs et des lits fixes, comme par exemple en terme de rapport surface/volume très élevé conduisant à des taux de transfert de chaleur et de matière intensifiés. Par conséquent, la caractérisation hydrodynamique des micro-lits fixes est nécessaire afin d’appréhender de manière objective les phénomènes de transfert et les modes de contact entre phases. Ensuite l'importance des micro-lits fixes est mise en évidence tandis que les approches pour construire des bases de recherche sur les micro-lits fixes y sont explicitées. Notre recherche commence par l'étude des régimes d'écoulement, des transitions de régime d'écoulement de la multiplicité de l’hydrodynamique et du transfert de matière liquide-solide dans les micro-lits fixes. Cette étude est réalisée au moyen d’une méthode de visualisation par microscopie optique à la paroi et le traitement d’image qui s’en suit pour la partie hydrodynamique et d’une méthode électrochimique basée sur l’oxydoréduction du couple complexes ferri/ferreux hexacyanure pour la partir sur le transfert de matière. Les résultats de perte de charge et de rétention de liquide ont été discutés par rapport aux régimes d’écoulement mis en place et des observations pariétales rendues possibles par microscopie optique. L'effet de la taille des particules et de la géométrie du canal sur les transitions de régimes d’écoulement, le comportement transitoire et le phénomène d'hystérèse ont également été abordés. Finalement, les résultats des expériences hydrodynamiques ont été obtenus en faisant face à de nombreux défis pour lesquels nous avons formulé de nombreuses recommandations en vue d’investigations futures. La détermination expérimentale du coefficient de transfert de masse liquide-solide (kLS) par la technique électrochimique a été effectuée dans un micro-lit fixe rempli de couches de particules de graphite non-sphériques servant de cathode et d'anode. Les expériences ont été réalisées pour un écoulement monophasique en régime de diffusion limitée. Finalement, la correspondance de valeurs de kLS avec les corrélations construites sur la base d’études sur les lits fixes à l’échelle macroscopique a été discutée.Micro-packed beds are miniaturized packed beds having the advantages of both microreactors (high surface-to-volume ratios leading to intensified heat and mass transfer rates, increased safety, etc.) and packed beds (effective contact between the phases) that have the potential to be successfully employed for purposes such as catalyst screening and production of hazardous materials. To assess this potential, hydrodynamic characterization of micro-packed beds is necessary as they address the actual flow phenomena and provide suggestions to improve the contacting patterns between phases for enhanced performances. This work starts with a brief review on process intensification via microreactors. Then the importance of micro-packed beds is highlighted while the approaches to build research foundations on micro-packed beds are discussed. Our research begins by studying the flow regimes, transitions in flow regime and hydrodynamic multiplicity in micro-packed beds mostly by means of microscopic wall visualization and image processing. Results on pressure drop and liquid holdup have been obtained and discussed in terms of flow regimes and wall-flow image analyses. In addition, residence time distributions of the liquid in micro-packed beds have been obtained according to two techniques, by an impulse tracing method (electrolyte tracer injection) and wall visualization with optical microscopy. The effect of particle size and channel geometry (circular vs. square) has also been investigated in terms of flow regime transitions, transient behavior and hysteresis. Finally, challenges and recommendations thereof to surpass the many difficulties encountered are methodically explained to facilitate future investigations. Experimental determination of liquid-solid mass transfer coefficient (kLS) via a linear polarization method was also carried out in a micro-packed bed filled with layers of non-spherical graphite particles serving as cathode and anode for the Redox ferri/ferrocyanide electrochemical reaction. Experiments concerned single-phase liquid flow within the diffusion-limited regime. Particle size analysis and image processing were used to evaluate deviations from spherical geometry of the graphite particles to determine liquid-solid mass transfer coefficient. Finally, the correspondence of kLS values with macro-scale packed bed correlations was discussed