Application of a bayesian regression method to the estimation of diffusivity in hydrophilic gels

Knowledge of intraparticle reactant and product diffusivities is important for catalytic reaction engineering purposes, including systems where enzymes or microbial cells are entrapped within hydrophilic gel particles. In this work, a Bayesian regression method was applied to estimate diffusivities from dynamic solute uptake experimental data. This method accounted for non-uniformity in the particle sizes. Typically, diffusivities are experimentally determined for these gel matrices by monitoring the dynamic uptake of a solute into several hundred small particles. The diffusivity is then estimated using a mathematical approach based on a single particle case. This approach is only appropriate when variations in radius are small. The Bayesian regression technique was found to be suitable for accounting for the nonlinear effect of radius distribution on diffusivity estimates. It was also possible by this method, to incorporate experimental data for partition coefficients, so that appropriate confidence limits on the diffusivity estimate could be obtained.     

Modeling and simulation of titania formation and growth in temporal mixing layers

Direct numerical simulation of the formation and growth of titanium dioxide nanoparticles in two-dimensional, temporal mixing layers is performed. Titania is produced by the gas-phase hydrolysis of titanium tetrachloride at a temperature of 300 K. The flow field is obtained by solving the Navier–Stokes equations and evolution of the particle field is obtained via a nodal method. The approach approximates the aerosol general dynamic equation and is advantageous in that there are no a priori assumptions regarding the nature of the particle size distribution. The formation and growth of particles up to and including 128 nm in diameter in iso-thermal flows are studied. Simulations are performed for two initial reactant concentration levels. The evolution of the particle field as a function of space, time and size is presented. Results indicate that particle formation and growth is mixing limited and particles grow faster with increasing initial reactant levels. Additionally, the results indicate rather large geometric standard deviations that vary significantly throughout the computational domain.     

Mixing of solid particles of different density in a horizontal batch mixer. Measurement of axial diffusion coefficients

Axial diffusion coefficients of tracer particles were obtained by the method of impulse response. The results show that the diffusion coefficients of the particles of different densities are larger than those of identical particles. The assumption of completely reflecting barriers for the end walls is inapplicable to the mixing of heterogeneous particle systems.     

考虑颗粒凝并情况下充分发展圆管湍流场中的纳米颗粒的迁移(英文)

Numerical simulations of nanoparticle migration in a fully developed turbulent pipe flow are performed.The evolution of particle number concentration,total particle mass,polydispersity,particle diameter and geometric standard deviation is obtained by using a moment method to approximate the particle general dynamic equation.The effects of Schmidt number and Damkhler number on the evolution of the particle parameters are analyzed.The results show that nanoparticles move to the pipe center.The particle number concentration and total particle mass are distributed non-uniformly along the radial direction.In an initially monodisperse particle field,the particle clusters with various sizes will be produced because of coagulation.As time progresses,the particle cluster diameter grows from an initial value at different rates depending on the radial position.The largest particle clusters are found in the pipe center.The particle cluster number concentration and total particle mass decrease with the increase of Schmidt number in the region near the pipe center,and the particles with lower Schmidt number are of many dif-ferent sizes,i.e.more polydispersity.The particle cluster diameter and geometric standard deviation increase with the increase of Damkhler number at the same radial position.The migration properties for nano-sized particles are different from that for micro-sized particles.     

Mean field theory for condensation on aerosols and application to multi-component organic vapours

The timescale is calculated for a particle to equilibrate by vapour condensation from a surrounding volume equal to the volume per particle in an aerosol, and is compared to the timescale to transport vapour by diffusion to neighbouring particle volumes. For practically all aerosols, the diffusive timescale is much smaller, showing that vapour diffusion, and, in the same way heat conduction, ensure that the vapour concentration and temperature in the vapour–gas mixture assume mean field values with which the whole of the aerosol equilibrates. Recent claims that individual particles equilibrate with the mixture are refuted. The concept is applied to obtain equations for the condensation of organic vapours whose equilibrium with condensate is governed by absorption partitioning coefficients together with a Kelvin term at small sizes. These dynamic equations, which contain vapour production and condensational loss terms, have steady-state solutions when these terms are changing slowly with time. Such solutions are obtained for non-volatile and semi-volatile constituents, their difference being defined to be that the equilibrium concentration is small compared to the actual concentration in the non-volatile case. For semi-volatile material, the concentration will generally be maintained at a value close to equilibrium over plane surfaces, so that it cannot contribute to nucleation and growth at small sizes. As for water condensation in the atmosphere, particles need to reach a certain size to be activated for growth by condensation of semi-volatile organics.     

Effect of Polymer Structure on Precursor Diffusion and Particle Formation in Polymer Matrix Nanocomposites

Palladium nanoparticles were synthesized in a semi-crystalline poly[tetrafluoroethylene-co-(perfluoropropyl vinyl ether)] matrix using a chemical infusion technique where a chemical precursor is vaporized and diffused into the polymer matrix. Once in the matrix, the precursor is made to decompose resulting in nanoparticle formation. The effect of polymer structure on precursor diffusion was investigated by comparing the diffusion behavior of the precursor molecules in the as-received polymer as well as in a heat-treated polymer matrix. Results from the diffusivity measurements were interpreted using a free volume model to gain a physical and conceptual understanding of precursor diffusion in fluoropolymers. In addition, transmission electron microscopy analysis was performed on the polymer matrix nanocomposites, and significant differences in particle size and spatial distributions were found between nanocomposites synthesized using as-received and heat-treated polymer matrices. Both precursor diffusivity and particle formation changed as a result of modifications to the polymer matrix suggesting that the particle size and spatial distribution are determined by the structure and morphology of the polymer matrix and are likely linked to the free volume of the polymer.     

A Model of Deposition of Hygroscopic Particles in the Human Lung

Many aerosols in the environment are hygroscopic and grow in size once inhaled into the humid respiratory tract. The deposited amount and the distribution of the deposited particles among airways differ from insoluble particles of the same initial diameter. As particles grow in size, diffusive behavior tends to diminish while impaction and sedimentation effects increase. A multiple-path model for deposition of hygroscopic particles in the respiratory tract was developed for symmetric and asymmetric lung geometries by implementing particle size change in a model of insoluble particle deposition in lungs. Particle growth by molecular diffusion of water vapor to the particle surface was formulated. The growth model included temperature depression, solute, Kelvin, and Fuchs effects. Particle growth during travel time in each lung airway was computed. Average loss efficiency per airway was calculated by incorporating contributions from particles of various sizes acquired in that airway. A mass balance on the number of particles that entered, exited, deposited, or remained suspended was performed per airway to obtain regional and local deposition fractions of particles in the lung. The deposition fractions calculated for salt particles showed a drop for submicrometer particles in the tracheobronchial region and a significant increase in deposition for micrometer particles or larger. Consequently, very few fine and coarse salt particles reached the alveolar region to be available for deposition. Overall, lung deposition of ultrafine particles decreased for salt particles. Deposition for fine and coarse salt particles in the lung was larger than that of insoluble particles of the same initial particle size.     

Predictive simulation of nanoparticle precipitation based on the population balance equation

Nanoparticle precipitation is an interesting process to generate particles with tailored properties. In this study we investigate the impact of various process steps such as solid formation, mixing and agglomeration on the resulting particle size distribution (PSD) as representative property using barium sulfate as exemplary material. Besides the experimental investigation, process simulations were carried out by solving the full 1D population balance equation coupled to a model describing the micromixing kinetics based on a finite-element Galerkin h-p-method. This combination of population balance and micromixing model was applied successfully to predict the influence of mixing on mean sizes (good quantitative agreement between experimental data and simulation results are obtained) and gain insights into nanoparticle precipitation: The interfacial energy was identified to be a critical parameter in predicting the particle size, poor mixing results in larger particles and the impact of agglomeration was found to increase with supersaturation due to larger particle numbers. Shear-induced agglomeration was found to be controllable through the residence time in turbulent regions and the intensity of turbulence, necessary for intense mixing but undesired due to agglomeration. By this approach, however, the distribution width is underestimated which is attributed to the large spectrum of mixing histories of fluid elements on their way through the mixer. Therefore, an improved computational fluid dynamics-based approach using direct numerical simulation with a Lagrangian particle tracking strategy is applied in combination with the coupled population balance-micromixing approach. We found that the full DNS-approach, coupled to the population balance and micromixing model is capable of predicting not only the mean sizes but the full PSD in nanoparticle precipitation.     

The Effect of Size and Concentration of Nanoparticles on the Mass Transfer Coefficients in Irregular Packed Liquid–Liquid Extraction Columns

This investigation explored the effects of nanofluids on mass transfer enhancement using an irregularly packed liquid–liquid extraction column and the chemical systems of water–acetic acid–toluene. SiO₂ nanoparticles with sizes of 10, 30, or 80 nm are dispersed in toluene–acetic acid to produce nanofluids with different volume fractions of 0, 0.01, 0.05, and 0.1 vol.%. The effects of nanoparticle size and concentration on dispersed phase mass transfer coefficient were discussed based on the experimental data. This is for the first time that the effect of nanoparticle size is studied in liquid–liquid extraction systems. It was found that the mass transfer enhancement was more significant in nanofluids with smaller particles. It was also observed that mass transfer coefficient is larger in nanofluids compared to that in dispersed phase without nanoparticles, with a peak enhancement at a nanoparticle volume fraction of 0.05 vol.% for 10-nm particles and 0.01 vol.% for 30- and 80-nm particles. The maximum mass transfer coefficient enhancement was approximately 42% at 0.05% concentration of nanoparticles using smaller particles (10 nm). Finally, a novel correlation for prediction of effective diffusivity in the presence of nanoparticles has been proposed, which is a function of nanoparticle size and its concentration. The main advantage of this approach is that the principal effect of these two parameters is considered in correlation without which the experimental data could not be fitted with an acceptable accuracy.     

Dispersion and Deposition of Spherical Particles from Point Sources in a Turbulent Channel Flow

The dispersion and deposition of particles from a point source in a turbulent channel flow are studied. An empirical mean velocity profile and the experimental data for turbulent intensities are used in the analysis. The instantaneous turbulence fluctuation is simulated as a continuous Gaussian random field, and an ensemble of particle trajectories is generated and statistically analyzed. A series of digital simulations for dispersion and deposition of aerosol particles of various sizes from point sources at different positions from the wall is performed. Effects of Brownian diffusion on particle dispersion are studied. The effects of variation in particle density and particle-surface interaction are also discussed.     

Importance of sample intraparticle diffusivity in investigations of the mass transfer mechanism in liquid chromatography

The effective diffusivity of a nonretained (thiourea) and of a strongly retained (phenol) compounds were measured with the peak parking method in two different columns (both 150 × 4.6 mm) packed with two types of porous particles having different mesopore sizes [5 μm Jupiter‐C₁₈, 320 Å and Luna(2)‐C₁₈, 100 Å]. The eluent was a methanol–water mixture (10/90 v/v) and the temperature 294 K. The effective diffusivity data acquired were used to determine the intraparticle diffusivity, D_p, based on two different diffusion models. The first one assumes that the diffusion fluxes across the particles and in the interparticle volume are additive (parallel diffusion model). The second model was rigorously derived on the basis of the effective medium theory of diffusion (diffusion model) in a binary composite medium (particles + interparticle volume). In both models, it was assumed that the rate of equilibrium between the liquid and the solid phases was infinitely faster than the rate of axial diffusion along the column at zero flow rate. Both models provide physically meaningful intraparticle diffusivity coefficients that take into account the average mesopore size of the particles, their specific surface area, and the retention factor of the analyte. Although the actual effective intraparticle diffusivity remains unknown, these result confirm that the mass transfer resistance due to diffusion through the porous particles has almost negligible effects in reversed phase liquid chromatography due to the importance of surface diffusion. Combining the results of the peak parking method with the h data measured at high linear velocities allows the unambiguous measurement of the film mass transfer and the surface diffusion coefficients. © 2010 American Institute of Chemical Engineers AIChE J, 2011     

Study of Carbon Dioxide Transport in a Samaria Aerogel Catalyst by High Field Diffusion NMR

Pulsed field gradient (PFG) NMR employing a high magnetic field of 17.6 T was used to study self‐diffusion of carbon dioxide in alumina stabilized samaria aerogel, a promising porous catalyst for gas‐phase reactions. Such rare‐earth aerogels exhibit high porosity and surface area with active sites directly integrated into the pore framework. In the reported diffusion NMR studies, application of a high magnetic field was essential for obtaining sufficiently high signal‐to‐noise ratios under conditions of relatively low CO₂ densities in the primarily mesoporous catalyst particles. The diffusion studies were performed with the catalyst that was formed into the following two types of samples: macroscopic monoliths and beds of particles with sizes around 200 μm. The sorbate diffusivity inside the monolith was compared with the corresponding diffusivity in the bed under conditions of fast exchange of CO₂ between the particles and the interparticle voids of the bed. The two‐domain exchange model proposed by Kärger for zeolites was used to describe the latter diffusivity. The reported results are expected to be useful for elucidating an influence of possible transport limitations under reaction conditions in aerogel catalysts.     

Particle diffusion in porous media investigated by dynamic light scattering

Dynamic light scattering as a non-invasive method was applied to the investigation of the diffusion of polystyrene (PS) particles in controlled pore glasses (CPG) as a function of the tracer particle to pore size ratio. These micro-/macro-porous glasses exhibit a bicontinuous randomly distributed microstructure and were saturated with mixtures of water and dimethylsulfoxide (DMSO) to achieve almost perfect optical matching. While the scattering of the glassy matrix vanishes under such conditions the polystyrene tracer particles show a suitable scattering intensity allowing for the implementation of a homodyne detection scheme. In the experiments two distinct diffusion modes can be identified which are related to the diffusion in the voids of the CPG grains and inside the CPG matrix, respectively, where the latter is significantly lowered in comparison to the free bulk diffusion. The diffusion coefficients within the confinement are quantified on basis of the ratio of particle to pore sizes.     

Penetration of Sub-50 nm Nanoparticles Through Electret HVAC Filters Used in Residence

Pleated electret HVAC filters are often used in residence to mitigate the particles that originate both indoors and outdoors. These filters are usually tested with particles larger than 300 nm. However, residential particles can contain a significant amount of nanoparticles with size below 50 nm due to cooking, smoking, cleaning, wood burning, and outdoor infiltration. In order to characterize the nanoparticle removal by electret HVAC filters, penetrations of 3–50 nm silver nanoparticles through five different flat sheet electret media used in commercial residential HVAC filters were tested with face velocities of 0.05, 0.5, and 1.0 m s^–1. Experimental results showed that all media had significantly high penetrations with 0.35–0.8 at the most penetrating particle sizes (MPPSs) for all three velocities, which were in the sizes of 10–30 nm. A model based on single fiber theory for particle penetration predictions was used and compared with the experimental data. Results showed that the model predicted the nanoparticle penetrations very well for all media and all face velocities tested. According to the model, for enhancing the nanoparticle efficiency of the current commercial HVAC filters, the fiber diameter should be reduced or the number of pleats should be increased. However, by doing these, pressure drop and cost may be largely increased. On the other hand, this study found the existing commercial mechanical HVAC filters were much capable for sub–50 nm nanoparticle removal when their minimum efficiency reporting values (MERVs) were larger than 13 and it is concluded mechanical HVAC filters can do a better job than electret ones. However, the quality factor analysis showed electret filters could be regarded as the best filter media for removing particles smaller than 300 nm.

Copyright 2015 American Association for Aerosol Research     

Zur Bewegung feiner Partikeln,die in turbulent strömenden Medien suspendiert sind

Motion of fine grained particles, suspended in turbulent flow . This article considers the motion of particles, suspended in turbulent flow. If the particles are sufficiently small to respond to turbulence, their motion includes stochastic components. Concerning processes like air classification or separation of fine powders the stochastic contribution – characterized by the conception of a particle diffusivity – the particle motion exhibits a detrimental influence. Sharpness of cut and separation efficiency are reduced. The paper aims to present the state of the art in particle diffusion. First, theoretical investigations are reported, attention being focused on the equation of motion of the particle which is the link between the motion of the fluid and the motion of the particle. Then, experimental results are reviewed. The following tendencies can be seen: Particles which response to turbulence of fluid flow show increasing diffusivity with increasing inertia. Field forces like gravity or electrical field forces exhibit a damping effect on diffusivity.     

Large Eddy Simulation of Titanium Dioxide Nanoparticle Formation and Growth in Turbulent Jets

Large eddy simulations (LES) of titanium dioxide nanoparticles in three dimensional turbulent reacting planar jets are performed. The spatio-temporal evolution of the particle field is obtained by utilizing a nodal representation of the general dynamic equation. Gradient-diffusion, Smagorinsky-type subgrid-scale closures are employed to account for the unresolved stresses, fluid-scalar fluxes, and fluid-particle fluxes. The effect of the unresolved fluctuations on coagulation are neglected. Simulations are performed at two different precursor concentration levels. Comparison between results obtained via direct numerical simulation (DNS) and LES is performed to assess the performance of the closures. The LES performs fairly well in predicting the particle concentration as a function of size as well as the mean diameter. Additionally the polydispersity of the LES particle field is greater than that of the DNS. The results also suggest that at as the precursor concentration increases, neglect of the unresolved particle-particle interactions may act to increase the nanoparticle growth-rate.     

Effects of Titanium Dioxide Nanoparticle Aggregate Size on Gene Expression

Titanium dioxide (titania) nanoparticle aggregation is an important factor in understanding cytotoxicity. However, the effect of the aggregate size of nanoparticles on cells is unclear. We prepared two sizes of titania aggregate particles and investigated their biological activity by analyzing biomarker expression based on mRNA expression analysis. The aggregate particle sizes of small and large aggregated titania were 166 nm (PDI = 0.291) and 596 nm (PDI = 0.417), respectively. These two size groups were separated by centrifugation from the same initial nanoparticle sample. We analyzed the gene expression of biomarkers focused on stress, inflammation, and cytotoxicity. Large titania aggregates show a larger effect on cell viability and gene expression when compared with the small aggregates. This suggests that particle aggregate size is related to cellular effects.     

The measurement of gas diffusivity in porous materials by temporal analysis of products (TAP)

The pulsing of argon in a temporal analysis of products (TAP) reactor and reactor modeling of the response curves were used to measure the effective intraparticle diffusivities in porous materials. The diffusivity that can be measured is limited: (1) at the low end by intraparticle diffusion being too slow such that just a small fraction of the pulse gets into the pores to give an indistinguishable tail, which only measures that the diffusivity is smaller than an upper limit and (2) at the high end by intraparticle diffusion being too fast such that it gives a constant concentration in the pores, which only measures that the diffusivity is larger than a lower limit. The limits and range are slightly different for different particle and bed dimensions. A 9 mm long packed bed has a sensitive range of about 300-fold where there are discernible changes in the normalized pulse shape due to diffusivity changes. If small particles of about 50 μm are used, the range is from 1 × 10⁻¹⁰ to 3 × 10⁻⁸ m²/s, and if large particles of about 500 μm are used, the range is from 2 × 10⁻⁹to 5 × 10⁻⁷ m²/s.     

A Quasi‐Steady State Shell and Shrinking Core Approach to the Drying of Porous Particles and an Example of Parameter Identification

A quasi‐steady state shell and shrinking core approach which recognizes heat and mass transfer resistances in both the gas and particle phases for drying of a porous particle is proposed. A mean field model (constant properties) using this approach was embedded in a spreadsheet combined with a genetic algorithm for parameter identification to provide an easy means of characterizing the drying process from drying data. In drying, assuming a mean field, four major parameters are typically unknown: two related to the process (heat and mass transfer coefficients) and two which incorporate porous particle properties (shell thermal conductivity and vapour diffusivity). It is shown how these four parameters may be determined from experimental drying data. The model was applied to data for spouted bed drying of rice. For the particular case studied, external heat transfer was found to be the controlling mode, although resistance to moisture diffusion within the particle is important. The approach presented admits of future refinements to improve its scope and utility.     

Inspiratory Deposition Efficiency of Ultrafine Particles in a Human Airway Bifurcation Model

The inspiratory deposition efficiency of ultrafine particles in a physiologically realistic bronchial airway bifurcation model, approximating the airway generation 3-4 juncture, was computed for different particle sizes, ranging from 1 to 500 nm, under three different flow conditions, representing resting to heavy exercise breathing conditions. For the smallest particle sizes, say between 1 and 10 nm, molecular diffusion is the primary deposition mechanism, as indicated by the inverse relationship with flow rate, except for the highest flow rate where the additional effect of convective diffusion has to be considered as well. For the larger particle sizes, say above 20 nm, the independence from particle size and dependence on flow rate suggests that convective diffusion plays the major role for ultrafine particle deposition in bifurcations. A semiempirical equation for the inspiratory deposition efficiency, m (D, Q), as a function of diffusion coefficient D and flow rate Q, due to the combined effect of molecular and convective diffusion was derived by fitting the numerical data. The very existence of a mixed term demonstrates that molecular and convective diffusion are not statistically independent from each other.