Transport properties and size exclusion effects in wide-pore superficially porous particles.

The effects of hydrodynamic radius on the transport of solute molecules in packed beds of wide-pore superficially porous particles (SPP) are studied using pore-scale simulation. The free molecular diffusion rate varies with radius through the Stokes-Einstein relation. Lattice Boltzmann and Langevin methods are used to model fluid motion and the transport of an ensemble of solute molecules in the fluid, providing statistics on solute concentration, flux, molecule age and residence time, as a function of depth in the SPP. Intraparticle effective diffusion and bed dispersion coefficients are calculated and correlated with the hydrodynamic radius and accessible porosity. The relative importance of convection and diffusion are found to depend on the molecule (tracer) size through the diffusion rate, and convection effects are more significant for larger, slower-diffusing molecules. When larger molecules are utilized, the intraparticle concentration is reduced in proportion to the local particle porosity, leading to a natural definition of the accessible porosity used in size exclusion chromatography (SEC). Although the pore shape is complex, the SEC constant K can be calculated directly from simulation. Simulation demonstrates that the effective diffusion coefficient is elevated near the particle hull, which is largely open to interstitial flow, and decreases with depth into the particle. All molecules studied here have transport access to the entire particle depth, although the accessible volume at a given depth depends on their size. The first passage time into the particle is well predicted by the diffusion rate, but residence time is influenced by convection, shortening the average visit duration. These results are of interest in "perfusion" chromatography where convection is thought to increase separation efficiency for large biomolecules.

Environmental determinants of and impact on childhood asthma by the bacterial community in household dust.

Asthma increased dramatically in the last decades of the 20th century and is representative of chronic diseases that have been linked to altered microbial exposure and immune responses. Here we evaluate the effects of environmental exposures typically associated with asthma protection or risk on the microbial community structure of household dust (dogs, cats, and day care). PCR-denaturing gradient gel analysis (PCR-DGGE) demonstrated that the bacterial community structure in house dust is significantly impacted by the presence of dogs or cats in the home (P = 0.0190 and 0.0029, respectively) and by whether or not children attend day care (P = 0.0037). In addition, significant differences in the dust bacterial community were associated with asthma outcomes in young children, including wheezing (P = 0.0103) and specific IgE (P = 0.0184). Our findings suggest that specific bacterial populations within the community are associated with either risk or protection from asthma.

Dynamic length-scale characterization and nonequilibrium statistical mechanics of transport in open-cell foams.

Nuclear magnetic resonance measurements of scale dependent dynamics in a random solid open-cell foam reveal a characteristic length scale for transport processes in this novel type of porous medium. These measurements and lattice Boltzmann simulations for a model foam structure indicate dynamical behavior analogous to lower porosity consolidated granular porous media, despite extremely high porosity in solid cellular foams. Scaling by the measured characteristic length collapses data for different foam structures as well as consolidated granular media. The nonequilibrium statistical mechanics theory of preasymptotic dispersion, developed for hierarchical porous media, is shown to model the hydrodynamic dispersive transport in a foam structure.

Ellipsoidal particles for liquid chromatography: Fluid mechanics, efficiency and wall effects.

Ellipsoidal particles are investigated as packing media for liquid chromatography using high resolution fluid mechanics and Brownian dynamics simulations. The simulations are conducted with packed capillary columns, as well as beds with periodic boundary conditions (PBCs) to study transport in the absence of wall effects. The performance of ellipsoidal particles is evaluated over a range of aspect ratios. The definition of effective diameter used to compare sphere and ellipsoidal particle performance metrics is presented and discussed along with scaling relationships which are necessary to compare sphere and ellipsoidal particle packs. Ellipsoidal particle packs are found to be inferior to sphere packs using PBCs to study chromatographic dispersion. The separation impedance was calculated with PBCs and shown to be approximately the same with ellipsoidal particles as those of spheres. Efficiency of ellipsoidal packs, as measured by plate height, is lower than spherical particle packs and the pressure drop is higher than sphere packs when using PBCs. However, a smaller wall effect is shown for ellipsoidal particles when packing cylindrical capillaries. Radial variations in packing porosity and in flow within the wall region are smaller for ellipsoidal packings. The minimum reduced plate height and the separation impedance for the packed capillaries clearly demonstrate the advantages of ellipsoidal particles compared to spherical particles. This predicted performance advantage remains to be demonstrated in actual practice.

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.

Simulation of ordered packed beds in chromatography.

A computer simulation of chromatographic dispersion in an ordered packed bed of spheres is conducted utilizing a detailed fluid flow profile provided by the Lattice Boltzmann technique. The ordered configurations of simple cubic, body-centered cubic, and face-centered cubic are employed in these simulations. It is found that zone broadening is less for the fcc structure than the sc and bcc structures and less than a random packed bed analyzed in a previous study in the low flow velocity region used for experimental chromatography. The factors which contribute to the performance of the ordered pack beds are analyzed in detail and found to be dependent both on the nearest surface to surface distance and on the distribution of velocities found in the various packing geometries. The pressure drops of the four configurations are compared and contrasted with the pressure drop from monolithic columns.

Modeling of dispersion in a polymeric chromatographic monolith.

Dispersion in a commercial polymeric monolith was simulated on a sample geometry obtained by direct imaging using high-resolution electron microscopy. A parallelized random walk algorithm, implemented using a velocity field obtained previously by the lattice-Boltzmann method, was used to model mass transfer. Both point particles and probes of finite size were studied. Dispersion simulations with point particles using periodic boundaries resulted in plate heights that varied almost linearly with flow rate, at odds with the weaker dependence suggested by experimental observations and predicted by theory. This discrepancy resulted from the combined effect of the artificial symmetry in the velocity field and the periodic boundaries implemented to emulate macroscopic column lengths. Eliminating periodicity and simulating a single block length instead resulted in a functional dependence of plate heights on flow rate more in accord with experimental trends and theoretical predictions for random media. The lower values of the simulated plate heights than experimental ones are attributed in part to the presence of walls in real systems, an effect not modeled by the algorithm. On the other hand, analysis of transient dispersion coefficients and comparison of lateral particle positions at the entry and exit hinted at non-asymptotic behavior and a strong degree of correlation that was presumably a consequence of preferential high-velocity pathways in the raw sample block. Simulations with finite-sized probes resulted in particle trajectories that frequently terminated at narrow constrictions of the geometry. The amount of entrapment was predicted to increase monotonically with flow rate, evidently due to the relative contributions to transport by convection that carries particles to choke-points and diffusion that dislodges these entrapped particles. The overall effect is very similar to a flow-dependent entrapment phenomenon previously observed experimentally for adenovirus.

Preasymptotic hydrodynamic dispersion as a quantitative probe of permeability.

We interpret a generalized short-time expansion of stochastic hydrodynamic dispersion dynamics in the case of small Reynolds number flow through macroscopically homogenous permeable porous media to directly determine hydrodynamic permeability. The approach allows determination of hydrodynamic permeability from pulsed field gradient spin-echo nuclear magnetic resonance measurement of the short-time effective hydrodynamic dispersion coefficient. The analytical expansion of asymptotic dynamics agrees with experimental NMR data and lattice Boltzmann simulation of hydrodynamic dispersion in consolidated random sphere pack media.

Modeling of flow in a polymeric chromatographic monolith.

The flow behavior of a commercial polymeric monolith was investigated by direct numerical simulations employing the lattice-Boltzmann (LB) methodology. An explicit structural representation of the monolith was obtained by serial sectioning of a portion of the monolith and imaging by scanning electron microscopy. After image processing, the three-dimensional structure of a sample block with dimensions of 17.8 µm × 17.8 µm × 14.1 µm was obtained, with uniform 18.5 nm voxel size. Flow was simulated on this reconstructed block using the LB method to obtain the velocity distribution, and in turn macroscopic flow properties such as the permeability and the average velocity. The computed axial velocity distribution exhibits a sharp peak with an exponentially decaying tail. Analysis of the local components of the flow field suggests that flow is not evenly distributed throughout the sample geometry, as is also seen in geometries that exhibit preferential flow paths, such as sphere pack arrays with defects. A significant fraction of negative axial velocities are observed; the largest of these are due to flow along horizontal pores that are also slightly oriented in the negative axial direction. Possible implications for mass transfer are discussed.

Lamé polynomials, hyperelliptic reductions and Lamé band structure.

The band structure of the Lamé equation, viewed as a one-dimensional Schrödinger equation with a periodic potential, is studied. At integer values of the degree parameter l, the dispersion relation is reduced to the l=1 dispersion relation, and a previously published l=2 dispersion relation is shown to be partly incorrect. The Hermite-Krichever Ansatz, which expresses Lamé equation solutions in terms of l=1 solutions, is the chief tool. It is based on a projection from a genus-l hyperelliptic curve, which parametrizes solutions, to an elliptic curve. A general formula for this covering is derived, and is used to reduce certain hyperelliptic integrals to elliptic ones. Degeneracies between band edges, which can occur if the Lamé equation parameters take complex values, are investigated. If the Lamé equation is viewed as a differential equation on an elliptic curve, a formula is conjectured for the number of points in elliptic moduli space (elliptic curve parameter space) at which degeneracies occur. Tables of spectral polynomials and Lamé polynomials, i.e. band-edge solutions, are given. A table in the earlier literature is corrected.

Tight-binding molecular dynamics study of the role of defects on carbon nanotube moduli and failure.

We performed tight-binding molecular dynamics on single-walled carbon nanotubes with and without a variety of defects to study their effect on the nanotube modulus and failure through bond rupture. For a pristine (5,5) nanotube, Young's modulus was calculated to be approximately 1.1 TPa, and brittle rupture occurred at a strain of 17% under quasistatic loading. The predicted modulus is consistent with values from experimentally derived thermal vibration and pull test measurements. The defects studied consist of moving or removing one or two carbon atoms, and correspond to a 1.4% defect density. The occurrence of a Stone-Wales defect does not significantly affect Young's modulus, but failure occurs at 15% strain. The occurrence of a pair of separated vacancy defects lowers Young's modulus by approximately 160 GPa and the critical or rupture strain to 13%. These defects apparently act independently, since one of these defects alone was independently determined to lower Young's modulus by approximately 90 GPa, also with a critical strain of 13%. When the pair of vacancy defects adjacent, however, Young's modulus is lowered by only approximately 100 GPa, but with a lower critical strain of 11%. In all cases, there is noticeable strain softening, for instance, leading to an approximately 250 GPa drop in the apparent secant modulus at 10% strain. When a chiral (10,5) nanotube with a vacancy defect was subjected to tensile strain, failure occurred through a continuous spiral-tearing mechanism that maintained a high level of stress (2.5 GPa) even as the nanotube unraveled. Since the statistical likelihood of defects occurring near each other increases with nanotube length, these studies may have important implications for interpreting the experimental distribution of moduli and critical strains.

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.