On the relationship between band broadening and the particle-size distribution of the packing material in liquid chromatography: theory and practice

The influence of the particle size distribution (PSD) on the band broadening and the efficiency of packed columns is investigated on both theoretical and practical viewpoints. Each of the classical contributions to mass transfer kinetics, those due to longitudinal diffusion, eddy dispersion, and solid–liquid mass transfer resistance are measured and analyzed in terms of their expected and observed intensity as a function of the PSD of mixtures of the commercially available packing materials, 5 and 3 μm Luna-C₁₈(2) particles (Phenomenex, Torrance, CA, USA). Six 4.6 mm × 150 mm columns were packed with different mixtures of these two materials. The efficiencies of these columns were measured for a non-retained and a retained analytes in a mixture of acetonitrile and water. The longitudinal diffusion coefficient was directly measured by the peak parking method. The solid–liquid mass transfer coefficient was measured from the combination of the peak parking method, the best model of effective diffusion coefficient and the actual PSDs of the different particle mixtures measured by Coulter counter experiments. The eddy diffusion term was measured according to a recently developed protocol, by numerical integration of the peak profiles. Our results clearly show that the PSD has no measurable impact on any of the coefficients of the van Deemter equation. On the contrary and surprisingly, adding a small fraction of large particles to a batch of small particles can improve the quality of the packing of the fine particles. Our results indirectly confirm that the success of sub-3 μm shell particles is due to the roughness of their external surface, which contributes to eliminate most of the nefarious wall effects.     

A study on performance characteristics of granular-media trickling filters

Mass transfer within microbial films is described using Monod type biological kinetics in terms of the properties of packing material and the feed solution. For this purpose computer techniques have been first developed for the numerical evaluation of the normalized biofilm mathematical model. A second-order partial differential equation describing the mechanism of dispersion phenomena inside the liquid layer is then solved to determine the mass transfer coefficient. The application of the theory to experimental data reported in literature has also been demonstrated using the values of mass transfer coefficients and the computer programs developed.     

Shell-side mass transfer of hollow fibre modules in osmotic distillation process

The effect of packing density of hollow fibre modules on mass transfer in the shell side of osmotic distillation process was studied. The osmotic distillation experiments were carried out with several modules of the packing densities ranging from 30.6 to 61.2%. It was found that the Reynolds number was a function of packing density and packing density affected mass transfer performance. The shell-side mass transfer coefficient increased with the brine velocity. The membrane permeability can be predicted from the experimental flux at the maximum brine velocity. The mass transfer correlation was proposed in order to determine the shell-side mass transfer coefficient in the randomly packed modules for osmotic distillation process. The empirical correlation proposed was fitted to the experimental results and it was found that the mass transfer coefficients calculated from the proposed correlation were in good agreement with those from the experimental data. Comparison of the results obtained from the proposed correlation with other correlations in the literature was discussed.     

Effect of colloidal particle size on adsorbed monodisperse and bidisperse monolayers

Coating hydrogel films or microspheres by an adsorbed colloidal shell is one synthesis method for forming colloidosomes. The colloidal shell allows control of the release rate of encapsulated materials, as well as selective transport. Previous studies found that the packing density of self-assembled, adsorbed colloidal monolayers is independent of the colloidal particle size. In this paper we develop an equilibrium model that correlates the packing density of charged colloidal particles in an adsorbed shell to the particle dimensions in monodisperse and bidisperse systems. In systems where the molar concentration in solution is fixed, the increase in adsorption energy with increasing particle size leads to a monotonic increase in the monolayer packing density with particle radius. However, in systems where the mass fraction of the particles in the adsorbing solutions is fixed, increasing particle size also reduces the molar concentration of particles in solution, thereby reducing the probability of adsorption. The result is a nonmonotonic dependence of the packing density in the adsorbed layer on the particle radius. In bidisperse monolayers composed of two particle sizes, the packing density in the layer increases significantly with size asymmetry. These results may be utilized to design the properties of colloidal shells and coatings to achieve specific properties such as transport rate and selectivity.     

Knudsen effect on plasma-particle mass transfer. I. Formulation and application to self-diffusion

The Knudsen effect on mass transfer between a plasma gas and a small particle is investigated. A predictive model is developed by incorporating the Z-potential approach into the jump theory. The predictions of the model are explored through a case study. The results indicate that the Knudsen effect is significant and depends strongly on the particle size and the surface conditions. The plasma and the particle surface temperatures are also found to be determining factors. Under certain conditions, it is observed that the Knudsen effect can enhance the plasma-particle mass transfer, contrary to the predictions of the previous near-isothermal models.     

Aggregation phenomena in the suspension polymerization of VCM

In the suspension polymerization of VCM, insoluble polymer particles are formed inside the monomer droplets. The growth and aggregation of these particles are responsible for important polymer properties, such as porosity. It is well established that the most characteristic polymer particles, the primary particles, are of a narrow distribution with a size (diameter) ranging from 0.10–0.20 m. This work studied the formation of primary particles based on the aggregation phenomena that take place inside a monomer droplet. This was done by formulating a population balance equation, which was based on the following considerations: a) polymerization occurs in both the monomer and the polymer phases; b) there is continuous formation of the basic particles in the monomer phase; c) the growth of the polymer particles occurs as a result of both polymerization in the polymer phase and aggregation of the particles; d) the colloidal properties of the particles that are responsible for the aggregation phenomena were considered to be the net result of attraction and repulsion energies.It was shown that for particles carrying a constant charge it was not possible to predict the formation of primary particles of size 0.10–0.20 m. The particle size distribution had a mode diameter equal to the diameter of the basic particles. Consequently, the particle charge was allowed to vary in a way proportional to the particle radius raised to a power coefficient. For values of the coefficient greater than zero, i. e., when the particle charge increased during polymerization, the aggregation of the basic particles was efficient enough to result in the formation of large primary particles.     

固体粒子对板式膜吸收过程的传质强化

分别采用纯CO2-去离子水和不同浓度的NaOH溶液为实验体系,在板式膜器中研究了第三相固体粒子对膜吸收过程传质效果的影响．分别考察了在不同粒子种类、搅拌转速、传质体系、化学反应强度、膜孔隙率等因素下固体粒子对传质强化的影响．结果表明,随着粒子固含率的增大,传质系数和增强因子均有所提高,当粒子固含率增大到一定范围后,传质系数和增强因子的变化趋于平缓．在固含率一定的条件下,不同种类的固体粒子对膜吸收过程的强化效果随着固体粒子密度的增加而减小．传质系数随着搅拌转速的增大而增大,但高搅拌转速下固体粒子的强化作用减弱．膜吸收过程的传质系数和增强因子随着化学反应强度的增强而增加．随着粒子固含率的增大,不同膜孔隙率对传质效果的差异减小,且孔隙率越小,固体粒子对膜吸收传质过程的强化效果越好．其中,对于纯CO2-去离子水体系,当孔隙率为20％,粒子固含率为1．5gL^（-1）时,固体粒子的加入可使传质系数提高1．45倍,增强因子可达2．45．     

Pore structure of the packing of fine particles

This paper presents a numerical study of the pore structure of fine particles. By means of granular dynamics simulation, packings of mono-sized particles ranging from 1 to 1000 microm are constructed. Our results show that packing density varies with particle size due to the effect of the cohesive van der Waals force. Pores and their connectivity are then analysed in terms of Delaunay tessellation. The geometries of the pores are represented by the size and shape of Delaunay cells and quantified as a function of packing density or particle size. It shows that the cell size decreases and the cell shape becomes more spherical with increasing packing density. A general correlation exists between the size and shape of cells: the larger the cell size relative to particle size, the more spherical the cell shape. This correlation, however, becomes weaker as packing density decreases. The connectivity between pores is represented by throat size and channel length. With decreasing packing density, the throat size increases and the channel length decreases. The pore scale information would be useful to understand and model the transport and mechanical properties of porous media.     

Bioreactor design studies for a hydrogen-producing bacterium

Carbon monoxide (CO) can be metabolized by a number of microorganisms along with water to produce hydrogen (H₂) and carbon dioxide. National Renewable Energy Laboratory researchers have isolated a number of bacteria that perform this so-called water-gas shift reaction at ambient temperatures. We performed experiments to measure the rate of CO conversion and H₂ production in a trickle-bed reactor (TBR). The liquid recirculation rate and the reactor support material both affected the mass transfer coefficient, which controls the overall performance of the reactor. A simple reactor model taken from the literature was used to quantitatively compare the performance of the TBR geometry at two different size scales. Good agreement between the two reactor scales was obtained.     

An Experimental Study of the Kinetics of Particle Deposition in a Wall-Jet Cell Using Total Internal Reflection Microscopy

The deposition of polystyrene latex particles of 0.46 μm diameter was studied in situ using a wall-jet cell in combination with total internal reflection microscopy. The particles were deposited onto an indium tin oxide surface in a laminar flow field for up to 13 h. The initial particle flux was found to be mass-transfer-controlled. It was shown that one period of the time-dependent deposition rate period was of first-order nature. The effective particle transfer coefficient during this period appeared to be correlated inversely to the wall shear rate. With the help of three characteristic empirical constants, one of them being a mass transfer coefficient, the overall deposition process was described by a model equation. The concentration dependency was elucidated using a Langmuir-type pseudoisotherm. Copyright 2000 Academic Press.     

Optimization of large-scale chromatography for biotechnological applications

An economic evaluation of a chromatographic separation is discussed. The effects of particle size, cycle time, solvent, and column costs are analyzed. With small particles (<20 µm), the cost of the packing can be as much as 99% of the total cost of the process, whereas with large particles (>60 µm), resin costs are less than half of the total. A strong optimum is found between 20–40 µm for maximum productivity, using both Gaussian models and the mass transfer model of Lapidus and Amundson to generate peaks. A new compilation of resin costs, column costs, and pump costs is given.

     

Modeling of supercritical fluid extraction of phenanthrene from clayey soil

The supercritical fluid (SFC) extraction efficiency of phenanthrene from clayey soils was modeled. The model accounts for effective diffusion of the phenanthrene in the solid pores, axial dispersion in the fluid phase, and external mass transfer to the fluid phase from the particle surface. This model, involving partial differential equations, was solved using the finite difference. The model showed the relationship between diffusivity, mass transfer coefficient, and properties of porous media (clay texture). The porous media analysis was performed with a microscope and by an image analysis. The proposed model compared well with the experimental data available in the literature.     

Preparation of TiO2 Powder by Modified Two-Stage Hydrolysis

Nano-sized TiO₂ powders were synthesized by modified hydrolysis reaction using two-stage treatments of acid/base catalyst. Using an acidic catalyst, the primary particle size of assynthesized TiO₂ was smaller than using basic catalyst, but rutile ratio and the particle size were increased after heat treatment due to the dense packing of particles. However, in the synthesized TiO₂ powder using a basic catalyst persist the anatase phase and a loosely aggregation of particle after heat treatment. It was found that the catalyst used in the first stage determines the primary particle size. However the phase, the packing density and degree of dispersion of TiO₂ powder were determined by the secondly applied catalyst. Therefore, the addition sequence of catalysts is the most important key to prepare fine powders for photocatalytic use and solar cell. In this study, an acid treatment followed by a base is suggested as best route to obtaining fine size and distribution of particles and high content of anatase phase.     

Transport through self-assembled colloidal shells (colloidosomes)

Colloidosomes, namely, microcapsules coated by a colloidal shell, have been widely studied as potential carriers of active compounds for various applications. The colloidal shell differs from the shells of other ‘somes’ (liposomes, polymersomes) since it is a composite material with an impenetrable phase—the particles, and a penetrable one—the voids or pores between them. Recent analysis shows that in the shells composed of monodisperse and charged particles, the maximal volume fraction of colloids in the self-assembled layer depends on the size ratio between the particle's hard-sphere radius and the effective radius, which includes the range of repulsive electrostatic interactions. Thus, somewhat counter-intuitively, the density of particles in the shell increases with increasing particle radius. However, mixing particle sizes can lead to highly packed shells where the impenetrable phase volume fraction approaches 100%. The diffusional flux through the colloidal shell is highly sensitive to the packing density (or particle volume fraction); this parameter sets the average size of the pores, their distribution through the shell, and their tortuosity. However, while in thick multi-layer shells the flux increases with increasing particle size, in the case of monolayer-thick shells there is no apparent dependence of the flux on the colloid dimensions.     

α-Al2O3与Co-Ni合金电化学共沉积动力学模型

在经典复合电沉积机理基础上,考虑到粒子与电极表面之间的多种作用力,以吸附强度来表征粒子与电极表面的作用力大小,根据粒子在电极表面的临界吸附强度,把粒子的吸附分为有效吸附和非有效吸附.当吸附强度大于临界吸附强度时,粒子能被有效吸附嵌入到沉积层中,粒子被有效吸附的概率和平均吸附强度有关.建立了相应的复合电沉积动力学模型.该模型在α-Al2O3与Co-Ni合金的复合共沉积体系中,在电流密度为1～20 A•dm2范围内得到了验证.通过数学模型和实验结果研究了电流密度对粒子沉积量φc、吸脱附常数K、有效吸附概率P和平均吸附强度的影响规律.     

Numerical simulation and experimental verification of particle coagulation dynamics for a pulsed input

Mathematical simulation of particle coagulation dynamics was carried out using improved sectional modeling techniques for a system with a pulsed input of primary particles. The methodological improvement included the modification of the size density function based on a realistic assumption of particle size distributions, the application of a new and comprehensive curvilinear collision model, and special adjustment for the mass transfer of a doublet of particles that were very different in size. The simulation results demonstrated that the rectilinear model over-predicted the rate of particle coagulation and that the degree of over-prediction increased as the particles increased in size and the system became more heterogeneous. The coagulation rate increased remarkably as the fractal dimension of the particle aggregates decreased. The curvilinear model and the fractal scaling relationship in place of the rectilinear model and the Euclidean sizing geometry are two important modifications to the conventional Smoluchowski modeling approach. However, both modifications, rather than only one of them, should be applied together to produce more accurate and realistic simulations of coagulation dynamics. As indicated by the simulation, the importance of fluid shear rate to particle coagulation is reduced according to the curvilinear model compared to that previously described with the rectilinear model. As particles increased in size, the role of shear rate in coagulation became even less significant according to the curvilinear view of particle collisions. The results of numerical simulations in terms of the evolution of particle size distributions compared reasonably well with the observations of the jar-test coagulation experiments, which suggested the applicability of the modeling system, including the modified curvilinear-fractal approach, established in the present study.     

Kinetic investigation of narrow-bore columns packed with prototype sub-2 μm superficially porous particles with various shell thickness

The recent successful breakthrough of sub-3 μm shell particles in HPLC has triggered considerable research efforts toward the design of new brands of core-shell particles. We investigated the mass transfer mechanism of a few analytes in narrow-bore columns packed with prototype 1.7 μm shell particles, made of 1.0, 1.2, and 1.4 μm solid nonporous cores surrounded by porous shells 350, 250, and 150 nm thick, respectively. Three probe solutes, uracil, naphthalene, and insulin, were chosen to assess the kinetic performance of these columns. Inverse size exclusion chromatography, peak parking experiments, and the numerical integration of the experimental peak profiles were carried out in order to measure the external, internal, and total column porosities, the true bulk diffusion coefficients of these analytes, the height equivalent to a theoretical plate, the longitudinal diffusion term, and the trans-particle mass transfer resistance term. The residual eddy diffusion term was measured by difference. The results show the existence of important trans-column velocity biases (7%) possibly due to the presence of particle multiplets in the slurry mixture used during the packing process. Our results illustrates some of the difficulties encountered by scientists preparing and packing shell particles into narrow-bore columns.     

Transport processes in the sorption of colored ions by peat particles

A three-step model has been proposed for the adsorption of Astrazone Blue dye (Basic Blue 69) on peat. The initial rate of uptake of dye ions due to physical adsorption and chemisorption (ion exchange) has been correlated using a surface mass transfer coefficient. These coefficients have been determined and expressed in the dimensionless mass transfer form, Sh/Sc^0.33, as a function of agitation, initial dye concentration, peat particle size range, dye solution temperature, and mass of peat.     

Mass transfer performance for hollow fibre modules with shell-side axial feed flow: using an engineering approach to develop a framework

For several membrane separation processes, hollow fibre modules are either an already established or a promising type of module. Based on the analogy between mass and heat transfer, an engineering approach is proposed to estimate the shell-side mass transfer coefficient for axial flow in hollow fibre modules with due allowance for the void fraction. The approach enables one to take the entrance effects of the hydrodynamic and concentration profile into account. The trends obtained by this generalised approach are similar to those of empirical correlations found in the literature over a wide range of Reynolds numbers and module packing densities. The empirical correlations differ significantly one from the other. The differences between the mass transfer coefficients obtained by the empirical correlations compared to those obtained following the approach proposed in this study are discussed. The different effects influencing mass transfer in hollow fibre modules are identified and discussed as a function of void fraction. Further, an approach to reflect the influence of maldistribution on mass transfer performance is provided.     

Pyrolysis of chromated copper arsenate (CCA) treated wood waste at elevated pressure: Influence of particle size, heating rate, residence time, temperature and pressure

Lab-scale pyrolysis experiments with weathered CCA treated wood chips have been performed and the influence of particle size, residence time (10-40 min), heating rate (5-20 °C/min), temperature (330-430 °C) and pressure (0 bar, 5 bar) has been investigated. Few data, covering the pyrolysis of weathered wood was found in the literature and the literature data on pyrolysis experiments with a controlled CCA wood input, showed that results were often highly affected by experimental uncertainty. In order to reduce the uncertainty on the results, a thorough characterization of the wood input has been performed and a ratio method has been proposed which allows to study the effect of particle size on arsenic and chromium volatilization. Larger wood particles show a higher arsenic and chromium retention during pyrolysis which is attributed to the higher mass transfer resistance in these particles. Residence time has a limited effect on arsenic retentions. Increasing heating rate results in a limited increase in arsenic retentions and a more profound increase in chromium retentions. The latter is attributed to a lower average particle temperature during heating caused by the thermal lag in larger particles. Elevated pressure results in a significant increase of arsenic retentions, which is probably due to higher mass transfer resistance. Increasing temperature results in a slight decrease in arsenic retentions till 390 °C, with a sharp decrease at higher temperatures. Chromium retentions are less affected by increasing temperature, especially at higher temperatures. To conclude, a mechanism is proposed for the volatilization of chromium and arsenic during low temperature pyrolysis of CCA wood. Mass transfer resistance and the formation of As₄O₆ are crucial for the control of arsenic volatilization, while heat transfer resistance and thermal lag are more important for the control of chromium volatilization.