Macroscopic Heterogeneities in Electroosmotic and Pressure-Driven Flow through Fixed Beds at Low Column-to-Particle Diameter Ratio

Effect of Packing Structure Evolution on the Flow Characteristics in a Binary Composite Packed Bed Based on DEM-CFD Method

The evolution of mesoscale structures of particle packing in binary composite packed beds and their effects on flow characteristics and wall effects were investigated using the discrete element method (DEM) and computational fluid dynamics (CFD). The DEM model was used to build a series of randomly mixed packing structures of particles in accordance with the dynamic change of mass ratio between particles in two size ranges, which were then confirmed by the findings of an X-ray tomography (CT) scan. The results show that the packing structure of b25s75 was conducive to reducing the influence of wall effect in packed bed reactors. For b25s75, the dimensionless distance of radial porosity fluctuation from the wall is 0.3705, which is the smallest among the five packing models, indicating that this structure plays a suppressive role on the wall effect. In addition, the uniformity of velocity and temperature distributions in both the radial and axial directions of different packing structures were compared. The standard deviations of radial relative velocity distributions in the packed beds of b100, b75s25, b25s75 and s100 are 0.28, 0.178, 0.139 and 0.156, respectively, indicating that the stacking mode of b25s75 can make the fluid flow and the gas–solid interactions more uniform.

PGSE NMR measurement of the non-local dispersion tensor for flow in porous media

The non-local dispersion tensor provides a fundamental description of velocity correlations and displacement information in a pre-asymptotic dispersive system. Here we describe in detail how PGSE NMR may be used to measure this tensor, outlining the pulse sequences needed for signal superposition, as well as the data analysis procedures. The sequence is inherently two-dimensional, the first dimension giving the displacement resolution, the second giving correlation information. The technique is verified against simulated echo attenuation data from a lattice-Boltzmann simulation.

Modeling wall effects in capillary electrochromatography

A volume averaging technique for modeling electroosmotic and pressure driven flow in microchannels is applied to a packed capillary electrochromatography column. This model can be applied to fluid flow in both porous and open channels and can account for porosity variation in the column due to packing and zeta potential mismatches between the wall and the packing material. Numerical results are presented and compared with experimental results from the literature. Several different porosity models are shown to produce similar concentration profiles and allow the model to reproduce wall effects observed in experimental columns.

Determining NMR flow propagator moments in porous rocks without the influence of relaxation

Flow propagators, used for the study of advective motion of brine solution in porous carbonate and sandstone rocks, have been obtained without the influence of Nuclear Magnetic Resonance (NMR) relaxation times, T1 and T2. These spin relaxation mechanisms normally result in a loss of signal that varies depending on the displacement zeta of the flowing spins, thereby preventing the acquisition of quantitative propagator data. The full relaxation behaviour of the system under flow needs to be characterised to enable the implementation of a true quantitative measurement. Two-dimensional NMR correlations of zeta-T2 and T1-T2 are used in combination to provide the flow propagators without relaxation weighting. T1-zeta correlations cannot be used due to the loss of T1 information during the displacement observation time Delta. Here the moments of the propagators are extracted by statistical analysis of the full propagator shape. The measured displacements (first moments) are seen to correlate with the expected mean displacements for long observation times Delta. The higher order moments of the propagators determined by this method indicate those obtained previously using a correction were overestimated.

Fluid dynamics in capillary and chip electrochromatography

This review is concerned with the phenomenological fluid dynamics in capillary and chip electrochromatography (EC) using high-surface-area random porous media as stationary phases. Specifically, the pore space morphology of packed beds and monoliths is analyzed with respect to the nonuniformity of local and macroscopic EOF, as well as the achievable separation efficiency. It is first pointed out that the pore-level velocity profile of EOF through packed beds and monoliths is generally nonuniform. This contrasts with the plug-like EOF profile in a single homogeneous channel and is caused by a nonuniform distribution of the local electrical field strength in porous media due to the continuously converging and diverging pores. Wall effects of geometrical and electrokinetic nature form another origin for EOF nonuniformities in packed beds which are caused by packing hard particles against a hard wall with different zeta potential. The influence of the resulting, systematic porosity fluctuations close to the confining wall over a distance of a few particle diameters becomes aggravated at low column-to-particle diameter ratio. Due to the hierarchical structure of the pore space in packed beds and silica-based monoliths which are characterized by discrete intraparticle (intraskeleton) mesoporous and interparticle (interskeleton) macroporous spatial domains, charge-selective transport prevails within the porous particles and the monolith skeleton under most general conditions. It forms the basis for electrical field-induced concentration polarization (CP). Simultaneously, a finite and -- depending on morphology -- often significant perfusive EOF is realized in these hierarchically structured materials. The data collected in this review show that the existence of CP and its relative intensity compared to perfusive EOF form fundamental ingredients which tune the fluid dynamics in EC employing monoliths and packed beds as stationary phases. This addresses the (electro)hydrodynamics, associated hydrodynamic dispersion, as well as the migration and retention of charged analytes.

Pore-Scale Dispersion in Electrokinetic Flow through a Random Sphere Packing

The three-dimensional velocity field and corresponding hydrodynamic dispersion in electrokinetic flow through a random bulk packing of impermeable, nonconducting spheres are studied by quantitative numerical analysis. First, a fixed bed with interparticle porosity of 0.38 is generated using a parallel collective-rearrangement algorithm. Then, the interparticle velocity field is calculated using the lattice-Boltzmann (LB) method, and a random-walk particle-tracking method is finally employed to model advection-diffusion of an inert tracer in the LB velocity field. We demonstrate that the pore-scale velocity profile for electroosmotic flow (EOF) is nonuniform even under most ideal conditions, including a negligible thickness of the electrical double layer compared to the mean pore size, a uniform distribution of the electrokinetic potential at the solid-liquid interface, and the absence of applied pressure gradients. This EOF dynamics is caused by a nonuniform distribution of the local electrical field strength in the sphere packing and engenders significant hydrodynamic dispersion compared to pluglike EOF through a single straight channel. Both transient and asymptotic dispersion behaviors are analyzed for EOF in the context of packing microstructure and are compared to pressure-driven flow in dependence of the average velocity through the bed. A better hydrodynamic performance of EOF originates in a still much smaller amplitude of velocity fluctuations on a mesoscopic scale (covering several particle diameters), as well as on the microscopic scale of an individual pore.

Chromatographic and electrophoretic characterization of protein variants

Almost all proteins are expressed in several variants, also known as isoforms. Individual protein variants differ by modifications of the individual amino acid side chains, or the N- or C-terminus. Typical modifications are glycosylation, phosphorylation, acetylation, methylation, deamidation or oxidation. It is of utmost interest to either get a quantitative picture of the variants of a particular protein or to separate the variants in order to be able to identify their molecular structure. Protein variants are present in native as well as in recombinant proteins. In the case of protein production it is interesting, how variants are generated during fermentation, purification processes, storage, and how present individual variants influence the biological activity. This review provides a comparison of chromatographic and electrophoretic separation methods to analyze and to prepare protein variants.

Transition from creeping via viscous-inertial to turbulent flow in fixed beds

This review is concerned with the analysis of flow regimes in porous media, in particular, in fixed beds of spherical particles used as reactors in engineering applications, or as separation units in liquid chromatography. A transition from creeping via viscous-inertial to turbulent flow is discussed based on macro-scale transport behaviour with respect to the pressure drop-flow rate dependence, in particular, the deviation from Darcy's law, as well as direct microscopic data which reflect concomitant changes in the pore-level hydrodynamics. In contrast to the flow behaviour in straight pipes, the transition from laminar to turbulent flow in fixed particulate beds is not sharp, but proceeds gradually through a viscous-inertial flow regime. The onset of this steady, nonlinear regime and increasing role of inertial forces is macroscopically manifested in the failure of Darcy's law to describe flow through fixed beds at higher Reynolds numbers. While the physical reasons for this failure still are not completely understood, it is not caused by turbulence which occurs at Reynolds numbers about two orders of magnitude above those for which a deviation from Darcy's law is observed. Microscopic analysis shows that this steady, nonlinear flow regime is characterized by the development of an inertial core in the pore-level profile, i.e., at increasing Reynolds number velocity profiles in individual pores become flatter towards the center of the pores, while the velocity gradient increases close to the solid-liquid interface. Further, regions with local backflow and stationary eddies are demonstrated for the laminar flow regime in fixed beds. The onset of local fluctuations (end of laminar regime) is observed at superficial Reynolds numbers on the order of 100. Complementary analysis of hydrodynamic dispersion suggests that this unsteady flow accelerates lateral equilibration between different velocities in fixed beds which, in turn, reduces spreading in the longitudial (macroscopic flow) direction.

How does column packing microstructure affect column efficiency in liquid chromatography?

Full three-dimensional computer simulations of the fluid flow and dispersion characteristics of model nonporous chromatographic packings are reported. Interstitial porosity and packing defects are varied in an attempt to understand the chromatographic consequences of the packing microstructure. The tracer zone dispersion is calculated in the form of plate height as a function of fluid velocity for seven model particle packs where particles are selectively removed from the packs in clusters of varying size and topology. In an attempt to examine the consequences of loose but random packs, the velocities and zone dispersion of seven defect-free packs are simulated over the range 0.36< or =epsilon< or =0.50, where epsilon is the interstitial porosity. The results indicate that defect-free loose packings can give good chromatographic efficiency but the efficiency can vary depending on subtle details of the pack. When the defect population increases, the zone dispersion increases accordingly. For a particle pack where 6% of the particles are removed from an epsilon=0.36 pack, approximately 33% of the column efficiency is lost. These results show that it is far more important in column packing to prevent defect sites leading to inhomogeneous packing rather than obtaining the highest density pack with the smallest interstitial void volume.

Optically transparent porous medium for nondestructive studies of microbial biofilm architecture and transport dynamics

We describe a novel and noninvasive, microscopy-based method for visualizing the structure and dynamics of microbial biofilms, individual fluorescent microbial cells, and inorganic colloids within a model porous medium. Biofilms growing in flow cells packed with granules of an amorphous fluoropolymer could be visualized as a consequence of refractive index matching between the solid fluoropolymer grains and the aqueous immersion medium. In conjunction with the capabilities of confocal microscopy for nondestructive optical sectioning, the use of amorphous fluoropolymers as a solid matrix permits observation of organisms and dynamic processes to a depth of 2 to 3 mm, whereas sediment biofilms growing in sand-filled flow cells can only be visualized in the region adjacent to the flow cell wall. This method differs fundamentally from other refractive index-matching applications in that optical transparency was achieved by matching a solid phase to water (and not vice versa), thereby permitting real-time microscopic studies of particulate-containing, low-refractive-index media such as biological and chromatographic systems.

Joule heating induced transient temperature field and its effects on electroosmosis in a microcapillary packed with microspheres

The Joule heating induced transient temperature field and its effect on the electroosmotic flow in a capillary packed with microspheres is analyzed numerically using the control-volume-based finite difference method. The model incorporates the coupled momentum equation for the electroosmotic velocity, the energy equations for the Joule heating induced temperature distributions in both the packed column and the capillary wall, and the mass and electric current continuity equations. The temperature-dependent physical properties of the electrolyte solution are taken into consideration. The characteristics of the Joule heating induced transient development of temperature and electroosmotic flow fields are studied. Specifically, the simulation shows that the presence of Joule heating causes a noticeable axial temperature gradient in the thermal entrance region and elevates a significant temperature increment inside the microcapillary. The temperature changes in turn greatly affect the electroosmotic velocity by means of the temperature-dependent fluid viscosity, dielectric constant, and local electric field strength. Furthermore, the model predicts an induced pressure gradient to counterbalance the axial variation of the electroosmotic velocity so as to maintain the fluid mass continuity. In addition, under specific conditions, the present model is validated by comparing with the existing analytical model and experimental data from the literature.

Numerical analysis of electroosmotic flow in dense regular and random arrays of impermeable, nonconducting spheres

We present a numerical scheme for analyzing steady-state isothermal electroosmotic flow (EOF) in three-dimensional random porous media, involving solution of the coupled Poisson, Nernst-Planck, and Navier-Stokes equations. While traditional finite-difference methods were used to resolve the Poisson-Nernst-Planck problem, the (electro)hydrodynamics has been addressed with high efficiency using the lattice-Boltzmann method. The developed model allows simulation of electrokinetic transport under most general conditions, including arbitrary value and distribution of electrokinetic potential at the solid-liquid interface, electrolyte composition, and pore space morphology. The approach provides quantitative information on a spatial distribution of simulated velocities. This feature was utilized to characterize EOF fields in regular and random, confined and bulk packings of hard (i.e., impermeable, nonconducting) spheres. Important aspects of pore space morphology (sphere size distribution), surface heterogeneity (mismatch in electrokinetic potentials at confining wall and sphere surface), and fluid phase properties (electrical double layer thickness) were investigated with respect to their influence on the EOF dynamics over microscopic and macroscopic spatial domains. Most important is the observation of a generally nonuniform pore-level EOF velocity profile in the sphere packings (even in the thin double layer limit) which is caused by pore space morphology and which is in contrast to the pluglike velocity distribution in a single, straight capillary under the same conditions.

Perspective on concentration polarization effects in electrochromatographic separations

This work illustrates the appearance and electrohydrodynamic consequences of concentration polarization in the particulate and monolithic fixed beds used in capillary electrochromatography and related electrical-field assisted processes. Key property of most porous materials is the co-existence of bulk, quasi-electroneutral macroporous regions and mesoporous compartments which are ion-permselective (due to electrical double-layer overlap) causing different transport numbers for co-ionic and counterionic species, e.g., background electrolyte components, or the analytes. For a cathodic electroosmotic flow the (cation) permselectivity, together with diffusive and electrokinetic transport induces depleted and enriched concentration polarization zones at the anodic and cathodic interfaces, respectively, in dependence of the mobile phase ionic strength and applied electrical fields. At high field strength a secondary, nonequilibrium electrical double layer may be created in the depleted concentration polarization zones of a material stimulating electroosmosis of the second kind. The potential of this induced-charge electroosmosis with respect to nonlinear flow velocities and electrokinetic instability mixing (basically destroying the concentration polarization zones) is analyzed in view of the pore space morphology in random-close packings of spherical-shaped, porous particles and hierarchically structured monoliths. Possible applications based on a fine-tuning of the illustrated effects emerge for microfluidic pumping and mixing, or the intensification of sample recovery in adsorption processes. With this perspective we want to focus the attention on concentration polarization in electrochromatographic systems by presenting and discussing original data acquired on relevant microscopic as well as macroscopic scales, and point towards the importance of related effects in colloid and membrane science.*

Simulation of packed-bed chromatography utilizing high-resolution flow fields: comparison with models

A computer simulation of a section of the interior region of a liquid chromatographic column is performed. The detailed fluid flow profile is provided from a microscopic calculation of low Reynolds number flow through a random packed bed of nonporous spherical particles. The fluid mechanical calculations are performed on a parallel processor computer utilizing the lattice Boltzmann technique. Convection, diffusion, and retention in this flow field are calculated using a stochastic-based algorithm. This computational scheme provides for the ability to reproduce the essential dynamics of the chromatographic process from the fundamental considerations of particle geometry, particle size, flow velocity, solute diffusion coefficient, and solute retention parameters when retention is utilized. The simulation data are fit to semiempirical models. The best agreement is found for the "coupling" model of Giddings and the four-parameter Knox model. These models are verified over a wide range of particle sizes and flow velocities at both low and high velocity. The simulations appear to capture the essential dynamics of the chromatographic flow process for non-dimensional flow velocities (Péclet number) less than 500. Since the same packing geometry is utilized for different particle size studies, the interpretation of the parameter estimates from these models can be extended to the physical column model. The simulations reported here agree very well with a number of experiments reported previously.

Influence of stagnant zones on transient and asymptotic dispersion in macroscopically homogeneous porous media

The role of stagnant zones in hydrodynamic dispersion is studied for creeping flow through a fixed bed of spherical permeable particles, covering several orders of characteristic time and length scales associated with fluid transport. Numerical simulations employ a hierarchical model to cope with the different temporal and spatial scales, showing good agreement with our experimental results on diffusion-limited mass transfer, transient, and asymptotic longitudinal dispersion. These data demonstrate that intraparticle liquid holdup in macroscopically homogeneous porous media clearly dominates over contributions caused by the intrinsic flow field heterogeneity and boundary-layer mass transfer.